Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: timey on 07/11/2016 10:33:21
-
How can the frequency of a clock in relative motion appear to decrease, when its KE is increased?
Light falling to earth experiences a decrease in gravity potential energy, and an increase in KE, and the lights frequency is increased.
The clock in relative motion on the horizontal experiences a constant gravity potential energy, and an increased KE.
Why is the clock losing frequency?
-
Firstly momentum for the photon is p = E/c. Secondly momentum for particles with non zero rest mass is p = mv. Neither rest mass nor a variable velocity in vacuum can be associated with the photon. So expecting kinetic energy to be expressed in the same terms for both is unreasonable and wrong.
-
It would be instructive to look at the diagram of relationships on the following page.
http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/relmom.html (http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/relmom.html)
-
I assume you are still ignoring the answer I gave elsewhere, can you explain why?
You need to differentiate between what happens to the clock and what happens to the light, this is just a simple case of the passage of time experienced being different in 2 frames.
Simple example. Let's say a rocket passes earth at high speed. On the rocket a torch is flashed 100 times in 10s, that's 10Hz leaving the rocket. On earth time is our clock is ticking more quickly so let's say we see those 100 flashes in 20s, that's 5Hz. The clock might experience increased KE but the light it emits is the same frequency it would have been in a stationary frame, but it then enters a different frame, different measurement.
You can replace counting and timing the flashes of the torch with counting and timing wavecrests of the light and will be able to see why frequency decreases, then use std formula to calculate the KE.
Just remember the moving clock ticks more slowly as seen from our frame so our frame appears to tick faster compared to the clock's proper time. The clock itself is not losing frequency, just it is lower as measured in our frame.
I've tried to keep this explanation non maths, also explained why KE is not conserved as measured from different frames, and how if you wanted to you could consider the frequency as moving from aa frame with higher KE to a lower one - this last is not the best way to look at it, see note from Jeff.
Not sure how I could make it any simpler. Anyone else any ideas of how to explain it?
-
How can the frequency of a clock in relative motion appear to decrease, when its KE is increased?
Light falling to earth experiences a decrease in gravity potential energy, and an increase in KE, and the lights frequency is increased.
The clock in relative motion on the horizontal experiences a constant gravity potential energy, and an increased KE.
Why is the clock losing frequency?
The light we receive is giving us information about the clock that sent it. depending on the situation we have to interpret what this information is.
First let's consider two clocks at different heights in a gravity field. Each clock keeps time by counting the constant vibrations od an atom. This atom, as a result of it vibration emits electromagnetic radiation of an equal frequency. I am at the lower clock. The EMR emitted by the upper clock gains energy on its way to me, and expresses this as an increase of frequency. I see a higher frequency than emitted locally by the upper clock. This means I also see the atom vibrating faster, and thus the upper clock running faster. The information I am getting via the light tells me that the upper clock is running fast compared to my own.
Now let's consider two clocks outside of a gravity field and separating at some high fraction of the speed of light. If I am sitting by one clock watching the other, I will receive The EMR emitted by the other clock as being at a lower frequency by a given amount. However, in this case I must account for the fact that the distance between the other clock and myself is changing (something we didn't have to account for above), This in of itself will lower the frequency of the EMR I receive. I have to factor this effect out from my observation in order to get a true idea of the rate that the other clock is ticking. It turns out that if I do so, I still end up with a lower frequency, which means that the other clock is running slow compared to mine.
I can do the same type of comparison if the clocks are approaching each other. This time, I will see a higher frequency coming from the other clock, however once I account for the effect of the constantly decreasing distance between us, it will work out that the other clock is again running slow compared to mine.
The increase or decrease in the frequency of the light gives us information to work with, but you have to know what to do with this information in order to glean what is happening to the clock that emitted it.
-
How can the frequency of a clock in relative motion appear to decrease, when its KE is increased?
Light falling to earth experiences a decrease in gravity potential energy, and an increase in KE, and the lights frequency is increased.
The clock in relative motion on the horizontal experiences a constant gravity potential energy, and an increased KE.
Why is the clock losing frequency?
The light we receive is giving us information about the clock that sent it. depending on the situation we have to interpret what this information is.
First let's consider two clocks at different heights in a gravity field. Each clock keeps time by counting the constant vibrations od an atom. This atom, as a result of it vibration emits electromagnetic radiation of an equal frequency. I am at the lower clock. The EMR emitted by the upper clock gains energy on its way to me, and expresses this as an increase of frequency. I see a higher frequency than emitted locally by the upper clock. This means I also see the atom vibrating faster, and thus the upper clock running faster. The information I am getting via the light tells me that the upper clock is running fast compared to my own.
Now let's consider two clocks outside of a gravity field and separating at some high fraction of the speed of light. If I am sitting by one clock watching the other, I will receive The EMR emitted by the other clock as being at a lower frequency by a given amount. However, in this case I must account for the fact that the distance between the other clock and myself is changing (something we didn't have to account for above), This in of itself will lower the frequency of the EMR I receive. I have to factor this effect out from my observation in order to get a true idea of the rate that the other clock is ticking. It turns out that if I do so, I still end up with a lower frequency, which means that the other clock is running slow compared to mine.
I can do the same type of comparison if the clocks are approaching each other. This time, I will see a higher frequency coming from the other clock, however once I account for the effect of the constantly decreasing distance between us, it will work out that the other clock is again running slow compared to mine.
The increase or decrease in the frequency of the light gives us information to work with, but you have to know what to do with this information in order to glean what is happening to the clock that emitted it.
Here is what Richard Feynman says in his "The Feynman Lectures on Physics, The New Millennium Edition, Volume II: Mainly on electromagnetism and matter", page 42-8:
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Ftheelectromagneticnatureofthings.com%2Fimg%2Fi7%2Fep01.png&hash=e72ade143a41f1387e90cd793ecfdf03)
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Ftheelectromagneticnatureofthings.com%2Fimg%2Fi7%2Fep02.png&hash=7089c683d2f1fc5154b2ee48e1b3b696)
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Ftheelectromagneticnatureofthings.com%2Fimg%2Fi7%2Fep03.png&hash=fbcb6ea24f902e05b859cd01ec0a6359)
Here is the problem though.
A short thought experiment: let us have 2 clocks in the middle of the ship
1-when rocket stands on the Earth and the gravitational acceleration at the middle of the ship is 1g exactly;
2-when the rocket accelerates at 1g in the inter-galactic space where gravity is close to 0;
a) at time T0 = 0s we move the first clock to the top and the second clock to the bottom of the ship; we do it for both 1, 2 scenarios.
b) after a period of time at T1=8hrs we bring the clocks back to the middle.
What results we are going to see?
The 1TC - the first scenario top clock will show 8.001hrs (.001 delta is not calculated, just an arbitrary value to show there is a difference between the clocks)
The 1BC - the first scenario bottom clock will show 7.999hrs
The 2TC = 8hrs
The 2BC = 8hrs
Why is that? The answer is simple, the gravitational acceleration g for 1TC is less than 1g during the 8hours, 1BC g>1g; 2TC g=1g; 2BC g=1g;
It appears there are two problems:
1. The appeared time, transmitted by light is not equal to proper time.
2. The equivalence principal for the gravitational acceleration and the linear acceleration does not hold.
-
I can do the same type of comparison if the clocks are approaching each other. This time, I will see a higher frequency coming from the other clock, however once I account for the effect of the constantly decreasing distance between us, it will work out that the other clock is again running slow compared to mine.
Janus adds a good point to my post.
I had answered your original question which involved slow moving clocks and no motion directly towards or away from the receiver. As you can see the frequency decreases and as a consequence the KE can be calculated as less.
Janus extends this by considering motion towards or away from the receiver at speeds where you would expect to see a Doppler effect. If the speed of either source or receiver are a significant proportion of c then, as Janus points out, the correction I describe has to be factored in to the Doppler shift.
-
Jeff - your use of the words 'unreasonable', and 'wrong' are a 2 way street.
Colin - I know you are tearing your hair out over explaining to me, and I'm not saying 'your explanation' is faulty, I'm good with the atom side, (until relativistic speeds that is), its the already emitted light that's bothering me.
Janus - I'm very happy you decided to join the discussion. I've been monitoring your posts since your arrival at the forum, and indeed I believe we have spoken before on ThePhysicsForum. Is it you?
I take on board your description and would like to consider these points in relation to the NIST 2010 ground level relativity tests.
I'd like you to consider a hypothetical situation were 1 observer is observing 2 clocks ticking 1 metre apart in elevation at ground level...
The clocks are cesium atomic clocks, but the observer is not viewing the cesium fountain in order to read the clocks time, much the same as I do not view the pendulum of my grandfather clock to read the time given by its count. The frequency of the clock is transmitted to its read out. The observer and both clocks are being lit by the light of the sun, the readout can be read by the virtue of this light, and the emission of the photons from each cesium atomic clock are now NOT observer dependant. This can also be said of the clocks in the relative motion tests.
The clocks in these ground level tests were observed by a computer at the ends of unstated lengths of fibre optic cable. The computer has recorded what the difference is between the frequency of the clocks, and is giving the observer both sets of information that the observer is then reading after the fact.
Now looking at light that has already been emitted and is changing frequency as it changes position in a gravitational field:
Placing both a cesium atomic clock and an FE57(terminology?) at top of tower and bottom of tower (Pound Rebka), The clock is emitting at a higher frequency than clock at bottom of tower, according to the computer rigged to both clocks via fibre optic cable.
The FE57 held in a stationary position emits a gamma ray that cannot be received by the receiver at bottom of tower, but we 'can' now remember that the cesium atomic clock is emitting at a lower frequency at bottom of tower...
And then, when the correct degree of movement (frequency) is applied to the FE57 at top of tower, and this movement (frequency) is cancelled by 'something' in the gravitational field - the gamma ray is then received by the receiver at bottom of tower.
Now we can take a brief view of how this Mossbauer effect behaves on the horizontal if the atom is 'not' placed in the crystal lattice. The recoil of the nucleus absorbs some energy and the gamma ray is emitted at a lower energy and frequency...and the receiver does not receive the gamma ray...
...And now we 'can' remember that the cesium atom is emitting at higher frequency at top of tower...
Raising the question, for me, as to if the FE57 coukd be emitting at a higher frequency at the top of tower?
We now have a distinct opportunity to view how things are occurring a little differently if we should choose to do so...
I can continue this line of logic further Janus, all the way into a review of the equivalence principle, but want to check first that we are all good so far...?
Jaaanosik - Also thanks for joining the discussion...
I'd be interested to hear what someone other than myself has to say about your observation.
-
very nice Janus, but
'I can do the same type of comparison if the clocks are approaching each other. This time, I will see a higher frequency coming from the other clock, however once I account for the effect of the constantly decreasing distance between us, it will work out that the other clock is again running slow compared to mine. '
Are they at a same speed. mass, etc? Or you define one to move faster relative the other? I presume they're at a same 'gravitational potential' naturally. Do you define them to different frames of reference there depending on ? the (orbit) they choose relative f. ex. Earth?
=
Hmm, are we talking 'who accelerated'? They are in a uniform motion, right?
assuming everything 'equal' for both. then I will presume that you mean that each observer reads the other clock as 'running slow'? By a equal amount of time then? This one is hurting my head a little :)
-
...
Jaaanosik - Also thanks for joining the discussion...
I'd be interested to hear what someone other than myself has to say about your observation.
What would you say about the observation?
Do you see any error in the observation?
There is a difference in the apparent time and proper time. This puts the twin paradox into a different light :)
The traveling twin can return older than the twin that stayed behind on the Earth.
What is the "proper time" of the clock traveling at constant velocity 0.1c in the intergalactic space where the gravitational acceleration g is close to 0, meaning the clock is not moving through a gravitational field (gravitational background)?
-
very nice Janus, but
'I can do the same type of comparison if the clocks are approaching each other. This time, I will see a higher frequency coming from the other clock, however once I account for the effect of the constantly decreasing distance between us, it will work out that the other clock is again running slow compared to mine. '
Are they at a same speed. mass, etc? Or you define one to move faster relative the other? I presume they're at a same 'gravitational potential' naturally. Do you define them to different frames of reference there depending on ? the (orbit) they choose relative f. ex. Earth?
=
Hmm, are we talking 'who accelerated'? They are in a uniform motion, right?
assuming everything 'equal' for both. then I will presume that you mean that each observer reads the other clock as 'running slow'? By a equal amount of time then? This one is hurting my head a little :)
"Spherical Cows"
In case you are not familiar with the joke, it refers to the idea simplifying a problem by ignoring or eliminating all factors except for the one you are considering. So in my example you can assume that the only thing in consideration is the relative speed between the clocks at the time the measurements are being made.
And yes, this does mean that both clocks would say that the other clock is the one running slow and by the same factor.
-
...
Hmm, are we talking 'who accelerated'? They are in a uniform motion, right?
assuming everything 'equal' for both. then I will presume that you mean that each observer reads the other clock as 'running slow'? By a equal amount of time then? This one is hurting my head a little :)
There is a solution to the headaches.
The apparent/observed time is not equal to the proper time.
The relative motion between the clocks/observer is useless for the calculation of the time.
What counts is the position in the gravitational field and how fast the clock moves through the gravitational field. This gives us the proper time.
That's proven by the Hafele-Keating and many other experiments.
-
...
"Spherical Cows"
In case you are not familiar with the joke, it refers to the idea simplifying a problem by ignoring or eliminating all factors except for the one you are considering. So in my example you can assume that the only thing in consideration is the relative speed between the clocks at the time the measurements are being made.
And yes, this does mean that both clocks would say that the other clock is the one running slow and by the same factor.
What is the model, math, theory good for if it does not give us a correct description of what is happening in the reality? Where is the truth?
-
Here is the problem though.
A short thought experiment: let us have 2 clocks in the middle of the ship
1-when rocket stands on the Earth and the gravitational acceleration at the middle of the ship is 1g exactly;
2-when the rocket accelerates at 1g in the inter-galactic space where gravity is close to 0;
a) at time T0 = 0s we move the first clock to the top and the second clock to the bottom of the ship; we do it for both 1, 2 scenarios.
b) after a period of time at T1=8hrs we bring the clocks back to the middle.
What results we are going to see?
The 1TC - the first scenario top clock will show 8.001hrs (.001 delta is not calculated, just an arbitrary value to show there is a difference between the clocks)
The 1BC - the first scenario bottom clock will show 7.999hrs
The 2TC = 8hrs
The 2BC = 8hrs
Why is that? The answer is simple, the gravitational acceleration g for 1TC is less than 1g during the 8hours, 1BC g>1g; 2TC g=1g; 2BC g=1g;
It appears there are two problems:
1. The appeared time, transmitted by light is not equal to proper time.
2. The equivalence principal for the gravitational acceleration and the linear acceleration does not hold.
Okay, From this I gather that you are comparing clocks in two situations.
1) clocks at the top and bottom of a rocket sitting on the surface of the Earth. (with the midpoint of the clock at the 1g point)
2) clocks at the top and bottom of a rocket accelerating in deep space at 1 g.
You then compare how much time passes on the clocks after a given time. Since you never gave an actual frame of reference by which this time is measured, we will assume that in each rocket, we will assume that for each rocket the 8 hrs is measured by a clock in the center of the Rocket.
Your assumption that, in the accelerating rocket case, that the clock will show no difference is incorrect, in fact the bottom clock will have ticked off less time and the top clock more time. Not only that, but this time difference will be greater than that between the top and bottom clock for the rocket sitting on the surface of the Earth.
There is a very common misconception among laymen concerning gravitational time dilation. They assume that it is due to the difference in gravitational force felt by the Clocks, and that the reason a higher elevation clock runs faster is because gravity is weaker at the higher elevation.
This is not the case. Gravitational time dilation is due to the difference in gravitational potential. If I had a 1 kg mass at sea level and another at an altitude of 1km, the 1km mass is at a higher gravitational potential (I would have had to expend energy to lift that mass from sea level to 1km). It is this difference that gravitational time dilation is tied to, not to the fact that gravity is weaker one km further away from the center of the Earth
Now imagine that you are on a much larger world, but with a mass such that you still have a 1g acceleration at its surface. Same scenerio, with clocks on the surface and 1km altitude. Now the difference in g force between the two heights is less (due to 1 km being a smaller fraction of the this world's radius). However, the difference in potential is larger. (since gravity doesn't fall off as fast with distance, you end up exerting more energy lifting that 1 kg mass to 1km.) And since time dilation is tied to potential difference, the difference in tick rate for clocks at these altitudes will be greater than that for the same situation on the Earth, even though the g-force difference is smaller.
If we keep increasing the radius of the Planet (and it mass to keep a 1g surface gravity), the gradient between g-force between the two altitudes becomes smaller and smaller. In fact, it begins to approach 0.
A zero difference in G-force is what we see in the accelerating rocket. However, if I wanted to move a 1 kg mass from the bottom of the rocket to the top, I would need to expend energy. It would be no different than climbing upwards against a constant 1 g gravitational force. It is just like the top of the rocket being at a different gravitational potential than the Bottom. The top clock runs faster than the bottom clock. This is what the equivalence principle is about. An equal difference in potential results in an equal difference in time dilation, the difference in g-force, while it can be a factor in determining the difference in potential, is not the primary cause for time dilation.
It is a matter of correlation vs. causation. When you are dealing with the gravity fields of planets there is a correlation between increasing clock rate with increasing altitude and weaker gravity, but weaker gravity with increasing altitude is not a causation for the increasing clock rate.
-
Janus - I posted to you earlier in post 7, perhaps you missed it?
Jaaanisok - when time is running at a faster rate for your head than it is for your feet (when you are standing up that is), then 'proper time' ceases to have any relevant meaning as anything other than a means by which to calculate different rates of time against, and 'can' be arbitrarily attributed to any reference frame one finds convenient, far as I can see.
Yor-on - the remits of relativity have been argued every which way for how many years now? I'm talking about the use of relativistic mass here, in relation to kinetic energy and the difference in an increase in KE and frequency in already emitted light, and an increase in KE for a clock in relative motion, and the observation of a decrease in frequency of the clock.
-
Try telling a particle that one part of it experiences a different rate of time to another. It can get ridiculous. Usually it is a particle or particles and not someone's head that is under observation. Macroscopic systems do not generally behave in a noticeable quantum manner. So let's be sensible.
-
Now here is a situation. We have two clocks at exactly the same gravitational potential and a base station to record the time on each. Each clock is initially synchronised and attached to the base station by a fibre optic cable. One clock is attached by a 1 light second long cable and the other by a 100 light second long cable. The base station will not show the clocks as synchronised. One time will lag behind the other. So time dilation is not the only consideration that needs to be taken into account.
-
Just for fun lets modify the above scenario so that the shorter fibre optic cable is filled with a medium that slows down photons. This would be indistinguishable from time dilation to anyone monitoring the base station. Does this mean that the gravitational field can be considered as a medium?
-
Just for fun lets modify the above scenario so that the shorter fibre optic cable is filled with a medium that slows down photons. This would be indistinguishable from time dilation to anyone monitoring the base station. Does this mean that the gravitational field can be considered as a medium?
No, it wouldn't. Slowing down the light in one of the cables will introduce an offset between the clock readings you see, but not the increasing time difference you get with time dilation. So for example, if you took two clocks at the same potential attached by cables 1 light sec long each to our monitoring station, with the speed of light in one of the cables being 1/2 that of the other, the monitoring station will note a ~1.45 sec (assuming the speed of transmission in the faster cable is a typical 0.69c) difference between the clock readings it receives, but no matter how long you run the experiment, this difference will remain constant and does not increase. This is different form time dilation where the difference in clock readings grows the longer you run the experiment
-
Janus, thank you for your post.
It's very good and I understand what you are saying. Please, see my responses below.
...
Okay, From this I gather that you are comparing clocks in two situations.
1) clocks at the top and bottom of a rocket sitting on the surface of the Earth. (with the midpoint of the clock at the 1g point)
2) clocks at the top and bottom of a rocket accelerating in deep space at 1 g.
You then compare how much time passes on the clocks after a given time. Since you never gave an actual frame of reference by which this time is measured, we will assume that in each rocket, we will assume that for each rocket the 8 hrs is measured by a clock in the center of the Rocket.
Yes, there would be a clock at the center of the Rocket, that would measure time in addition to the clocks that were moved to the top and to the bottom.
Your assumption that, in the accelerating rocket case, that the clock will show no difference is incorrect, in fact the bottom clock will have ticked off less time and the top clock more time. Not only that, but this time difference will be greater than that between the top and bottom clock for the rocket sitting on the surface of the Earth.
Are you sure?
If the rocket is not accelerating and we place the one of the synchronized clocks at the top of the rocket and the second at the bottom, then we start 1g acceleration, then we stop the acceleration after 8hrs and now we compare the clocks. Is the top clock going to show more time? Did the top clock run faster?
How is it possible?
Feynman never discussed the initial conditions how he put clocks A and B at the rocket. He just concluded that all the time during the acceleration the top clock A would run faster based on the emitted light.
There is a very common misconception among laymen concerning gravitational time dilation. They assume that it is due to the difference in gravitational force felt by the Clocks, and that the reason a higher elevation clock runs faster is because gravity is weaker at the higher elevation.
This is not the case. Gravitational time dilation is due to the difference in gravitational potential. If I had a 1 kg mass at sea level and another at an altitude of 1km, the 1km mass is at a higher gravitational potential (I would have had to expend energy to lift that mass from sea level to 1km). It is this difference that gravitational time dilation is tied to, not to the fact that gravity is weaker one km further away from the center of the Earth
Now imagine that you are on a much larger world, but with a mass such that you still have a 1g acceleration at its surface. Same scenerio, with clocks on the surface and 1km altitude. Now the difference in g force between the two heights is less (due to 1 km being a smaller fraction of the this world's radius). However, the difference in potential is larger. (since gravity doesn't fall off as fast with distance, you end up exerting more energy lifting that 1 kg mass to 1km.) And since time dilation is tied to potential difference, the difference in tick rate for clocks at these altitudes will be greater than that for the same situation on the Earth, even though the g-force difference is smaller.
If we keep increasing the radius of the Planet (and it mass to keep a 1g surface gravity), the gradient between g-force between the two altitudes becomes smaller and smaller. In fact, it begins to approach 0.
A zero difference in G-force is what we see in the accelerating rocket. However, if I wanted to move a 1 kg mass from the bottom of the rocket to the top, I would need to expend energy. It would be no different than climbing upwards against a constant 1 g gravitational force. It is just like the top of the rocket being at a different gravitational potential than the Bottom. The top clock runs faster than the bottom clock. This is what the equivalence principle is about. An equal difference in potential results in an equal difference in time dilation, the difference in g-force, while it can be a factor in determining the difference in potential, is not the primary cause for time dilation.
It is a matter of correlation vs. causation. When you are dealing with the gravity fields of planets there is a correlation between increasing clock rate with increasing altitude and weaker gravity, but weaker gravity with increasing altitude is not a causation for the increasing clock rate.
If I understand you correctly you would say that the cesium atom in the atomic clock would become more energized (was in higher potential) because there was work done on the atom when moved from the middle of the rocket to the top during the 1g acceleration. This energized, pumped up atom would run faster as the clock.
Is it correct?
That does not make sense to me though.
Imagine a 1kg weight on the spring at the center of the rocket at 1g acceleration. We move the spring to the top of the rocket. It means we have to accelerate the spring and the weight system towards the top and the weight will show more then 1kg because of the additional acceleration. Once at the top the weight will stabilize at 1kg again because there is 1g acceleration at the top.
This is what would happen to the cesium atoms. 'The springs in them' would stabilize at 1g acceleration again.
If we used tiny pendulums as our clocks then what is the formula for the pendulum? There is g local gravitational acceleration.
There is no problem for the pendulums to be moved around the rocket. After a stabilization period the pendulums will measure the local proper time with the local linear 1g acceleration.
The apparent/observed time is not equal to the proper time.
The real question is how can a pendulum clock go faster at the top compare the bottom when they both have the same 1g acceleration.
-
Janus - I posted to you earlier in post 7, perhaps you missed it?
I looked at the post. Here's the problem. Adding all the additional condition, (reflected vs. emitted light, fiber optic cables, etc.) don't add to the clarity of the discussion. If anything, they muddy the waters, by adding factors that have to be accounted for in addition to the effect you are interested in.
Having said that, Let's look at the seeing the clock by reflected sunlight. The light strikes the upper clock and is reflected into our eyes at the lower clock. To simplify, we will only consider 1 particular wavelength of the visual spectrum. As the light hits the upper clock, X number of waves hits it between the clock reading 0 and the clock reading 1. As each wave hits it is reflected to our eye. The waves are frequency shifted as they travel from one height to the other and since the wave must remain continuous and X number of waves of a higher frequency take less time to occur for you than it took for the original light to hit the upper clock. So again, you see the upper clock go from 0 to 1 in less time than the upper clock would.
It doesn't matter what method you try to use to transfer the information from the upper to lower clock or vice-versa, in the end you get the same answer.
-
There would be a slowdown "traffic jam" of photons in the cable containing the medium. I was in a rather lengthy traffic jam today and time passed very slowly for me, I assure you of that. Think it through properly.
-
Janus, thank you for your post.
It's very good and I understand what you are saying. Please, see my responses below.
...
Okay, From this I gather that you are comparing clocks in two situations.
1) clocks at the top and bottom of a rocket sitting on the surface of the Earth. (with the midpoint of the clock at the 1g point)
2) clocks at the top and bottom of a rocket accelerating in deep space at 1 g.
You then compare how much time passes on the clocks after a given time. Since you never gave an actual frame of reference by which this time is measured, we will assume that in each rocket, we will assume that for each rocket the 8 hrs is measured by a clock in the center of the Rocket.
Yes, there would be a clock at the center of the Rocket, that would measure time in addition to the clocks that were moved to the top and to the bottom.
Your assumption that, in the accelerating rocket case, that the clock will show no difference is incorrect, in fact the bottom clock will have ticked off less time and the top clock more time. Not only that, but this time difference will be greater than that between the top and bottom clock for the rocket sitting on the surface of the Earth.
Are you sure?
If the rocket is not accelerating and we place the one of the synchronized clocks at the top of the rocket and the second at the bottom, then we start 1g acceleration, then we stop the acceleration after 8hrs and now we compare the clocks. Is the top clock going to show more time? Did the top clock run faster?
How is it possible?
Feynman never discussed the initial conditions how he put clocks A and B at the rocket. He just concluded that all the time during the acceleration the top clock A would run faster based on the emitted light.
Yes I'm sure. If the clocks start synchronized, the difference between them will grow as the rocket accelerates, At the end of the experiment, the upper clock will have recorded more time.
It doesn't matter how the clocks were placed where they are. They could have been placed there and not started until the rocket was under acceleration. Consider Feynman's Explanation again. As he notes, the lower clock will see the light emitted by the upper one as frequency shifted. Imagine that the upper clock gives off X waves of light as it ticks off one second. The lower clock observer sees those waves at higher frequency, and sees those same X waves arrive over a duration of less than 1 sec. He sees the upper clock tick off one sec in less time than the clock next to him ticks off one sec. As he continues to watch, the difference in time between the clocks increases. After some time, we bring the clocks together while watching them. Now while some small time change in the clocks can occur by bringing them together again, this correction amounts to the same value regardless of how long we accelerated the rocket with the clocks separated. As long as this phase lasts long enough you can be assured that the time difference between the clocks will exceed effect caused by bringing them together.
There is a very common misconception among laymen concerning gravitational time dilation. They assume that it is due to the difference in gravitational force felt by the Clocks, and that the reason a higher elevation clock runs faster is because gravity is weaker at the higher elevation.
This is not the case. Gravitational time dilation is due to the difference in gravitational potential. If I had a 1 kg mass at sea level and another at an altitude of 1km, the 1km mass is at a higher gravitational potential (I would have had to expend energy to lift that mass from sea level to 1km). It is this difference that gravitational time dilation is tied to, not to the fact that gravity is weaker one km further away from the center of the Earth
Now imagine that you are on a much larger world, but with a mass such that you still have a 1g acceleration at its surface. Same scenerio, with clocks on the surface and 1km altitude. Now the difference in g force between the two heights is less (due to 1 km being a smaller fraction of the this world's radius). However, the difference in potential is larger. (since gravity doesn't fall off as fast with distance, you end up exerting more energy lifting that 1 kg mass to 1km.) And since time dilation is tied to potential difference, the difference in tick rate for clocks at these altitudes will be greater than that for the same situation on the Earth, even though the g-force difference is smaller.
If we keep increasing the radius of the Planet (and it mass to keep a 1g surface gravity), the gradient between g-force between the two altitudes becomes smaller and smaller. In fact, it begins to approach 0.
A zero difference in G-force is what we see in the accelerating rocket. However, if I wanted to move a 1 kg mass from the bottom of the rocket to the top, I would need to expend energy. It would be no different than climbing upwards against a constant 1 g gravitational force. It is just like the top of the rocket being at a different gravitational potential than the Bottom. The top clock runs faster than the bottom clock. This is what the equivalence principle is about. An equal difference in potential results in an equal difference in time dilation, the difference in g-force, while it can be a factor in determining the difference in potential, is not the primary cause for time dilation.
It is a matter of correlation vs. causation. When you are dealing with the gravity fields of planets there is a correlation between increasing clock rate with increasing altitude and weaker gravity, but weaker gravity with increasing altitude is not a causation for the increasing clock rate.
If I understand you correctly you would say that the cesium atom in the atomic clock would become more energized (was in higher potential) because there was work done on the atom when moved from the middle of the rocket to the top during the 1g acceleration. This energized, pumped up atom would run faster as the clock.
Is it correct?
No, you are falling into another common trap; trying to find a "mechanistic" reason for the difference in clock rates. In other words thinking in terms of something having a physical effect on the clock that alters its "natural" tick rate. In Relativity, gravity is a space-time curvature. It is this that leas to the difference in time rates. Basically, the clocks at the different altitudes tick at their natural time rates, they just don't agree what that rate is. Time itself is different at these two altitudes.
That does not make sense to me though.
Imagine a 1kg weight on the spring at the center of the rocket at 1g acceleration. We move the spring to the top of the rocket. It means we have to accelerate the spring and the weight system towards the top and the weight will show more then 1kg because of the additional acceleration. Once at the top the weight will stabilize at 1kg again because there is 1g acceleration at the top.
This is what would happen to the cesium atoms. 'The springs in them' would stabilize at 1g acceleration again.
If we used tiny pendulums as our clocks then what is the formula for the pendulum? There is g local gravitational acceleration.
There is no problem for the pendulums to be moved around the rocket. After a stabilization period the pendulums will measure the local proper time with the local linear 1g acceleration.
The apparent/observed time is not equal to the proper time.
The real question is how can a pendulum clock go faster at the top compare the bottom when they both have the same 1g acceleration.
Again, it works out to being that time itself progresses at a different rate at the top of the rocket than at the bottom. If I'm sitting next to the top pendulum, I will note that it swings away at exactly the proper rate for 1g. If I'm sitting at the bottom pendulum I note the same about it, However if I'm next to one pendulum and comparing its swing rate against mine, I will note that it swings at a different rate from mine.
The thing about Relativity is that, at its core, it is not about how gravity or speed physically effect clocks, but about the very nature of time and space and how they are measured. We can use moving light clocks, or light traveling between clocks at different altitudes or different points of an accelerating rocket to examine and demonstrate the effects, but the cause is more fundamentally built into space, time and reality.
-
Janus - I posted to you earlier in post 7, perhaps you missed it?
I looked at the post. Here's the problem. Adding all the additional condition, (reflected vs. emitted light, fiber optic cables, etc.) don't add to the clarity of the discussion. If anything, they muddy the waters, by adding factors that have to be accounted for in addition to the effect you are interested in.
Having said that, Let's look at the seeing the clock by reflected sunlight. The light strikes the upper clock and is reflected into our eyes at the lower clock. To simplify, we will only consider 1 particular wavelength of the visual spectrum. As the light hits the upper clock, X number of waves hits it between the clock reading 0 and the clock reading 1. As each wave hits it is reflected to our eye. The waves are frequency shifted as they travel from one height to the other and since the wave must remain continuous and X number of waves of a higher frequency take less time to occur for you than it took for the original light to hit the upper clock. So again, you see the upper clock go from 0 to 1 in less time than the upper clock would.
It doesn't matter what method you try to use to transfer the information from the upper to lower clock or vice-versa, in the end you get the same answer.
http://www.nature.commk/news/2010/100923/full/news.2010.487.html
https://www.nist.gov/news-events/news/2010/09/nist-pair-aluminum-atomic-clocks-reveal-einsteins-relativity-personal-scale
Janus - here we see that such experiments have been conducted a metre apart in elevation and with clocks in relative motion.
And really the sunlight consideration was just to illustrate that we are reading a 'read out' of the clocks frequency in order to tell the time the clock is running at, and we are not viewing the emission of light from the clock's cesium fountain. There is a read out that is counting the frequency of the clock's cesium fountain in its own reference frame, and we are reading that read out from another reference frame.
The reason why it is an important factor that we can view the read out the frequency the clock is ticking at by the virtue of a light source that is not the clocks cesium fountain, is because light emitted from the clocks fountain will have been changed by the gravitational field (elevated clock), or by Doppler shift (clock in relative motion, before it reaches the observer in the other reference frame.
Light can only be seen once it has reached ones eyes!!! Therefore any experiment in any reference frame that relies on a light source as its sole mechanics to transmit information to another reference frame, is only going to represent the light as it appears in the observers frame, not as the light would have appeared to an observer in the reference frame the light originated from.
So the observer observing both clocks that are 1 metre apart in elevation is not observing light arriving from either of the clocks reference frames to read the read out of either of the clocks, and the light that is illuminating the read out from both clocks is incidental to the experiment...
(Indeed, it mentions in the links that the computer reading the clocks is not even in the same room, or possibly even at a similar elevation. Yes the length of the cable will effect how long the read out from the clock takes to get to the computer. But, and this is important, the length of time the information takes to get to the computer does not change the information being transmitted. I think it also worth noting that neither of the clocks in either experiment were being read from either of the reference frame the clocks were located at.)
I was then making a comparison between light that is already emitted increasing in frequency travelling a gravitational gradient (Pound Rebka), and the atom that emits this light (as part of the Mossbauer effect), in comparison to the observed increase in frequency of a cesium atomic clock at elevation.
(This being the more interesting part of the discussion as far as I'm concerned, as it leads back to the original question)
-
There would be a slowdown "traffic jam" of photons in the cable containing the medium. I was in a rather lengthy traffic jam today and time passed very slowly for me, I assure you of that. Think it through properly.
Comparing photons entering a fiber optic cable to cars traveling at speed and hitting a slow spot on the road only works to a point and then it breaks down.
Imagine you have a string of cars spaced one mile apart and traveling at 60 mph. Then they hit a 10 mile stretch with a 30 mph speed limit. The first car hits it and slows down, one minute later, the second car reaches it and slows down. it will be 1/2 mile behind the first car. Successive cars will hit the speed limit and slow down each 1 min after the other, and 1/2 mile behind the car that entered the speed zone ahead of it. After 20 minutes, the first reaches the end of the speed zone. you will at this moment,have 20 cars in the zone 1/2 mile apart. the car leaves and speeds back up as a new car is entering at the other end. 1 min later the next car in line leaves (it is 1/2 mile behind the first car, and it takes 1 min to travel 1/2 mile at 30 mph.) So you end up with cars leaving the zone at 1 per minute and entering at one per minute. Same frequency in as out and no traffic jam.
The only way you get a traffic jam is if the cars were so closely placed that the car entering the zone doesn't clear the entry point before the next car arrives. ( there are other factors with real traffic jams, but we will keep it simple.) This happens due to the fixed length of each car the speed change and the rate at which the cars enter the zone.
Photons, however are not cars. they do not have fixed lengths. Their wavelengths are determined by their frequency. The higher the frequency, the shorter the wavelength. Not only that, but the relationship between between wavelength and frequency depends on the speed of light in medium through which they are traveling the relationship is Wavelength = speed in the medium/frequency. So if a photon of a given frequency enters a medium where it is traveling 1/2 as fast, its wavelength decreases by 1/2.
To use the car analogy above, it is as if the cars shrink in length as they enter the speed zone. Not only that but the length of the cars before they reach the speed zone is determined by the rate at which they enter it. the higher the rate, the shorter the cars to start with. The result is that you never can get to a point where photons enter the cable at a rate greater than space is cleared for them to enter and you never get a "traffic jam". You always end up with light leaving the cable with the same frequency as it enters.
And this is fully demonstrated in real life. We use fiber optic cables for communication, and as I noted above, the typical speed for light in a fiber optic cable is ~69% of c. but we don't hear the person on the other end talking slowly, as we would if there were a time dilation type of effect.
-
...
Yes I'm sure. If the clocks start synchronized, the difference between them will grow as the rocket accelerates, At the end of the experiment, the upper clock will have recorded more time.
It doesn't matter how the clocks were placed where they are. They could have been placed there and not started until the rocket was under acceleration. Consider Feynman's Explanation again. As he notes, the lower clock will see the light emitted by the upper one as frequency shifted. Imagine that the upper clock gives off X waves of light as it ticks off one second. The lower clock observer sees those waves at higher frequency, and sees those same X waves arrive over a duration of less than 1 sec. He sees the upper clock tick off one sec in less time than the clock next to him ticks off one sec. As he continues to watch, the difference in time between the clocks increases. After some time, we bring the clocks together while watching them. Now while some small time change in the clocks can occur by bringing them together again, this correction amounts to the same value regardless of how long we accelerated the rocket with the clocks separated. As long as this phase lasts long enough you can be assured that the time difference between the clocks will exceed effect caused by bringing them together.
The thought experiment that I posted is different from what you are describing here.
There is the A clock at the top and it has its own clock counter. The counter is next to the clock, essentially part of the clock.
The B clock at the bottom is the same. It has its own counter as well.
I introduced the third clock at the middle based on your feedback.
At T0=0hrs the clocks are physically at the middle and they are synchronized. Then the A clock is move up and the B clock is moved down, let us say in one minute.
At T0=8hrs as measured by the middle clock the clocks are brought back and compared the delta on the counters that were all the time next to the clocks measuring the proper time.
There is no counter at the bottom next to the B clock that is counting A clock light. Our A clock has no capability to send the light anywhere. We are not interested in the apparent/observed time that is measured at a distance in this thought experiment. The reason is we want to find out what is happening to the time locally at the clock.
The remote observer is not a factor/cause/has no influence on how the proper local time is measured.
This is how Hafele-Keating did their experiment. There was synchronization at the beginning and at the end.
No light exchange in between.
No, you are falling into another common trap; trying to find a "mechanistic" reason for the difference in clock rates. In other words thinking in terms of something having a physical effect on the clock that alters its "natural" tick rate. In Relativity, gravity is a space-time curvature. It is this that leas to the difference in time rates. Basically, the clocks at the different altitudes tick at their natural time rates, they just don't agree what that rate is. Time itself is different at these two altitudes.
Again, it works out to being that time itself progresses at a different rate at the top of the rocket than at the bottom. If I'm sitting next to the top pendulum, I will note that it swings away at exactly the proper rate for 1g. If I'm sitting at the bottom pendulum I note the same about it, However if I'm next to one pendulum and comparing its swing rate against mine, I will note that it swings at a different rate from mine.
The thing about Relativity is that, at its core, it is not about how gravity or speed physically effect clocks, but about the very nature of time and space and how they are measured. We can use moving light clocks, or light traveling between clocks at different altitudes or different points of an accelerating rocket to examine and demonstrate the effects, but the cause is more fundamentally built into space, time and reality.
Please, show me a cause for different "natural" tick rate for proper time of the A, B clocks when they are accelerated on the rocket with the same 1g linear acceleration. The only difference is that A clock is at the top and the B clock is at the bottom.
What is the cause?
-
...
Jaaanisok - when time is running at a faster rate for your head than it is for your feet (when you are standing up that is), then 'proper time' ceases to have any relevant meaning as anything other than a means by which to calculate different rates of time against, and 'can' be arbitrarily attributed to any reference frame one finds convenient, far as I can see.
...
Here are the results of Hafele-Keating experiment from Wikipedia:
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Ftheelectromagneticnatureofthings.com%2Fimg%2Fi7%2Fep04.png&hash=e764263ff20c56efee38625c8937a33e)
I am not sure about your reference frame comment.
The question is why is the kinematic (special relativity) value negative eastward and positive westward.
Why the reference frame was not chosen with the clock that stayed on the ground and both values should be negative (time is running slower for the moving clock) in that case?
-
...
Jaaanisok - when time is running at a faster rate for your head than it is for your feet (when you are standing up that is), then 'proper time' ceases to have any relevant meaning as anything other than a means by which to calculate different rates of time against, and 'can' be arbitrarily attributed to any reference frame one finds convenient, far as I can see.
...
Here are the results of Hafele-Keating experiment from Wikipedia:
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Ftheelectromagneticnatureofthings.com%2Fimg%2Fi7%2Fep04.png&hash=e764263ff20c56efee38625c8937a33e)
I am not sure about your reference frame comment.
The question is why is the kinematic (special relativity) value negative eastward and positive westward.
Why the reference frame was not chosen with the clock that stayed on the ground and both values should be negative (time is running slower for the moving clock) in that case?
No - the question is why does a clock in relative motion decrease in frequency when its kinetic energy is increased, when lights frequency increases with increased kinetic energy...
...and I don't see why we have to consider rockets and speeds close to the speed of light when we have real life experiments that are displaying these symptoms of increase and decrease in frequency on, or near the ground, Earth, at elevations 1 metre apart and at speeds of 36km/h... Please see links provided a few posts ago.
Surely it is more beneficial to consider the data, set up and interpretation of real life experimental observations, and not made up hypothetical scenarios?
Yes, the data you provided showed that there was a difference in the Eastbound and Westbound clocks. I'm not disputing time dilation here, far from it...
I'm sorry, but I do not think that discussing 'proper time' is a relevant means to understanding why a clock decreases in frequency, and already emitted light increases in frequency, when kinetic energy is increased.
-
...
Yes I'm sure. If the clocks start synchronized, the difference between them will grow as the rocket accelerates, At the end of the experiment, the upper clock will have recorded more time.
It doesn't matter how the clocks were placed where they are. They could have been placed there and not started until the rocket was under acceleration. Consider Feynman's Explanation again. As he notes, the lower clock will see the light emitted by the upper one as frequency shifted. Imagine that the upper clock gives off X waves of light as it ticks off one second. The lower clock observer sees those waves at higher frequency, and sees those same X waves arrive over a duration of less than 1 sec. He sees the upper clock tick off one sec in less time than the clock next to him ticks off one sec. As he continues to watch, the difference in time between the clocks increases. After some time, we bring the clocks together while watching them. Now while some small time change in the clocks can occur by bringing them together again, this correction amounts to the same value regardless of how long we accelerated the rocket with the clocks separated. As long as this phase lasts long enough you can be assured that the time difference between the clocks will exceed effect caused by bringing them together.
The thought experiment that I posted is different from what you are describing here.
There is the A clock at the top and it has its own clock counter. The counter is next to the clock, essentially part of the clock.
The B clock at the bottom is the same. It has its own counter as well.
I introduced the third clock at the middle based on your feedback.
At T0=0hrs the clocks are physically at the middle and they are synchronized. Then the A clock is move up and the B clock is moved down, let us say in one minute.
At T0=8hrs as measured by the middle clock the clocks are brought back and compared the delta on the counters that were all the time next to the clocks measuring the proper time.
There is no counter at the bottom next to the B clock that is counting A clock light. Our A clock has no capability to send the light anywhere. We are not interested in the apparent/observed time that is measured at a distance in this thought experiment. The reason is we want to find out what is happening to the time locally at the clock.
The remote observer is not a factor/cause/has no influence on how the proper local time is measured.
This is how Hafele-Keating did their experiment. There was synchronization at the beginning and at the end.
No light exchange in between.
It makes no difference whether there is, or is not an actual outside observer or whether the clocks exchange light signals in the experiment you set up. The point is that the experiment must turn out the same way whether these elements exist or not. All observers, even hypothetical ones, have to agree that if the clocks start synced, are separated to the ends of the rocket, for some period and then brought back together that they will now be out of sync and by how much. Anything else would result in a universe that allows real physical contradictions.No, you are falling into another common trap; trying to find a "mechanistic" reason for the difference in clock rates. In other words thinking in terms of something having a physical effect on the clock that alters its "natural" tick rate. In Relativity, gravity is a space-time curvature. It is this that leas to the difference in time rates. Basically, the clocks at the different altitudes tick at their natural time rates, they just don't agree what that rate is. Time itself is different at these two altitudes.
Again, it works out to being that time itself progresses at a different rate at the top of the rocket than at the bottom. If I'm sitting next to the top pendulum, I will note that it swings away at exactly the proper rate for 1g. If I'm sitting at the bottom pendulum I note the same about it, However if I'm next to one pendulum and comparing its swing rate against mine, I will note that it swings at a different rate from mine.
The thing about Relativity is that, at its core, it is not about how gravity or speed physically effect clocks, but about the very nature of time and space and how they are measured. We can use moving light clocks, or light traveling between clocks at different altitudes or different points of an accelerating rocket to examine and demonstrate the effects, but the cause is more fundamentally built into space, time and reality.
Please, show me a cause for different "natural" tick rate for proper time of the A, B clocks when they are accelerated on the rocket with the same 1g linear acceleration. The only difference is that A clock is at the top and the B clock is at the bottom.
What is the cause?
The "cause" is the inherent relationship between time and space build into the Universe. I know that it is not the type of answer you want. You want a more "mechanistic" explanation. You want an answer based on your terms, however the universe is not obliged to adhere to your terms.
-
when lights frequency increases with increased kinetic energy
Why do you focus on the kinetic energy of light?
I expect that most of the photon's energy will be embedded in the electric and magnetic fields of which it is composed.
-
when lights frequency increases with increased kinetic energy
Why do you focus on the kinetic energy of light?
I expect that most of the photon's energy will be embedded in the electric and magnetic fields of which it is composed.
Because light is increasing in kinetic energy and in frequency as it falls towards earth... and the clock in relative motion is increasing in kinetic energy, but 'decreasing' in frequency.
As light is being attributed mass via kinetic energy, one would have thought that light should behave the same as mass does, and that either a clock in relative motion would increase in frequency as light does, or that light would decrease in frequency as the clock in relative motion does...
...but you cannot attribute light with mass, and then state that light with mass behaves differently to an atom with mass when kinetic energy is increased.
-
Janus, you're a treasure, and we like those. Don't mean we will always agree though :)
welcome to TNS
-
when lights frequency increases with increased kinetic energy
Why do you focus on the kinetic energy of light?
I expect that most of the photon's energy will be embedded in the electric and magnetic fields of which it is composed.
Because light is increasing in kinetic energy and in frequency as it falls towards earth... and the clock in relative motion is increasing in kinetic energy, but 'decreasing' in frequency.
As light is being attributed mass via kinetic energy, one would have thought that light should behave the same as mass does, and that either a clock in relative motion would increase in frequency as light does, or that light would decrease in frequency as the clock in relative motion does...
...but you cannot attribute light with mass, and then state that light with mass behaves differently to an atom with mass when kinetic energy is increased.
You're comparing apples to oranges and wondering why they don't taste alike. The frequency of light is not in any related to some tick rate of an internal clock. It's how many waves pass a given point per sec. Light doesn't even have a "internal clock" that an observer can measure the tick rate of, as c is not a valid inertial frame.
It no use complaining that we treat light and physical object differently, as they are different. Physical object can travel at any speed up to but not equal to c, light in a vacuum can only travel at c. You can be at rest with respect a physical object, you cannot be so with respect to light. There is a distinct dividing line between the two.
A single similar characteristic does not imply similar behavior in all things. My car is driven by an internal combustion engine, so is a small private aircraft, so why can't my car fly?
-
Heh :)
you are perfectly right in that there is no 'global' frame in where 'c has a 'clock rate' that we all can agree on as being the same. There is always the local frame though, the one where you and me share a same frame of reference. It's about how you look at it, to me. If we can join a same frame of reference, if Lorentz transformations holds true. Then there is a 'clock rate', locally defined.
-
It's defined relative your clock and ruler, and it gives you 'c', generally speaking. We can argue about 'accelerations' of different kinds, but the principle is that every 'inertial frame' measure 'c'. That's also what give you 'physics'.
-
It's a constant, and what makes a constant, is that though one can change values, one still should reach a constant. If one find that wrong, then one need to check ones mathematics :) and then there should be a Nobel prize awaiting somewhere.
-
when lights frequency increases with increased kinetic energy
Why do you focus on the kinetic energy of light?
I expect that most of the photon's energy will be embedded in the electric and magnetic fields of which it is composed.
Because light is increasing in kinetic energy and in frequency as it falls towards earth... and the clock in relative motion is increasing in kinetic energy, but 'decreasing' in frequency.
As light is being attributed mass via kinetic energy, one would have thought that light should behave the same as mass does, and that either a clock in relative motion would increase in frequency as light does, or that light would decrease in frequency as the clock in relative motion does...
...but you cannot attribute light with mass, and then state that light with mass behaves differently to an atom with mass when kinetic energy is increased.
You're comparing apples to oranges and wondering why they don't taste alike. The frequency of light is not in any related to some tick rate of an internal clock. It's how many waves pass a given point per sec. Light doesn't even have a "internal clock" that an observer can measure the tick rate of, as c is not a valid inertial frame.
It no use complaining that we treat light and physical object differently, as they are different. Physical object can travel at any speed up to but not equal to c, light in a vacuum can only travel at c. You can be at rest with respect a physical object, you cannot be so with respect to light. There is a distinct dividing line between the two.
A single similar characteristic does not imply similar behavior in all things. My car is driven by an internal combustion engine, so is a small private aircraft, so why can't my car fly?
You know I really wouldn't of minded at all if you had up-taken the dialogue presented concerning the NIST 2010 relativity tests in relation to only being able to observe already emitted light in the reference frame that one is located in, versus it being possible to view the read out of a clock while it is actually in another reference frame 1 metre away, as I posted in response to your previous reply to me...
We understand that both oranges and apples belong to a subgroup called fruit, and that they share a commonality in that they both grow on trees... and, not that I recommend it, but your car will most definitely fly if you drive it off a cliff...
Couldn't care a less how light experiences its own time, it's irrelevant to the discussion... although lights speed is supposed to render it as timeless according to some interpretations.
Frequency is related to energy. If something has more energy it's frequency is increased, and this is how light is being calculated...
If physics is attributing light with mass, then all mass must follow as light behaves, and it doesn't. The frequency of a clock in relative motion decreases where kinetic energy is increased, and lights frequency increases where kinetic energy is increased.
-
There would be a slowdown "traffic jam" of photons in the cable containing the medium. I was in a rather lengthy traffic jam today and time passed very slowly for me, I assure you of that. Think it through properly.
Comparing photons entering a fiber optic cable to cars traveling at speed and hitting a slow spot on the road only works to a point and then it breaks down.
Imagine you have a string of cars spaced one mile apart and traveling at 60 mph. Then they hit a 10 mile stretch with a 30 mph speed limit. The first car hits it and slows down, one minute later, the second car reaches it and slows down. it will be 1/2 mile behind the first car. Successive cars will hit the speed limit and slow down each 1 min after the other, and 1/2 mile behind the car that entered the speed zone ahead of it. After 20 minutes, the first reaches the end of the speed zone. you will at this moment,have 20 cars in the zone 1/2 mile apart. the car leaves and speeds back up as a new car is entering at the other end. 1 min later the next car in line leaves (it is 1/2 mile behind the first car, and it takes 1 min to travel 1/2 mile at 30 mph.) So you end up with cars leaving the zone at 1 per minute and entering at one per minute. Same frequency in as out and no traffic jam.
The only way you get a traffic jam is if the cars were so closely placed that the car entering the zone doesn't clear the entry point before the next car arrives. ( there are other factors with real traffic jams, but we will keep it simple.) This happens due to the fixed length of each car the speed change and the rate at which the cars enter the zone.
Photons, however are not cars. they do not have fixed lengths. Their wavelengths are determined by their frequency. The higher the frequency, the shorter the wavelength. Not only that, but the relationship between between wavelength and frequency depends on the speed of light in medium through which they are traveling the relationship is Wavelength = speed in the medium/frequency. So if a photon of a given frequency enters a medium where it is traveling 1/2 as fast, its wavelength decreases by 1/2.
To use the car analogy above, it is as if the cars shrink in length as they enter the speed zone. Not only that but the length of the cars before they reach the speed zone is determined by the rate at which they enter it. the higher the rate, the shorter the cars to start with. The result is that you never can get to a point where photons enter the cable at a rate greater than space is cleared for them to enter and you never get a "traffic jam". You always end up with light leaving the cable with the same frequency as it enters.
And this is fully demonstrated in real life. We use fiber optic cables for communication, and as I noted above, the typical speed for light in a fiber optic cable is ~69% of c. but we don't hear the person on the other end talking slowly, as we would if there were a time dilation type of effect.
You are correct but only if the cars spend the start and end of the journey out of the jam. If the jam extends along the whole journey and involves a negative acceleration then it is indistinguishable. So if the force of the field varies this is akin to the acceleration in the jam.
-
.
Frequency is related to energy. If something has more energy it's frequency is increased, and this is how light is being calculated...
If physics is attributing light with mass, then all mass must follow as light behaves, and it doesn't.
Energy is calculated from frequency E=hf remember. Higher frequency greater energy.
Light does not have mass as other particles, rest mass is 0 leaving only the momentum part of the equation.
EDIT: Just been out for a run and mulling over how to explain what is going on here.
Perhaps this helps:
Energy is a measure of the state of a system, abstract energy is not the determinator of it's state. Sometimes where we measure from determines what value of energy is measured. Consider something with real mass such as a car, if 2 people use stopwatches to measure the speed and one has a watch which runs fast, that faster watch will measure the speed as lower (like I describe frequency in #3) so the calculation of KE - which is proportional to speed - is lower with the watch which is running fast.
I think you also need to think about the time at your head running faster than at your feet, so it is correct to say that the proper time at your feet is different from the proper time at your head, these are 2 different frames with different rates of time.
Also think about what is happening with the clocks.
-
.
Frequency is related to energy. If something has more energy it's frequency is increased, and this is how light is being calculated...
If physics is attributing light with mass, then all mass must follow as light behaves, and it doesn't.
Energy is calculated from frequency E=hf remember. Higher frequency greater energy.
Light does not have mass as other particles, rest mass is 0 leaving only the momentum part of the equation.
EDIT: Just been out for a run and mulling over how to explain what is going on here.
Perhaps this helps:
Energy is a measure of the state of a system, abstract energy is not the determinator of it's state. Sometimes where we measure from determines what value of energy is measured. Consider something with real mass such as a car, if 2 people use stopwatches to measure the speed and one has a watch which runs fast, that faster watch will measure the speed as lower (like I describe frequency in #3) so the calculation of KE - which is proportional to speed - is lower with the watch which is running fast.
I think you also need to think about the time at your head running faster than at your feet, so it is correct to say that the proper time at your feet is different from the proper time at your head, these are 2 different frames with different rates of time.
Also think about what is happening with the clocks.
Colin - so, your head is experiencing a faster time than your feet. This means that the atoms in your head are vibrating faster than the atoms in your feet. Start walking and both your feet and your head will experience additional kinetic energy, (your feet will be interesting (chuckle)). The head torch attached to your head will experience an increase in frequency, but the atoms that make up your head will experience a decrease in frequency.
Light is being given mass via kinetic energy. If light experiences an increase in frequency when kinetic energy is increased, then an atom should also increase in frequency when kinetic energy is increased.
Now then - its not as if Relativity does not realise this blatant anomaly. Relativity simply gets round the issue by stating the other reference frame as only 'appearing' to lose frequency to the observer in his own frame. If the observer went to that other frame, the frequency would be the same, the equivalent in the other frame as it was in his own. Thus the equivalence principle is upheld...
However... there are a few illogicalities at play here!
Firstly, the concept that a person ages in keeping with their clock. One cannot state that the frequency of a clock in the other frame is only appearing to differ from ones own frame, if one is stating that a person can 'actually' age at differing rates.
Secondly, the NIST 2010 ground level relativity tests, (as far as Im concerned), prove that the difference in frequency between clocks in elevation, and clocks in relative motion, is a real and physical effect.
So - an increase in kinetic energy is not increasing the frequency of a clock?
Is there opportunity to look at what is happening for light differently?
...Hence the top of tower, bottom of tower considerations I posted earlier this thread, that nobody has picked up on as of yet...
-
...
It makes no difference whether there is, or is not an actual outside observer or whether the clocks exchange light signals in the experiment you set up. The point is that the experiment must turn out the same way whether these elements exist or not. All observers, even hypothetical ones, have to agree that if the clocks start synced, are separated to the ends of the rocket, for some period and then brought back together that they will now be out of sync and by how much. Anything else would result in a universe that allows real physical contradictions.
The "cause" is the inherent relationship between time and space build into the Universe. I know that it is not the type of answer you want. You want a more "mechanistic" explanation. You want an answer based on your terms, however the universe is not obliged to adhere to your terms.
Thank you Janus,
here is the equation from the end of the Feynman quote that is on the page 1 of this thread.
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Ftheelectromagneticnatureofthings.com%2Fimg%2Fi7%2Fep05.png&hash=8bc94314425460cc7a502e96d3849c8e)
Clock A at the top updates its own counter at omega = omega_0 because H=0, meaning the light does not travel through an acceleration to remote observer.
Clock B at the bottom updates its own counter at omega = omega_0 because H=0 as well. The light does not travel through an acceleration to remote observer.
If the clocks are made identical then both clocks are going to record the same time intervals at their locations.
We agree that counting is happening locally and no remote observer is a factor.
Please, explain where the delta between A and B clocks is coming from for the linear acceleration at 1g?
How the equation about the apparent/observed time can lead to a conclusion about the delta in the proper time if you agree that the remote observer is not a factor/cause of anything that could influence remote counting?
The quoted equation (42.5) does not work, is there any other equation?
-
How can the frequency of a clock in relative motion appear to decrease, when its KE is increased?
Nothing to do with kinetic energy but a consequence of the source and observer being in different inertial frames. Special relativity.
Light falling to earth experiences a decrease in gravity potential energy, and an increase in KE, and the lights frequency is increased.
A gravitational field is equivalent to an accelerating frame of reference. General relativity.
The clock in relative motion on the horizontal experiences a constant gravity potential energy, and an increased KE.
Which clock? There being no universal inertial frame, each clock appears to be moving from the point of view of the other observer.
Why is the clock losing frequency?
Because the two effects are quite different, because an accelerating frame is not an inertial frame, i.e. the causes are different. Both relativistic effects are observed in the signals from moving satellites as seen from earth, plus the nonrelativistic Doppler shift which depends on whether the satellite is moving towards or away from the observer.
-
1: State the blooming obvious why don't you? However, energy 'is' related to frequency, and if kinetic energy is increased relative to another clock by movement relative to that other clock, then by rights an increase in energy 'should' increase frequency, which is not what is observed.
2: Just such a shame GR cannot state a physical cause though, aye!
3: The clock one states as stationary to compare the moving clock against... Have you read the NIST 2010 ground level relativity test links Alan?
4: So - an inertial frame will cause an increase in kinetic energy to increase frequency, and an accelerated frame will cause an increase in kinetic energy to decrease frequency... Hmmm, interesting!
...If we observe a clock in free fall, will its frequency then increase as it falls to earth, like lights frequency does Alan?
-
When light goes toward a massive object its frequency increases or when a laser is being accelerated in the direction of the beam the same happens. But, also if a clock is being accelerated it's internal structure (atoms) I think is increasing it's frequency as well (atoms vibration increase frequency, elements like protons increase their deBroglie frequency) , just like the light does. I have a simple model or idea that I can use for this problem. This idea could not be correct but enabled me to understand more from GR and the misteries of black matter. Applied to this problem, the increased frequency of the clock is the result of a greater space density which slows down processes. Is like traveling through a grid with constant time between each gridline and the gridlines are not homogenous. The same thing results from GR. When going towards an increasingly stronger gravity filed space itself is contracted and light takes more time to travel through, thus time slows down. Also frequency increases. Locally, within the contracted space we don't feel anything, when measuring speed of light, we still get the same result.
In conclusion de Broglie associated wave length decreases /frequency increases with speed but time dilates on the other hand and the clock slows down.
-
One cannot state that the frequency of a clock in the other frame is only appearing to differ from ones own frame, if one is stating that a person can 'actually' age at differing rates.
Secondly, the NIST 2010 ground level relativity tests, (as far as Im concerned), prove that the difference in frequency between clocks in elevation, and clocks in relative motion, is a real and physical effect.
I think there are some things here which are misunderstandings and are standing in the way of our understanding each other.
First, I have said a number of times that the difference in ageing is a real effect.
Secondly, many things are real and relative. Mains voltage is real and relative to the common line, 12v car is relative to the chassis.
Let's have a look at what happens in these real life NIST experiments. I'm going to simplify the numbers just to illustrate what is happening.
Let's start with an atomic clock. In its simplest form it is a frequency generator and a counter+display.
Let's say we have a clock at sea level running at a (simplified but unreal) frequency of 1000Hz. The counter counts off 1000 cycles and then increments the counter by 1 second.
Now we build an identical clock and take it higher, to keep the numbers understandable we will say that time at this higher point is passing at 2x relative to the lower clock. Let's place a light in between the clocks so we can signal them to start and then stop each time the light flashes and let's say between flashes the lower clock records 1s.
So the lower clock (L) counts 1000 and records 1s, but the upper clock (U) where time passes at 2x must now show 2s. However, the design of both clocks is the same so the upper clock must have counted 2000 cycles in order to display 2s, but 2000 cycles in 2s is 1000Hz so the frequency seen by both clocks is the same. This frequency is the one the atoms tick by, that cells age by, radioactivity decays by etc in other words things genuinely age faster for the upper clock relative to the lower clock, but for those at the U level they will never know it, they experience time at the same rate as those at L.
So let us now look at the NIST experiment described here http://ws680.nist.gov/publication/get_pdf.cfm?pub_id=905055 they connected both clocks by a fibre optic so they could compare the frequency of the upper clock relative to the lower clock (see equation 2 in the paper), if you then look at Fig3B you will see that when the clock was raised to the higher position the frequency of that upper clock relative to the lower clock increased.
So let's go back to our simplified example to see what is happening.
U and L are now connected via the fibre and L counts the wavecrests it sees from U over 1s, but this 1s is 2s for U so 2000 wavecrests have passed at U during L's 1s so L sees a frequency of 2000Hz relative to itself - just the same as in the NIST experiment the upper frequency is seen to be higher.
This experiment is also another version of the Pound Rebka, but we can make it more so by shining a light from L to U. Again keep it simple, light at 1000Hz shining from L where 1000 cycles take 1s, but when it arrives at U that 1s is now 2s so U counts 1000 cycles in 2s = 500Hz = redshift.
So, the ageing is real, but the frequency shifts are relative.
So - an
4: So - an inertial frame will cause an increase in kinetic energy to increase frequency, and an accelerated frame will cause an increase in kinetic energy to decrease frequency... Hmmm, interesting!
Only to those who haven't figured it out yet, to the rest of us mild bemusement that they haven't.
There is only so much time to waste on this one, but ....
As Alan said the horizontal moving clock is not gaining KE if the motion is constant relative to the 'stationary' clock, only if it is accelerating will it gain KE and gain frequency. If that gain in frequency is from f1 to f2 and all frequencies in between, each of those frequencies as viewed from the 'stationary' clock will appear decreased as I explained in #3 and other posts.
I can't think of any way to make this clearer so I'll leave it at that.
-
Colin - I am somewhat bemused that you are still trying to teach me relativity. I know how the books say it works. I've read dozens on the subject, including Einstein's own papers. I haven't read any more recently written relativity books that include the NIST ground level relativity tests though!
I have clearly outlined in 2 replies to Janus's posts, (that he has not answered), how light from another reference frame can only be seen by an observer in his reference frame when it REACHES his eyes...
Therefore the observer is observing the light AS AFFECTED by his own reference frame, and it's journey there.
The NIST experiments also experimented with 2 clocks at the same time just 1 metre apart in elevation. It IS physically possible to view both the reference frame's clock's read out from any position in the room. The read outs from the clocks are NOT changing 'appearance' from different positions in the room! What the observer is observing on the read out of each clock is a count of the frequency of that clock actually IN that clocks reference frame. The counter of the clock takes measurements that are being recorded as they happen by the counter that transfers the information to the clock read out after the fact. That read out is recorded evidence of that reference frame, IN that reference frame. Those reference frames, and indeed the lab, are illuminated by a light source that is incidental to the experiment, but causes the eye to be able to view all of the reference frames of the room.
The fibre optic cable becomes necessary because the differences between the clocks are so fractional the eye would have trouble detecting, so the clock read outs are connected to the computer, (which wasn't in the same room).
It is an illogicality to say that clock U will 'never know' that it runs faster than clock L. It is more logical to say that an observer from L who travelled to U will not experience himself moving in slow motion in a world that is running faster than he, because all atoms run at a faster time in the U reference frame, and his personal body atoms will be now be running faster too, so all in reference frame U will be as it was in reference frame L as far as he is concerned.
The equivalence principle is upheld...
But do take on board that an atom will emit a higher energy, higher frequency photon when at elevation, relative to that which it would on the ground...
P.S. Isn't freefall supposed to be inertia?
-
1: State the blooming obvious why don't you? However, energy 'is' related to frequency, and if kinetic energy is increased relative to another clock by movement relative to that other clock, then by rights an increase in energy 'should' increase frequency, which is not what is observed.
Forget energy nonsense, which doesn't affect the on-board clock time as a body in constant motion doesn't know it is moving, so it sends out the same number of pulses every second whether it is moving or not relative to the observer. Think Doppler. Approach speed increases the received frequency, departing speed reduces it. And then add special relativity, which slows it down.
2: Just such a shame GR cannot state a physical cause though, aye!
GR is the physical cause.
3: The clock one states as stationary to compare the moving clock against... Have you read the NIST 2010 ground level relativity test links Alan?
Many times, and each time it comes up with the expected answer. What's the problem?
4: So - an inertial frame will cause an increase in kinetic energy to increase frequency, and an accelerated frame will cause an increase in kinetic energy to decrease frequency... Hmmm, interesting!
if you say so, but it's meaningless to others.
...If we observe a clock in free fall, will its frequency then increase as it falls to earth, like lights frequency does Alan?
You need to distinguish between a clock at different altitudes, and a photon travelling through a gravitational potential gradient. We've been through this many times before, and the experimental results are depressingly identical to the predictions of general relativity. Viewed from the ground, both a clock in orbit and an incoming photon appear to have a higher frequency than signals generated by identical mechanisms on the ground.
It's worth reading a bit about GPS clocks. http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html is good:
Because an observer on the ground sees the satellites in motion relative to them, Special Relativity predicts that we should see their clocks ticking more slowly (see the Special Relativity lecture). Special Relativity predicts that the on-board atomic clocks on the satellites should fall behind clocks on the ground by about 7 microseconds per day because of the slower ticking rate due to the time dilation effect of their relative motion [2].
Further, the satellites are in orbits high above the Earth, where the curvature of spacetime due to the Earth's mass is less than it is at the Earth's surface. A prediction of General Relativity is that clocks closer to a massive object will seem to tick more slowly than those located further away (see the Black Holes lecture). As such, when viewed from the surface of the Earth, the clocks on the satellites appear to be ticking faster than identical clocks on the ground. A calculation using General Relativity predicts that the clocks in each GPS satellite should get ahead of ground-based clocks by 45 microseconds per day.
The combination of these two relativitic effects means that the clocks on-board each satellite should tick faster than identical clocks on the ground by about 38 microseconds per day (45-7=38)!
-
...
Let's start with an atomic clock. In its simplest form it is a frequency generator and a counter+display.
Let's say we have a clock at sea level running at a (simplified but unreal) frequency of 1000Hz. The counter counts off 1000 cycles and then increments the counter by 1 second.
Now we build an identical clock and take it higher, to keep the numbers understandable we will say that time at this higher point is passing at 2x relative to the lower clock. Let's place a light in between the clocks so we can signal them to start and then stop each time the light flashes and let's say between flashes the lower clock records 1s.
So the lower clock (L) counts 1000 and records 1s, but the upper clock (U) where time passes at 2x must now show 2s. However, the design of both clocks is the same so the upper clock must have counted 2000 cycles in order to display 2s, but 2000 cycles in 2s is 1000Hz so the frequency seen by both clocks is the same. This frequency is the one the atoms tick by, that cells age by, radioactivity decays by etc in other words things genuinely age faster for the upper clock relative to the lower clock, but for those at the U level they will never know it, they experience time at the same rate as those at L.
...
Colin,
your example should hold with the old grandfather clock as well.
There are a few issues here though. Every cycle costs different amount of energy for different heights because V=mgh of one cycle on the gf clocks weights depends on g. The gravitational acceleration g is different at different heights. There is an issue of pendulum cycle that depends on g as well.
The atomic clocks have the "springs" and the potential energy in them. I know, this gravitational potential energy V=mgh is orders of magnitude smaller than electromagnetic forces of the atomic clocks but if we want to be accurate we have to recongize the gravitational potential energy mgh.
The end result is a real physical cause for the cycles to have different frequencies based on a position in a gravitational field.
If we imagine a machine that can lift 1kg weight into 1m height in 1s at 1g. The machine is not capable of higher power output. This is our clock.
Now we take the machine to a gravitational field with 2g gravitational acceleration. How fast it's going to do one cycle in 2g now?
Just an idea how to think about measuring time.
The atomic clock is like that machine. It has a limited power output to do one cycle and it will deliver one cycle in different frequencies in different gravitational fields.
-
Timey,
You have a valid point. Many cannot understand relativity mechanics and focus on Relativity math. The math makes no sense without the mechanics behind the math. Rabbit hole math is very confusing just ask Alice.
GR and SR have equivalence but are not the same cause mechanically. Different elevations in GR actually have different accelerations so a clock tick rate is actually different as in different frames. Not the same as a rocket ship in space without GR. The clock tick rate in SR actually tick at the same rate. Because of light being independent of the source the distance is shorter between A->B than B--->A. It is the distance the image travels that appears to change the tick speed even though they tick at the same rate. If they were in sync in the center of the ship when you bring them together the will be in sync again. This is not the case in GR at different elevations.
GR is a dilation of space energy. Less energy density. So frequency of the "vibration" of the electron is a further length. Same as SR having a further length because of vector speed. That is the equivalence.
GR tick rate at 32 ft/s/s is not equivalent to SR 32 ft/s/s in tick rate of your clock. Acceleration has nothing to do with a clock tick rate. It is only the relationship to c that is important. The "vibration" of the electron is greater at relative rest as a relation to c. For proof deceleration increases tick rate with gravity in SR. Acceleration decreases tick rate with gravity. It is not gravity that has anything to do with tick rate. Relative speed to c as inertial motion is the effect on tick rate.
GR is a physical (dilation) increase of mass. SR is visual increase in mass length. The equivalence is the measurement of the speed of light in a vacuum. Mass does not increase with velocity but the equivalence of gravity as a reduction in available c is the equivalence. It is your mechanical understanding of a process that needs to be understood in order to make sense of the rabbit hole math. A understanding in Plane Geometry is all that is needed to understand the Lorentz contraction which is visual and not physical.
The curve in GR is a 2 dimensional representation of a 3 dimensional process. Dilation is a sphere of energy density. In the center of a spherical body the dilation of energy is the greatest. This means the energy density is less per volume of space. There is a gradient of increased space energy density towards the surface. Macro mass is attracted to the lower energy density. This is the cause of gravity Basic entropy. The energy of space is c. Mass reduces the energy density by moving electrons.
-
your example should hold with the old grandfather clock as well.
in theory it should, however an uncorrected pendulum will lose time at altitude rather than gain it. If the clock is well corrected, as per Huygens, it should gain time as the atomic clock does depending on the difference in gravitational potential. As you say, this is true for all types of clock including the ones built into our aging process and into GPS satellites.
The difficulty comes when you combine motion where time dilation is dependant on relative speed. So we can have places on 2 planets with the same gravitational potential but because they are moving relative to each other each sees a different time for the other - as shown by the other NIST experiment.
As you say, at the end of the day you have to take both effects into account.
-
your example should hold with the old grandfather clock as well.
in theory it should, however an uncorrected pendulum will lose time at altitude rather than gain it. If the clock is well corrected, as per Huygens, it should gain time as the atomic clock does depending on the difference in gravitational potential. As you say, this is true for all types of clock including the ones built into our aging process and into GPS satellites.
The difficulty comes when you combine motion where time dilation is dependant on relative speed. So we can have places on 2 planets with the same gravitational potential but because they are moving relative to each other each sees a different time for the other - as shown by the other NIST experiment.
As you say, at the end of the day you have to take both effects into account.
Colin,
I would like to ask you a question.
What do you think, are the clocks in your example going to maintain the 1000Hz frequency at different heights in the light of my previous post #47?
-
The equivalence between a mechanical clock and a light clock is only precise between the electron and photon travel distance. Mass has entropy and while time on our scale can appear accurate with a grand father clock it will always run slow due to entropy. The photon and the electron do not have entropy.
-
The equivalence between a mechanical clock and a light clock is only precise between the electron and photon travel distance. Mass has entropy and while time on our scale can appear accurate with a grand father clock it will always run slow due to entropy. The photon and the electron do not have entropy.
Mass has entropy.
The photon and the electron do not have entropy.
Does it mean that photon and electron do not have mass?
Electron and photon have mass. Photon does not have a rest mass but it has mass otherwise it would not be able to carry energy.
If they have mass then according to your first statement they have entropy.
Then you deny they have entropy in the second statement. It appears as a contradiction.
Can you explain?
-
1: State the blooming obvious why don't you? However, energy 'is' related to frequency, and if kinetic energy is increased relative to another clock by movement relative to that other clock, then by rights an increase in energy 'should' increase frequency, which is not what is observed.
Forget energy nonsense, which doesn't affect the on-board clock time as a body in constant motion doesn't know it is moving, so it sends out the same number of pulses every second whether it is moving or not relative to the observer. Think Doppler. Approach speed increases the received frequency, departing speed reduces it. And then add special relativity, which slows it down.
2: Just such a shame GR cannot state a physical cause though, aye!
GR is the physical cause.
3: The clock one states as stationary to compare the moving clock against... Have you read the NIST 2010 ground level relativity test links Alan?
Many times, and each time it comes up with the expected answer. What's the problem?
4: So - an inertial frame will cause an increase in kinetic energy to increase frequency, and an accelerated frame will cause an increase in kinetic energy to decrease frequency... Hmmm, interesting!
if you say so, but it's meaningless to others.
...If we observe a clock in free fall, will its frequency then increase as it falls to earth, like lights frequency does Alan?
You need to distinguish between a clock at different altitudes, and a photon travelling through a gravitational potential gradient. We've been through this many times before, and the experimental results are depressingly identical to the predictions of general relativity. Viewed from the ground, both a clock in orbit and an incoming photon appear to have a higher frequency than signals generated by identical mechanisms on the ground.
It's worth reading a bit about GPS clocks. http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html is good:
Because an observer on the ground sees the satellites in motion relative to them, Special Relativity predicts that we should see their clocks ticking more slowly (see the Special Relativity lecture). Special Relativity predicts that the on-board atomic clocks on the satellites should fall behind clocks on the ground by about 7 microseconds per day because of the slower ticking rate due to the time dilation effect of their relative motion [2].
Further, the satellites are in orbits high above the Earth, where the curvature of spacetime due to the Earth's mass is less than it is at the Earth's surface. A prediction of General Relativity is that clocks closer to a massive object will seem to tick more slowly than those located further away (see the Black Holes lecture). As such, when viewed from the surface of the Earth, the clocks on the satellites appear to be ticking faster than identical clocks on the ground. A calculation using General Relativity predicts that the clocks in each GPS satellite should get ahead of ground-based clocks by 45 microseconds per day.
The combination of these two relativitic effects means that the clocks on-
each satellite should tick faster than identical clocks on the ground by about 38 microseconds per day (45-7=38)!
Everyone should read this post. Alan IS an authority here. If you are in doubt [janus excepted :-)] then it will help.
-
Thank you all for your comments...
If someone were to tell you that by viewing the situation just a little bit differently, and that those GR, SR, maths that do make sense will 'still' make sense under the remit of this slightly different view where the other 93% of the universe would no longer be unexplained or unaccounted for, and the mechanics of Big Bang, expansion, and contraction of a novel cyclic universe emerge fully described... all without adding anything that we do not observe.
...Would anyone listen?
Or would everyone just assume that that person doesn't understand relativity?
Hmmm, I wonder...
Quote Wiki:
("The Foundation of the General Theory of Relativity," 1916), which ultimately provided a unified theory for bothinertial and noninertial (accelerated) reference frames. However, in order to accomplish this, in general relativity, Einstein found it necessary to redefine several fundamental concepts (such as gravity) in terms of a new concept of "curvature" of space-time, instead of the more traditional system of forces understood by Newton.[22]
As a result of this redefinition, Einstein also redefined the concept of "inertia" in terms of geodesic deviation instead, with some subtle but significant additional implications. The result of this is that, according to general relativity, inertia is the gravitational coupling between the matter and the spacetime."
It is actually physically possible to have a curved spacetime in a Newtonian geometry, and that a Newtonian-ish view of gravity can exist in a spacetime setting, and that under this remit the maths will be that of General Relativity, but without the cosmological constant for a contracting universe, inclusive of a redressed concept regarding Hubble's redshifts velocities, and a vastly reduced gravitational constant, the acceleration of said gravity having been transposed via the redressing of Hubble's velocities.
But for here:
If anyone 'can' uptake my in-depth investigation of the NIST 2010 relativity tests, into 'where' events of another reference frame are viewed by the observers eyes?
An observer viewing already emitted light as it is arriving in his reference frame, versus an atom's emitting frequency being directly translated, (unchanged by any journey), to a read out that can be read as a constant frequency, from any position in the room. (or computer in next room).
By Relativity's remit, (as ya'all keep saying), the observer should get different results when he changes the position in the room of his observation, right?
Does 'anyone' want to talk about the mechanical structure of how these experiments and theory are seemingly differing? ...This being actual experiment, and current theory ...cos' if not, then for me, if all we are doing is teaching relativity, well, I've kind of read a real lot about it already, understand it, and for my part I fully expect you all to be savvy with the subject - so to be quite frank, this constant rehashing over the basics is pretty damn boring, don't you think?
-
Would anyone listen? Certainly. But it would help if the author of this new approach did not begin with the assertion of experimental untruths.
-
Is it untrue that the NIST 2010 ground level relativity tests ran 2 identical clocks 1 metre apart in elevation?
Is it untrue that a fibre optic cable was connected to a counter, in the clocks own reference frame, that records the frequency of the clock, in the clocks own reference frame, and then sends that recorded information to a computer located in a room next door?
And is it untrue that, despite the location of the frequency counter being in the reference frame with the clock, or the location of the computer reading the information being next door at unspecified elevation, that the mathematical results of the data are as relativity predict that each observer will observe of the other clocks reference frame from his own clocks reference frame 'only'?
And is it untrue that relativity predicts that an observer in his own reference frame will observe an alternative frequency of the same other clock in the same other reference frame unchanged in any other way, if he changes the elevation, or acceleration of his own reference frame? (as Colin has said)
If the answer to all these questions is "no, those things are true" - then the NIST 2010 ground level relativity test results are not matching the Relativity prediction in exactly the manner that Relativity predicts.
Right? Or wrong?
-
Wrong, apparently
http://arstechnica.com/science/2010/09/einsteins-relativity-measured-in-newtons-domain/
A lesser known consequence of general relativity is that time will move slower in a stronger gravitational field. On Earth, one implication of this is that a clock on the second floor of an office building will move faster than one on the first floor. Using the ultra-precise clock setup, the NIST researchers tested this as well. One of the optical clocks was placed about a foot above the other and measurements were taken. They found a fractional frequency change of (4.1±1.6)x10-17; plugging this number back into relativity's formulas produced an equivalent height differential gave 14.5±5.9 inches, a result that nicely bracketed the 12 inch difference in the experimental setup.
You would do well to work out what
an observer in his own reference frame will observe an alternative frequency of the same other clock in the same other reference frame unchanged in any other way, if he changes the elevation, or acceleration of his own reference frame
means: I certainly have no idea. In this ordinary, everyday universe, an observer at a lower gravitational potential sees any clock at a higher potential as running faster than his own. But we scientists are simple folk, unaccustomed to the cunning language of priests, politicians and philosophers who can say "alternative frequency", or "same other" without blushing.
Meanwhile for light relief, here's a thought. I was in Geneva last week, and for a non-EU country that exports nothing but watches and chocolate, they seem to be doing very well - how many watches can one man wear, I wonder? Anyway all the watch advertisements, which cover about 90% of the wall area of the airport, have some connection with competitive speed, showing athletes (I'm sure they'd run faster without wearing a watch), racing cars, fighter jets....But surely the whole point of a watch is that it goes at exactly the same speed as all the others?
So here's an idea for the Swiss Tourist Agency: replace the lot with a single advert that says "all our fabulously expensive mechanical watches keep pretty much the same time and are nearly as accurate as a £50 Chinese radio watch."
-
I do not read anything in the link you provided that causes anything I have said to be wrong. You will have to explain where exactly it is that you apparently think it does...
The NIST experiment also recorded the frequency of a stationary clock in relation to a moving clock at speeds as low as 36km/h.
A lot of the previous discussion has been concerning how the clock in relative motion to the stationary clock will not observe a constant reading of the stationary clock. The reading the moving clock makes of the stationary clock is dependant on how fast the moving clock is moving, despite the fact that the stationary clock has not physically changed frequency.
This is why you keep telling me that a clock only 'appears' to change frequency from another reference frame... that in the clocks own reference frame the clock is ticking as 'normal', and that an observer in his own frame of reference will not notice any difference in his own rate of time.
Correct?
-
If the answer to all these questions is "no, those things are true" - then the NIST 2010 ground level relativity test results are not matching the Relativity prediction in exactly the manner that Relativity predicts.
If I've counted all the negatives correctly, your assertion was wrong. But I may have lost count.
Note that there is no such thing as a stationary clock. There is the observer's clock and the other clock. By convention we measure the speed of the other clock relative to the position of the observer, but the result must be reciprocal for constant speeds.
-
Is it untrue that the NIST 2010 ground level relativity tests ran 2 identical clocks 1 metre apart in elevation?
True
Is it untrue that a fibre optic cable was connected to a counter, in the clocks own reference frame, that records the frequency of the clock, in the clocks own reference frame, and then sends that recorded information to a computer located in a room next door?
Untrue for the experiment we were discussing which was performed in 2010. I gave a link to the actual paper and a summary of what they did in #44.
EDIT: Just to make it clear, even if there were counters and clocks sent to computer in another room it wouldn't make any difference. In the simplified example I gave you could imagine both clocks viewed from one location by video link, or if the gravitational potential were extreme, the clocks could be at different heights in the same room and creatures from the deep could see both at once, it wouldn't change anything. Remember the ground control station for GPS sees both the satellite and local clocks in the control room. Doesn't make any difference.
And is it untrue that, despite the location of the frequency counter being in the reference frame with the clock, or the location of the computer reading the information being next door at "unspecified elevation", that the mathematical results of the data are as relativity predict that each observer will observe of the other clocks reference frame from his own clocks reference frame 'only'?
As the previous quote is untrue I cannot speculate on what might have been other than what I added. However, I can't see what the computer being at an unspecified level has to do with it, the computer will see the same results from the clocks and frequency comparators no matter what height it is. I think you may be getting confused with the old concept of an observer, the computer is not an observer in a relativity sense.
And is it untrue that relativity predicts that an observer in his own reference frame will observe an alternative frequency of the same other clock in the same other reference frame unchanged in any other way, if he changes the elevation, or acceleration of his own reference frame? (as Colin has said)
You seem to be reinterpreting what I said, but I'm not sure what you are saying.
If the answer to all these questions is "no, those things are true" - then the NIST 2010 ground level relativity test results are not matching the Relativity prediction in exactly the manner that Relativity predicts.
QED
The NIST ground level tests are matching what relativity predicts. If they didn't the NIST team would be rubbing their hands and looking forward to receiving their Nobel prizes.
PS I have already suggested that you might like to start a new theory discussion on your ideas, the website link you provide doesn't give much info.
PPS I'm not trying to teach you relativity, just make sure we have a common understanding of what we are discussing as some of your interpretations don't match how I interpret the info.
-
What do you think, are the clocks in your example going to maintain the 1000Hz frequency at different heights in the light of my previous post #47?
I'm assuming you mean your comment " I know, this gravitational potential energy V=mgh is orders of magnitude smaller than electromagnetic forces of the atomic clocks but if we want to be accurate we have to recongize the gravitational potential energy mgh.".
If so, yes the clocks will maintain 1000Hz at different heights because mgh has been taken into account in calculating the gravitational potential difference between the clocks and hence the different 'flow rate' of time at the different altitudes.
You can check that this is the frequency seen by the counter/display by trying to substitute the relative frequency seen by the lower clock (in this eg 2000Hz) into the upper clock, in this case the upper clock will register exactly the same rate of time as the lower clock indicating that there is no time difference. Two problems with this, firstly we know from GPS and other experiments that there really is a time difference, secondly if you now move the 'corrected' clock to a new height it will begin to drift and no longer show same time as lower clock, so it would need a correction for every infinitesimal change of height.
-
Alan - I have painstakenly shown in many posts on this forum that I fully understand that what I'm referring to as a stationary clock, is a clock that is moving only with the earths movement. A clock in relative motion is a clock that is moving relative to the clock that is only moving with the earth's movement... Sorry, I understood that this was what the terminology 'clock in relative motion' means, unless it is specified that the clock in relative motion is moving relative to something other than a clock that is on motion with the movement of the planet.
Colin - Relativity predicts that an observer with the lower clock will observe that the higher clock is ticking faster than his own, and that an observer with the higher clock will observe the lower clock as ticking slower than his own.
You have previously mentioned about adding a 3rd clock into the mix at a different gravity potential. Now let me just check against what I thought you were saying by asking you these questions:
When the 3rd clock is viewing the 1st and 2nd clocks, does the 3rd clocks observation of both the other clock's agree with the 1st clock and the 2nd clocks observation of each other, or does the 3rd clock observe the 1st and 2nd clocks as running at different frequencies than they observe of each other?
When adding the 3rd clock as moving in relative motion to both the 1st clock and the 2nd clock, (at 1st clocks ground level gravity potential), does the 3rd clocks observation of the 1st and 2nd clocks frequency agree with the observation that the 1st and 2nd clock make of each other, or does the 3rd clock observe the frequency of the 1st and 2nd clocks as running at different frequencies than the 1st and 2nd clocks are observing each other running at?
-
The above discussions refer to "clocks", which are exterior mechanical devices purporting to display the passing of time.
But the passing of time is also displayed internally, and very intimately, in our human bodies. So as our bodies get older and wear out, more creases and wrinkles keep appearing. However, these deleterious bodily effects could supposedly be delayed or even almost nullified, if we travelled at a very high speed approaching a significant fraction of the speed of light.
Thus we're supposed to believe that a starship could set out from Earth, travelling at (say) 99.9% light-speed, visit a star 1,000 light years away, then return to Earth.
And when the ship's crew step out, they've not aged more than a few years. But the Earth they see has aged by a thousand years, and everyone they knew is long dead.
This seems an extraordinary claim. Is there any actual empirical evidence for it? And I don't mean the "evidence" of tiny particles in accelerators such as the LHC. Aren't LHC observations predicated on a theory which is bound to make the observations conform to it.
Wouldn't it be more convincing, if we built an actual starship and sent it on a 0.99c mission to Alpha Centauri. Then when the ship returns, observe whether the crew look 8 years younger than they should be?
-
Alas, the clock on the ship sees no difference at constant speed or in a constant gravitational potential (which would be zero for most of the trip) because it has no comparator, and once the ship has reached cruise speed, the passengers will continue to degrade at a rate determined only by the temperature.
As has been mentioned many times in this discussion, time dilatation is observed in near-earth and interplanetary experiments, and so far it seems to conform exactly to the predictions of conventional relativity and accelerator experiments. Relativity is not a theory but a means of calculating what actually happens, based on the single observation that c is constant.
-
Alas...I have not mentioned any ship - nor that relativity does not calculate what is observed.
What I do mention is that NIST compared a clock that was stationary, (as in moving only with the motion of the planet), to a clock that was traveling at speeds as low as 36km/h. The link does not suggest that the moving clock was gaining or losing acceleration as the measurement was taken. In order to state that a time dilation effect could be measured at speeds as low as 36km/h, the experimenters would have had to keep the clock at a constant 36km/h for quite some period of time...
Correct?
-
Colin - Relativity predicts that an observer with the lower clock will observe that the higher clock is ticking faster than his own, and that an observer with the higher clock will observe the lower clock as ticking slower than his own.
Can I check our understanding of terms here so we agree what we are talking about.
Early relativity texts used to refer to observers and although still used in popular texts this has largely been replaced by the use of reference frame and measurement relative to another frame. The problem was that people began to assume, as with QM, that it meant human observer.
For clarity, let's take the simplified eg I gave. If we put a video camera pointing to each of the upper and lower clocks, connect them to a screen, then a human observer can look at that screen and see the upper clock running faster relative to the lower clock. The human observer can be situated at any height and will see exactly the same thing because they are not an observer in the way the term is used in relativity.
In this example, the counter/display system is the observer, measuring the transitions of the oscillator (often called a clock in many NIST press releases) at the same gravitational potential as the oscillator.
In the NIST 2010 experiment the observer is a laser probe pulse fed into a frequency comparator. (It is possible that the comparator may have been described somewhere as a computer because it works out the frequency difference.)
The important thing is that the measurement has to be taken at the same height as whichever frequency is being measured, this is not a problem at NIST as the probe is in the same box as the oscillator. The fibre optic carries reference clock pulses from the lower clock and transfers the measurement to the comparator. In these experiments the reference was the frequency of the lower oscillator and the non-moving one (f0 in the paper I linked to).
When the 3rd clock is viewing the 1st and 2nd clocks, does the 3rd clocks observation of both the other clock's agree with the 1st clock and the 2nd clocks observation of each other, or does the 3rd clock observe the 1st and 2nd clocks as running at different frequencies than they observe of each other?
The 3rd clock agrees with relative differences that 1 and 2 see, but like the other two it counts it's own frequency as being the same as it measured at ground level - see the simplified example I gave.
When adding the 3rd clock as moving in relative motion to both the 1st clock and the 2nd clock, (at 1st clocks ground level gravity potential), does the 3rd clocks observation of the 1st and 2nd clocks frequency agree with the observation that the 1st and 2nd clock make of each other, or does the 3rd clock observe the frequency of the 1st and 2nd clocks as running at different frequencies than the 1st and 2nd clocks are observing each other running at?
The latter. It will see the clocks as time dilated as per Lorentz.
Alas...I have not mentioned any ship - nor that relativity does not calculate what is observed.
I think he was answering zx16.
What I do mention is that NIST compared a clock that was stationary, (as in moving only with the motion of the planet), to a clock that was traveling at speeds as low as 36km/h. The link does not suggest that the moving clock was gaining or losing acceleration as the measurement was taken. In order to state that a time dilation effect could be measured at speeds as low as 36km/h, the experimenters would have had to keep the clock at a constant 36km/h for quite some period of time...
Correct?
For the height difference measurements they took about 140,000 measurements.
For the relative motion experiment about 200 probe pulses were used. The researchers state that they don't view this as a highly accurate result, just a test of concept, they are looking at more accurate systems to measure the earth's geoid to within 1cm - I sent you the link on the proposed system.
-
The above discussions are very erudite, which is a polite way of saying that I - and probably most people - can't understand them.
It's all big words and abstract theory. What we need is practical empirical verification. This could be obtained by making the following test:
1. Build a starship.
2. Send it off on a round-trip to Alpha Centauri at near light-speed.
3. When the ship comes back to Earth, let doctors examine the ship's crew.
4. See whether the doctors report, with full medical and physical data, that the crew really have aged less than if they'd stayed on Earth.
Until such a test is carried out, I wouldn't accept anything as more than speculation. Isn't that how Science is supposed to work?
-
It's all big words and abstract theory. What we need is practical empirical verification. on Earth.
The NIST experiments are not abstract theory, they are practical empirical verification.
The relativistic corrections to GPS satellites are not abstract theory, they are practical empirical verification.
The gravity probe B was not abstract theory, it was practical empirical verification.
That's the way science is supposed to work. Unfortunately it can't all be described in words of one syllable.
-
Colin - Relativity predicts that an observer with the lower clock will observe that the higher clock is ticking faster than his own, and that an observer with the higher clock will observe the lower clock as ticking slower than his own.
Can I check our understanding of terms here so we agree what we are talking about.
Early relativity texts used to refer to observers and although still used in popular texts this has largely been replaced by the use of reference frame and measurement relative to another frame. The problem was that people began to assume, as with QM, that it meant human observer.
For clarity, let's take the simplified eg I gave. If we put a video camera pointing to each of the upper and lower clocks, connect them to a screen, then a human observer can look at that screen and see the upper clock running faster relative to the lower clock. The human observer can be situated at any height and will see exactly the same thing because they are not an observer in the way the term is used in relativity.
In this example, the counter/display system is the observer, measuring the transitions of the oscillator (often called a clock in many NIST press releases) at the same gravitational potential as the oscillator.
In the NIST 2010 experiment the observer is a laser probe pulse fed into a frequency comparator. (It is possible that the comparator may have been described somewhere as a computer because it works out the frequency difference.)
The important thing is that the measurement has to be taken at the same height as whichever frequency is being measured, this is not a problem at NIST as the probe is in the same box as the oscillator. The fibre optic carries reference clock pulses from the lower clock and transfers the measurement to the comparator. In these experiments the reference was the frequency of the lower oscillator and the non-moving one (f0 in the paper I linked to).
When the 3rd clock is viewing the 1st and 2nd clocks, does the 3rd clocks observation of both the other clock's agree with the 1st clock and the 2nd clocks observation of each other, or does the 3rd clock observe the 1st and 2nd clocks as running at different frequencies than they observe of each other?
The 3rd clock agrees with relative differences that 1 and 2 see, but like the other two it counts it's own frequency as being the same as it measured at ground level - see the simplified example I gave.
When adding the 3rd clock as moving in relative motion to both the 1st clock and the 2nd clock, (at 1st clocks ground level gravity potential), does the 3rd clocks observation of the 1st and 2nd clocks frequency agree with the observation that the 1st and 2nd clock make of each other, or does the 3rd clock observe the frequency of the 1st and 2nd clocks as running at different frequencies than the 1st and 2nd clocks are observing each other running at?
The latter. It will see the clocks as time dilated as per Lorentz.
Alas...I have not mentioned any ship - nor that relativity does not calculate what is observed.
I think he was answering zx16.
What I do mention is that NIST compared a clock that was stationary, (as in moving only with the motion of the planet), to a clock that was traveling at speeds as low as 36km/h. The link does not suggest that the moving clock was gaining or losing acceleration as the measurement was taken. In order to state that a time dilation effect could be measured at speeds as low as 36km/h, the experimenters would have had to keep the clock at a constant 36km/h for quite some period of time...
Correct?
For the height difference measurements they took about 140,000 measurements.
For the relative motion experiment about 200 probe pulses were used. The researchers state that they don't view this as a highly accurate result, just a test of concept, they are looking at more accurate systems to measure the earth's geoid to within 1cm - I sent you the link on the proposed system.
Colin - No, I do not refer to an observer's presence altering the outcome of the experiment, I refer to what is viewed from 1 reference frame by another.
As you have said, the NIST experiments are recording the frequency as seen by the counter 'in' that clocks reference frame, as per the predicted relativity, or Lorentz maths... But relativity is predicting that the relativity results that NIST are arriving at are that which will be viewed of the clock in that reference frame 'from' the other reference frame, not 'in' the reference frame of the time dilated clock itself...
...and it is this that I am trying to bring to your attention/s
-
For Colin #68:
I'll believe it when I see a 30-year old astronaut get into a starship, journey out to Alpha Centauri and back, while 8 years pass on Earth and everyone here is 8 years older, and when the astronaut gets out, he/she is still only 30 or 31.
That's the kind of proof I'd accept!
(GPS satellites may need corrections to their signals to achieve accuracy, but does this necessarily invoke a universal "time-dilation" effect. Couldn't it result from other more local causes)
-
(GPS satellites may need corrections to their signals to achieve accuracy, but does this necessarily invoke a universal "time-dilation" effect. Couldn't it result from other more local causes)
No. The timing corrections are preset by simple relativistic calculation before the satellites are launched, and lo and behold, each time you look at your GPS it tells you exactly where you are. If the calcs were wrong, your house would appear to move as different satellites came in and out of your reception field. So the choice of belief is yours: either relativity is correct or your GPS is broken.
-
My GPS just miscounts the number of exits on a roundabout. In the log jam we call rush hour this can be very annoying. Especially when traffic off the exit you have taken is moving at 1/2 a mile a month. However it always tells me with great precision where it has gotten me stuck.
-
How can the frequency of a clock in relative motion appear to decrease, when its KE is increased?
Light falling to earth experiences a decrease in gravity potential energy, and an increase in KE, and the lights frequency is increased.
The clock in relative motion on the horizontal experiences a constant gravity potential energy, and an increased KE.
Why is the clock losing frequency?
First of all the clock is loosing frequency during the process of acceleration but we can jump directly to the time where it has a certain velocity. Space is compressed and frequencies may appear higher. The clock being made of atoms, we need to see what happens to them when they reach a certain speed. Motion vector within the atoms is always at c, but if an atom has on x axis a lower speed than c, it means the y and/or z components are not zero. Conversely if the atom had y and z components which gave the clock frequency, when it moves on x axis, these y and z components will decrease thus reducing frequency. The space the clock occupies contracts but information still travels at c, because x/t=x'/t' is constant.
Next we need to see what happens to light. A laser a beam in the same direction the source is moving, will experience a Doppler effect. This is equivalent to increasing kinetic energy of the photons. But if you make a photon clock with light pulses bouncing on y axis between mirrors while moving on x axis, the speed vector being c, the y component will reduce.
Light falling directly towards earth experience a more complex process I don't know if I can explain correctly . While going towards Earth, space is also contracting increasingly as the light approaches Earth so apparently KE and frequency are increased. Rate of contraction is higher when approaching Earth. This is explained by GR.
My explanation is based on a principle that may not be correct which would say that any information including space waves (gravity waves), motion within atoms or even protons, in space travels at c, not only light. Speed differences are only the effect of different trajectories, circular, spiral patterns or space itself compressing/expanding. It is like the universe has a constant frequency clock.
Space contraction/expansion is explained by GR.
-
My GPS just miscounts the number of exits on a roundabout. In the log jam we call rush hour this can be very annoying. Especially when traffic off the exit you have taken is moving at 1/2 a mile a month. However it always tells me with great precision where it has gotten me stuck.
I think this is more a problem of cartography than physics! Roundabouts are sometimes built with temporarily unused exit kerbs, sometimes the traffic flow is re-routed so that a previous exit becomes a one-way on-ramp, sometimes the cartographers just get it wrong (this used to be a deliberate feature of OS maps to prevent breach of copyright) and most often, skinflints like me don't pay the update fees. It's particularly difficult inside airports, where road layouts and traffic flows change quickly but there are no clues like buildings, and a wrong turning can lead to disaster.
-
What do you think, are the clocks in your example going to maintain the 1000Hz frequency at different heights in the light of my previous post #47?
I'm assuming you mean your comment " I know, this gravitational potential energy V=mgh is orders of magnitude smaller than electromagnetic forces of the atomic clocks but if we want to be accurate we have to recongize the gravitational potential energy mgh.".
If so, yes the clocks will maintain 1000Hz at different heights because mgh has been taken into account in calculating the gravitational potential difference between the clocks and hence the different 'flow rate' of time at the different altitudes.
You can check that this is the frequency seen by the counter/display by trying to substitute the relative frequency seen by the lower clock (in this eg 2000Hz) into the upper clock, in this case the upper clock will register exactly the same rate of time as the lower clock indicating that there is no time difference. Two problems with this, firstly we know from GPS and other experiments that there really is a time difference, secondly if you now move the 'corrected' clock to a new height it will begin to drift and no longer show same time as lower clock, so it would need a correction for every infinitesimal change of height.
Hi Colin,
I am going to quote Feynman one more time.
"The Feynman Lectures on Physics, The New Millennium Edition, Volume II: Mainly on electromagnetism and matter", page 42-10, 11:
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Ftheelectromagneticnatureofthings.com%2Fimg%2Fi7%2Fep06.png&hash=1b1f3acec107b0791dc9d800e00df3b4)
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Ftheelectromagneticnatureofthings.com%2Fimg%2Fi7%2Fep07.png&hash=86b849fc396d83f1d50077963a2ef508)
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Ftheelectromagneticnatureofthings.com%2Fimg%2Fi7%2Fep08.png&hash=09058cba0b1e941010a4228ee7d41bc1)
The last equation here and the (42.5) from the quote on the first page of this thread clearly show that the frequencies are different at different heights.
The internal "springs" of the atom have different potential energy between E_0 and E_1 energies because there is different gravitational acceleration g at different heights.
When you say:Two problems with this, firstly we know from GPS and other experiments that there really is a time difference, secondly if you now move the 'corrected' clock to a new height it will begin to drift and no longer show same time as lower clock, so it would need a correction for every infinitesimal change of height.
I understand it that we agree that clocks have different frequency rate and GPS clock has adjusted/corrected frequency to account for its height in relation to the ground station.
It means that if the clock were made identical then higher clock would tick faster but they fine tune the GPS clock to tick slower.
Are we in an agreement on this point?
-
The internal "springs" of the atom have different potential energy between E_0 and E_1 energies because there is different gravitational acceleration g at different heights.
No. This is the same conceptual error that timey makes from time to time. If a "mass and spring" model was valid, the bandwidth of an atomic clock's primary transition would decrease with height and the spectral lines of stars would not only red-shift but also broaden, which they don't. The model works OK for infrared absorption by molecules, which is a genuine vibration or rotation phenomenon, but not for atomic hyperfine transitions which are spin-spin interactions.
-
The internal "springs" of the atom have different potential energy between E_0 and E_1 energies because there is different gravitational acceleration g at different heights.
No. The equations given in this explanation assumes no difference in g at the different heights. If it did, then Equation 42.8 would have been written as E1/c^2 (Gm/R-Gm/(r+H)) For this discussion the difference in g between the two heights was simple considered small enough to ignore
When you say:Two problems with this, firstly we know from GPS and other experiments that there really is a time difference, secondly if you now move the 'corrected' clock to a new height it will begin to drift and no longer show same time as lower clock, so it would need a correction for every infinitesimal change of height.
I understand it that we agree that clocks have different frequency rate and GPS clock has adjusted/corrected frequency to account for its height in relation to the ground station.
It means that if the clock were made identical then higher clock would tick faster but they fine tune the GPS clock to tick slower.
Are we in an agreement on this point?
GPS clocks are tuned to run slower because there is another factor in play, they are orbiting at a speed of 3.87 km/sec. The time dilation due to this swamps out the factor due to its increased altitude.
-
The internal "springs" of the atom have different potential energy between E_0 and E_1 energies because there is different gravitational acceleration g at different heights.
No. This is the same conceptual error that timey makes from time to time. If a "mass and spring" model was valid, the bandwidth of an atomic clock's primary transition would decrease with height and the spectral lines of stars would not only red-shift but also broaden, which they don't. The model works OK for infrared absorption by molecules, which is a genuine vibration or rotation phenomenon, but not for atomic hyperfine transitions which are spin-spin interactions.
What atomic clock you are talking about?
What stars spectral line broadening has to do with time measurement? By the way the lines broaden.
The sun's spectrum shows two lines of hydrogen 410.1 and 434.0 nm plus many other spectral lines. The spectrum of Vega, however, has the same two lines but they are much thicker and more intense.
From www. ph. surrey. ac. uk/astrophysics/files/spectroscopy.html#stars
(I cannot post links, I guess a restriction for new users?)
Going back to the "spring":
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Ftheelectromagneticnatureofthings.com%2Fimg%2Fi7%2Fep09.png&hash=aa81590efa416985f7a7091834d5da51)
From ws680. nist. gov/publication/get_pdf.cfm?pub_id=905055
The quote from the image: "it undergoes harmonic motion".
It means there is an oscillation and there is potential energy in the harmonic motion. When I use " double quotes I mean it's not a real spring but there is a potential energy in a harmonic motion, an oscillation.
The model itself is not important. What is important though is to recognize there is a potential energy between an electron and proton(s) that can be changed and it appears this energy is dependent on the background gravitational field.
-
The last equation here and the (42.5) from the quote on the first page of this thread clearly show that the frequencies are different at different heights.
This depends on how you are interpreting what Feynman says.
What you have quoted answers the second line of the OP:
"Light falling to earth experiences a decrease in gravity potential energy, and an increase in KE, and the lights frequency is increased."
This is gravitational redshift/blueshift and I describe it in my simplistic example by considering light leaving the lower clock and being measured at the upper clock (redshift), and yes the measured frequencies of the photons will vary with height.
However, Feynman does not say that the frequency of the emitter ω0 varies with height. Let us assume the frequency of the Al ion clock ω0 varies with height then, as I pointed out, the clocks would no longer show an increase of time with height consistent with the change of gravitational potential.
Also, how do we measure the redshift/blueshift? We measure it using clocks that have the built in assumption that ω0 is constant with height, if it varies then the clocks won't measure the shift predicted by Feynman's calculations.
So do we believe that the emitted frequency of the atom varies with height or do we believe that it is constant at each height where it is measured and hence that redshift/blueshift occurs as predicted and that clocks run faster at height in a way predicted by GR.
One last thought, Einstein didn't start his theory of GR by assuming that atoms contain a component which is influenced by gravity to create differential frequencies. His theory is consistent without such an assumption.
-
The internal "springs" of the atom have different potential energy between E_0 and E_1 energies because there is different gravitational acceleration g at different heights.
No. The equations given in this explanation assumes no difference in g at the different heights. If it did, then Equation 42.8 would have been written as E1/c^2 (Gm/R-Gm/(r+H)) For this discussion the difference in g between the two heights was simple considered small enough to ignore
When you say:Two problems with this, firstly we know from GPS and other experiments that there really is a time difference, secondly if you now move the 'corrected' clock to a new height it will begin to drift and no longer show same time as lower clock, so it would need a correction for every infinitesimal change of height.
I understand it that we agree that clocks have different frequency rate and GPS clock has adjusted/corrected frequency to account for its height in relation to the ground station.
It means that if the clock were made identical then higher clock would tick faster but they fine tune the GPS clock to tick slower.
Are we in an agreement on this point?
GPS clocks are tuned to run slower because there is another factor in play, they are orbiting at a speed of 3.87 km/sec. The time dilation due to this swamps out the factor due to its increased altitude.
One centimeter in heights gives us 30nm/s^2 difference in the gravitational acceleration g.
That's why it appears to me as a mistake to make that simplification.
-
The internal "springs" of the atom have different potential energy between E_0 and E_1 energies because there is different gravitational acceleration g at different heights.
No. The equations given in this explanation assumes no difference in g at the different heights. If it did, then Equation 42.8 would have been written as E1/c^2 (Gm/R-Gm/(r+H)) For this discussion the difference in g between the two heights was simple considered small enough to ignore
When you say:Two problems with this, firstly we know from GPS and other experiments that there really is a time difference, secondly if you now move the 'corrected' clock to a new height it will begin to drift and no longer show same time as lower clock, so it would need a correction for every infinitesimal change of height.
I understand it that we agree that clocks have different frequency rate and GPS clock has adjusted/corrected frequency to account for its height in relation to the ground station.
It means that if the clock were made identical then higher clock would tick faster but they fine tune the GPS clock to tick slower.
Are we in an agreement on this point?
GPS clocks are tuned to run slower because there is another factor in play, they are orbiting at a speed of 3.87 km/sec. The time dilation due to this swamps out the factor due to its increased altitude.
One centimeter in heights gives us 30nm/s^2 difference in the gravitational acceleration g.
That's why it appears to me as a mistake to make that simplification.
The difference in the answer you get by making the simplification and the answer you get by not doing so only differs by about 1 part in 63726. In other words, the actual answer you get using either method will be ~63726 times larger than the difference in the answers.
-
The last equation here and the (42.5) from the quote on the first page of this thread clearly show that the frequencies are different at different heights.
This depends on how you are interpreting what Feynman says.
What you have quoted answers the second line of the OP:
"Light falling to earth experiences a decrease in gravity potential energy, and an increase in KE, and the lights frequency is increased."
This is gravitational redshift/blueshift and I describe it in my simplistic example by considering light leaving the lower clock and being measured at the upper clock (redshift), and yes the measured frequencies of the photons will vary with height.
However, Feynman does not say that the frequency of the emitter ω0 varies with height. Let us assume the frequency of the Al ion clock ω0 varies with height then, as I pointed out, the clocks would no longer show an increase of time with height consistent with the change of gravitational potential.
Also, how do we measure the redshift/blueshift? We measure it using clocks that have the built in assumption that ω0 is constant with height, if it varies then the clocks won't measure the shift predicted by Feynman's calculations.
So do we believe that the emitted frequency of the atom varies with height or do we believe that it is constant at each height where it is measured and hence that redshift/blueshift occurs as predicted and that clocks run faster at height in a way predicted by GR.
One last thought, Einstein didn't start his theory of GR by assuming that atoms contain a component which is influenced by gravity to create differential frequencies. His theory is consistent such an assumption.
The slowing down of processes due to time dilation is all or nothing. In a time dilated frame it would be impossible to observe the effect. It matters not whether you consider this in terms of frequency or energy.
-
... It matters not whether you consider this in terms of frequency or energy.
Or time!
-
...
The difference in the answer you get by making the simplification and the answer you get by not doing so only differs by about 1 part in 63726. In other words, the actual answer you get using either method will be ~63726 times larger than the difference in the answers.
If there is a system in an equilibrium that has a harmonic motion then any acceleration no matter how small will affect the system. The gravitational field will influence the balance of the system, the potential energy of the system.
-
Difference in acceleration felt by clocks does not result in any time dilation. This is the basis of the Clock Postulate. The Clock Postulate has been experimentally confirmed with high speed centrifuges at accelerations up to thousands of gravities of acceleration. By spinning radio-isotopes at various speed and radii, you can create conditions so that that different samples experience the same acceleration but travel at different speeds or travel at the same speed while experiencing different accelerations. The results of all these tests show that the only factor that determined the rate at which the isotopes decayed was the speed they were traveling and the acceleration values had no effect.
You do not need a difference in gravitational force for there to be a difference in potential. That was the basic idea of the text you quoted. Even if you assume no difference in g force between the two altitudes, you still get a frequency change/time dilation. By focusing on that small g force difference over the 1 cm altitude change at the surface of the Earth, you are missing the forest for the trees.
-
...
GPS clocks are tuned to run slower because there is another factor in play, they are orbiting at a speed of 3.87 km/sec. The time dilation due to this swamps out the factor due to its increased altitude.
Janus, this is wrong.
The velocity factor is 7 microseconds per day and the altitude factor is 45.9 microseconds per day.
As per en.wikipedia .org/wiki/Error_analysis_for_the_Global_Positioning_System#Special_and_General_Relativity
The altitude factor is more than 6x bigger than the velocity factor. The velocity factor is not big enough to compensate so the GPS clocks are being made to run slower.
-
The last equation here and the (42.5) from the quote on the first page of this thread clearly show that the frequencies are different at different heights.
This depends on how you are interpreting what Feynman says.
What you have quoted answers the second line of the OP:
"Light falling to earth experiences a decrease in gravity potential energy, and an increase in KE, and the lights frequency is increased."
This is gravitational redshift/blueshift and I describe it in my simplistic example by considering light leaving the lower clock and being measured at the upper clock (redshift), and yes the measured frequencies of the photons will vary with height.
However, Feynman does not say that the frequency of the emitter ω0 varies with height. Let us assume the frequency of the Al ion clock ω0 varies with height then, as I pointed out, the clocks would no longer show an increase of time with height consistent with the change of gravitational potential.
Also, how do we measure the redshift/blueshift? We measure it using clocks that have the built in assumption that ω0 is constant with height, if it varies then the clocks won't measure the shift predicted by Feynman's calculations.
So do we believe that the emitted frequency of the atom varies with height or do we believe that it is constant at each height where it is measured and hence that redshift/blueshift occurs as predicted and that clocks run faster at height in a way predicted by GR.
One last thought, Einstein didn't start his theory of GR by assuming that atoms contain a component which is influenced by gravity to create differential frequencies. His theory is consistent without such an assumption.
Colin,
here is a thought experiment.
There are two identical clocks with the same ω0 at the North Pole. The clock A is at 10km above the ice held by a balloon, the clock B is on the ice at the sea level. Clocks A and B have their counters attached to them at the same height. The start switch is somewhere in the middle so the signal travels to both clocks with the same delay, when it's pushed the clocks set the counter to 0 and they start to count. We leave the clock running one month, then we push the stop switch in a similar way as the start and the clocks will stop counting.
Now we pull the clock A down check the counters.
Does the clock A run faster than the clock B? What delta (in nanoseconds) is going to be on the clock? If any?
This is a measurement of the proper time.
Why is GPS clock set to run slower? The ω0 is not the same for the GPS clock and the ground clock. This is the biggest hint to the questions above.
When you consider this then what is your answer to this question?
So do we believe that the emitted frequency of the atom varies with height or do we believe that it is constant at each height where it is measured and hence that redshift/blueshift occurs as predicted and that clocks run faster at height in a way predicted by GR.
Now the following issue:
Also, how do we measure the redshift/blueshift? We measure it using clocks that have the built in assumption that ω0 is constant with height, if it varies then the clocks won't measure the shift predicted by Feynman's calculations.
...
One last thought, Einstein didn't start his theory of GR by assuming that atoms contain a component which is influenced by gravity to create differential frequencies. His theory is consistent without such an assumption.
Let us call spade a spade. Einstein, Feynman got time dilation with a flawed thought experiment. Why do I say that?
Because as already posted by Janus:
And yes, this does mean that both clocks would say that the other clock is the one running slow and by the same factor.
This applies to two clocks on two spaceships flying against each other with the same velocity, transmitting the clock light ahead and observing each others clocks.
This is a proof that apparent/observed time of the other clock is useless in predicting the proper time of the other clock.
-
Difference in acceleration felt by clocks does not result in any time dilation. This is the basis of the Clock Postulate. The Clock Postulate has been experimentally confirmed with high speed centrifuges at accelerations up to thousands of gravities of acceleration. By spinning radio-isotopes at various speed and radii, you can create conditions so that that different samples experience the same acceleration but travel at different speeds or travel at the same speed while experiencing different accelerations. The results of all these tests show that the only factor that determined the rate at which the isotopes decayed was the speed they were traveling and the acceleration values had no effect.
You do not need a difference in gravitational force for there to be a difference in potential. That was the basic idea of the text you quoted. Even if you assume no difference in g force between the two altitudes, you still get a frequency change/time dilation. By focusing on that small g force difference over the 1 cm altitude change at the surface of the Earth, you are missing the forest for the trees.
It does not appear to me that I am missing the forest for the trees. If you give me a chance you might agree with me down the road.
It appears the Clock Postulate is true and I believe it holds. Here is the most important question for the CP though.
... the only factor that determined the rate at which the isotopes decayed was the speed they were traveling ...
What speed? Compare to what?
Everything will unfold from the answer to this question.
-
What speed? Compare to what?
Everything will unfold from the answer to this question.
The tangential speed of the sample relative to the lab.
Thus if I have a sample traveling at a radius of 1 meter in a centrifuge with a an angular velocity of 1000 rad/s, the sample has a speed of 6283.185 m/sec relative to the lab.
-
What speed? Compare to what?
Everything will unfold from the answer to this question.
The tangential speed of the sample relative to the lab.
Thus if I have a sample traveling at a radius of 1 meter in a centrifuge with a an angular velocity of 1000 rad/s, the sample has a speed of 6283.185 m/sec relative to the lab.
Before talking about the centrifuge we should discuss 'easier' example.
As per my post above, the clocks at the North Pole.
I assume we would agree that the A clock 10km above the sea goes faster compare to the B clock at the sea level.
Assuming the Clock Postulate holds were is 'the speed' as a cause of the time dilation of the proper time coming from?
What speed when the clocks have no relative motion? The both clocks are stationary in the gravitational field.
-
It's about the clock you use, relative the 'clock' you measure.
-
Hmm
Let's see. what does a constant build on?
And 'c'
Well, 'c' is the one interesting, from a view of 'quanta', isn't it?
-
If you give something the the 'status' of a 'constant'. Then you also defined a way to 'objectively' describe 'physics'. What Einstein did was to move that idea, from 'objective' to 'locally'. And if you don't get this you need to look at him again. That's what he did, and it revolutionized physics
-
What speed? Compare to what?
Everything will unfold from the answer to this question.
The tangential speed of the sample relative to the lab.
Thus if I have a sample traveling at a radius of 1 meter in a centrifuge with a an angular velocity of 1000 rad/s, the sample has a speed of 6283.185 m/sec relative to the lab.
Before talking about the centrifuge we should discuss 'easier' example.
As per my post above, the clocks at the North Pole.
I assume we would agree that the A clock 10km above the sea goes faster compare to the B clock at the sea level.
Assuming the Clock Postulate holds were is 'the speed' as a cause of the time dilation of the proper time coming from?
What speed when the clocks have no relative motion? The both clocks are stationary in the gravitational field.
In this case it is the difference in gravitational potential. The analogy with the centrifuge is to imagine that you are in the rotating frame of the centrifuge. In this frame, clocks at different radii are not moving with respect to you, but clocks closer to the axis run faster than those further away. The rate difference will be due to the potential between them. If you try to move from one radius to closer to the axis you have to expend energy to do so (Just like you were climbing against a gravity field. The fact that this gravity field weakens as you move towards the center instead of weaker as you move outward from the center of a planet makes no difference to the equivalence principle.)
It is this difference in potential that contributes to the difference in the clock rates, the fact that the clocks also experience different acceleration forces does not contribute an additional effect.
For example, let's assume you live on large rotating space colony with a 50 mile radius and 1 gravity on the inner surface. You have a tall 10 mile tower with a clock at the top and one at the bottom. The clock at the top will run faster the the one at the bottom. The force of simulated gravity felt by the clock at the top of the tower will be 4/5 of that at the bottom.
Now we will assume that our colony has a radius of 100 miles, and we have the same ten mile high tower. Now, the force of gravity felt at the top will be 9/10 of that of that at the bottom, a smaller difference with the 50 mile radius colony. The difference in time rates between the clocks however will be greater.
-
Looking just at gravity potential - as a clock gets further away from the 100 mile radius colony, if we keep the clock rotating at the same speed as the planet is, so that the relative motion between the elevated clock and comparison clock on ground is the same but we keep increasing distance - does gravity potential keep increasing as the gravity field gets weaker, or does the effect of gravity potential start to tail off at some point with increased distance?
Also, from your clocks rotating on an axis analogy - could it be said that adding gravity potential, as the energy that a clock would have to apply to get from 1 frame to another increases frequency, and the expending of energy moving from 1 frame to another, (be that through frames of differing gravity potential, or changing between frames of differing relative motion), decreases frequency?
-
Gravitational potential increases as -1/r as you move away from a point mass. By convention it is a maximum of zero in deep space and negative close to a mass.
Not sure about yor-on's rotating space station! if the tower is on the axis of rotation, it has no g force and all clocks in the tower run at the same rate. If it is radial, the g force increases with "height" (i.e. radius) and the outer clocks run more slowly, both due to potential gradient and relative speed.
-
Gravitational potential increases as -1/r as you move away from a point mass. By convention it is a maximum of zero in deep space and negative close to a mass.
Not sure about yor-on's rotating space station! if the tower is on the axis of rotation, it has no g force and all clocks in the tower run at the same rate. If it is radial, the g force increases with "height" (i.e. radius) and the outer clocks run more slowly, both due to potential gradient and relative speed.
Usually a rotating space centre looks like a cylinder not like a sphere.
....
I've drawn a space-time diagram and plot an acceleration curve AC, obviously anywhere on the curve there is the same acceleration. If you place two clocks one at point A and one further in time at B, their position in spacetime will be different. The clocks experience the same acceleration following the same curve AC. However it appears like the speed at point A is different than that at point B. I didn't check what happens to the distance between these points. This should explain the time difference. Is this how it works or I am also wrong ?
-
Looking just at gravity potential - as a clock gets further away from the 100 mile radius colony, if we keep the clock rotating at the same speed as the planet is, so that the relative motion between the elevated clock and comparison clock on ground is the same but we keep increasing distance - does gravity potential keep increasing as the gravity field gets weaker, or does the effect of gravity potential start to tail off at some point with increased distance?
What I meant by a rotating space colony was something like an O'Neil colony; a large spinning cylindrical object where you feel one gravity standing on the inside of the cylindrical wall. The rotation of both colonies is such that this is true at the bottom of the tower for each colony. So the "top' of the towers are nearer the center of the rotation than the "base" is. The point of comparing the two colonies was to point out that even though there would be less of a difference in between top and bottom in terms of froce felt with 100 mile radius colony, there would be a larger potential difference and a greater time dilation difference.
If you plot acceleration vs distance above the surface for the two colonies you will get the following graph. The potential is represented by the area under each line plotting the change in "gravity".
javascript:replaceText(' [ Invalid Attachment ] ',%20document.postmodify.message);
If we want to consider things from a planetary gravity situation, we can do the following. We will compare the Earth to "planet X" Planet X is both more massive and has twicethe radius of the Earth, but is is of a lesser enough density that the force of gravity on its surface is equal to that of the Earth's. In this case we will not consider rotation. This gives us the following graph;
javascript:replaceText(' [ Invalid Attachment ] ',%20document.postmodify.message);
Again, the areas under the curves represent the potential difference. As you note even as the force of gravity decreases with distance, the potential difference continue to increase. This is not an unbounded increase but increases to a limit equal to GM/r
Shading areas under the curve can provide a better illustration. Here the green shaded area is the potential difference between the surface of the Earth and an altitude of 0.2 Earth radii above it. For planet X, it is the green area plus the green cross-hatched area. The difference in gravity between for the same altitude difference is less for Planet X, but the potential difference is greater. The light blue area is the potential difference between the altitudes where gravity in 6 m/s^2 and 4 m/s^2 for the Earth, and the yellow is for the same difference in gravity for Planet X. Again planet X has a larger difference in potential.
javascript:replaceText(' [ Invalid Attachment ] ',%20document.postmodify.message);
Also, from your clocks rotating on an axis analogy - could it be said that adding gravity potential, as the energy that a clock would have to apply to get from 1 frame to another increases frequency, and the expending of energy moving from 1 frame to another, (be that through frames of differing gravity potential, or changing between frames of differing relative motion), decreases frequency?
No, I wouldn't put it this way,as it implies that moving the clock from one position to another appies a physical change to how the clock operates. It is more accurate to say that time itself is measured differently at the two altitudes.
-
...
The point of comparing the two colonies was to point out that even though there would be less of a difference in between top and bottom in terms of force felt with 100 mile radius colony, there would be a larger potential difference and a greater time dilation difference.
...
This statement is in contradiction to the Clock Postulate. The speed delta between the two examples is the same so how come there is going to be a greater time dilation difference?
-
...
The point of comparing the two colonies was to point out that even though there would be less of a difference in between top and bottom in terms of force felt with 100 mile radius colony, there would be a larger potential difference and a greater time dilation difference.
...
This statement is in contradiction to the Clock Postulate. The speed delta between the two examples is the same so how come there is going to be a greater time dilation difference?
No it isn't. The clock postulate states that a difference in the local acceleration felt by two clocks has no effect on their relative tick rate, it does not say that a difference in potential will not. You can have two clocks that experience exactly the same acceleration force but be at different potentials and they would tick at different rates, or you can have two clocks which experience different acceleration forces but are at the same potential, and they will tick at the same rate.
Again we will use Earth and Planet X to illustrate. Planet X has twice the radius of Earth and 4 times the mass, and has the same surface gravity.
However, if I apply the gravitational time dilation formula to clocks sitting on the surface of both, we get 0.9999999993 for a time dilation factor for the Earth and 0.9999999986 for planet X. The clock on planet X ticks at 0.9999999993 the rate of the Earth Clock even though they feel exactly the same force of gravity.
Conversely, if we move the clock on Planet X to a height of 2 Earth radii above its surface, its time dilation factor now matches that for the clock on the Earth's surface and they tick at the same rate. However, at this height, the Planet X clock experiences just 1/4 of the gravitational force as the one sitting on the Earth. Different magnitude of gravitational force acting on the two clocks, but they tick at the same rate.
-
You can get it a simpler way, using a wristwatch,
What Einstein did wasn't accusing that wristwatch :)
Do you really get that one?
If you do then frames of reference isn't about you locally
It's about you comparing what you have, to what you read.
Do anyone here see the difference?
-
Btw stop f*ng thank me.
I sort of hate that thing, and IQ tests
Bs
-
You're as good as anyone else. I wouldn't exist without you
-
Yeah, so we're 'different'
And?
I love
do you?
-
The explanation using gravitational potential looks clear but it only shows how the difference in gravitational potential is calculated, it is not easy to see how it affects the clocks rates.
At post #20 there is an explanation, by Feynman which, if I'm not wrong, which shows how SR handles acceleration and then using equivalence principle you can apply this to gravity.
-
...
The point of comparing the two colonies was to point out that even though there would be less of a difference in between top and bottom in terms of force felt with 100 mile radius colony, there would be a larger potential difference and a greater time dilation difference.
...
This statement is in contradiction to the Clock Postulate. The speed delta between the two examples is the same so how come there is going to be a greater time dilation difference?
No it isn't. The clock postulate states that a difference in the local acceleration felt by two clocks has no effect on their relative tick rate, it does not say that a difference in potential will not. You can have two clocks that experience exactly the same acceleration force but be at different potentials and they would tick at different rates, or you can have two clocks which experience different acceleration forces but are at the same potential, and they will tick at the same rate.
Again we will use Earth and Planet X to illustrate. Planet X has twice the radius of Earth and 4 times the mass, and has the same surface gravity.
However, if I apply the gravitational time dilation formula to clocks sitting on the surface of both, we get 0.9999999993 for a time dilation factor for the Earth and 0.9999999986 for planet X. The clock on planet X ticks at 0.9999999993 the rate of the Earth Clock even though they feel exactly the same force of gravity.
Conversely, if we move the clock on Planet X to a height of 2 Earth radii above its surface, its time dilation factor now matches that for the clock on the Earth's surface and they tick at the same rate. However, at this height, the Planet X clock experiences just 1/4 of the gravitational force as the one sitting on the Earth. Different magnitude of gravitational force acting on the two clocks, but they tick at the same rate.
You were talking about the colonies with 100 and 50 mile radius and comparing delta between the bottom and the top of the 10 mile tower.
Please, can you show us the speed calculation that will lead to different time dilation according to the Clock Postulate?
-
You were talking about the colonies with 100 and 50 mile radius and comparing delta between the bottom and the top of the 10 mile tower.
Please, can you show us the speed calculation that will lead to different time dilation according to the Clock Postulate?
Okay, First we'll sure we start on the same page. We are talking about an O'Neil cylinder. Basically a large drum shaped structure rotating on it's axis to provide simulated gravity to someone standing on the Inner surface. A cross-section diagram looking end on would look like this:
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fhome.earthlink.net%2F%7Eparvey%2Fsitebuildercontent%2Fsitebuilderpictures%2Foneil.jpg&hash=8ab5864c69c82592f6f013eb92b09f15)
Here we see a clock sitting at the base, at the top of the tower, and an additional clock, just outside the colony but not sharing in its rotation.
Consider what happens over one rotation of the cylinder. The floor clock travels in a circle and returns to it spot right next to the external clock. The tower clock starts 50 miles from the external clock, travels in a smaller circle and returns to a spot 50 miles from the external clock. What we have is a version of the Twin paradox setup. The only difference is that our "traveling" twins follow semi-circular shaped paths on their outbound and return legs instead of straight paths.
And like the original Twin paradox, both clocks will return to their original starting point showing less time than the external clock. The tower clock having both traveled a shorter path and at a slower speed will show a smaller difference. This means that the tower clock after one rotation, while being behind the external clock, will be ahead of the clock at the base of the tower.
And like the twin paradox, someone at the location of any of these clocks has to come to the same conclusion as to the respective readings of the clocks. If you don't see this, imagine that you stop the rotation of the cylinder at the end of the rotation. You can now bring the clocks together and compare them side.( you can even freeze the clocks' readings once they all are back in their respective starting positions and before stopping the rotation and bringing them together, to eliminate having to worry about what effect stopping the rotation and bringing the clocks together has on their respective readings.)
If you allow the cylinder to continue for multiple rotations, the difference between the clocks continues to grow. So Even if you were at the standing at the bottom of the tower, and from your perspective the top of the tower clock dos not move relative to you, nor you relative to it, the clock at the top will run faster than the one next to you.
The above diagram shows the 50 mile radius cylinder, and as such the acceleration force felt at the the top of the tower will be 4/5 that at the base.
If we expand the radius to 100 miles while keeping the same tower height, the top of the tower feels 9/10 the acceleration of the base. It we assume that the rotation rate is adjusted so that both colonies feel the same force of acceleration at the base of the their respective towers, then there will be a smaller difference between the top this tower and base than there is for the 50 mile radius cylinder.
Now in order the 100 mile radius cylinder to have the same effective gravity at "floor level" as the 50 mile radius cylinder, the speed of the floor clock has to be 1.414 times faster.
To keep thing simple. we will use units where the "floor level" speed for the 50 mile cylinder is 1.
This makes the speed of the clock at the top of the tower for this cylinder 0.8, a difference of 0.2
For the 100 mile cylinder, it is 1.414 and 1.2726 a difference of 0.1414
Now we can do the same comparison for the clocks with the 100 mile cylinder as we did for the 50 mile cylinder. Now at first it would seem that the since the speed difference between the two clocks for the 100 mile cylinder is less, so would the time difference. A however, this is not the case as the time dilation formula is not linear. As the speeds go up, the smaller the difference in speeds is needed for the same time dilation effect.
For example if speed 1 is 0.1 c and speed 2 is .08c, This gives time dilation factors of 0.994987 and 0.996795 respectively, or a difference of 0.0018
If they are 0.1414c and .12726 c, you get 0.989953 and 0.991869 respectively, for a difference of .0019. A greater time dilation difference with a smaller speed difference.
The same happens with our 100 mile cylinder, The difference between tick rates for the clocks at the top and bottom of the cylinder will be greater than it is with the 50 miles cylinder, even though the difference in acceleration between the two is less.
And that is what the clock postulate is all about, that the relative tick rate of two clocks is independent of the difference in readings between accelerometers co-located with the clocks. It doesn't matter if the accelerometers are measuring a difference due being at different radii from the center of a rotating structure, or from being at different altitudes in the same planetary gravity field, or sitting on the surface of two completely different planets.
That is not to say that these different clocks won't run at different rates, just that this difference is not due to the difference in acceleration felt by the clock.
-
...
It we assume that the rotation rate is adjusted so that both colonies feel the same force of acceleration at the base of the their respective towers, then there will be a smaller difference between the top this tower and base than there is for the 50 mile radius cylinder.
...
Thank you Janus,
this explains my misunderstanding. I assumed one colony with multiple 'floors' (100 mile and 50 mile) where the angular velocity is the same, therefore different accelerations at the base of the towers but the delta between the bottom and the top clocks would be the same in this scenario because the tangential velocity delta is the same.
The following train of thoughts is important for the Equivalence Principle.
...
To keep thing simple. we will use units where the "floor level" speed for the 50 mile cylinder is 1.
This makes the speed of the clock at the top of the tower for this cylinder 0.8, a difference of 0.2
For the 100 mile cylinder, it is 1.414 and 1.2726 a difference of 0.1414
...
What would be the difference for the 1000, 1000000 km radius? How about the infinity?
The infinity is for the straight line, linear acceleration. The speed delta is 0. The time flows at the same rate at the bottom and at the top of the 10 mile tower if the Clock Postulate is true.
That brings us back to my post #19 on the first page of this thread where I tried to make the following point.
Einstein/Feynman rocket thought experiment does not lead to the conclusion about the proper time delta between the bottom and the top of the rocket if the Clock Postulate is true. The CP was tested. The rocket thought experiment is flawed and it was not verified by the real experiment.
This link math.ucr .edu/home/baez/physics/Relativity/SR/clock.html
has a description of the "momentarily comoving inertial frame" (MCIF).
One centimeter in heights gives us 30nm/s^2 difference in the gravitational acceleration g on the Earth. It's like 30nm/s velocity change with every centimeter in the MCIF.
10 miles give us 0 velocity change between the bottom and the top MCIF's in the straight line linear acceleration.
Where does it leave the Equivalence Principle?
-
What would be the difference for the 1000, 1000000 km radius?
a difference in speed between top and bottom of 0.01 (along with a corresponding decrease in difference in acceleration) for the 1,000 km radius. and 0.001 for the 1,000,000. The velocities at floor level will increase by factors of 10 and 100, respectively. The time dilation between top and bottom will increase as you go from 10, to 1,000 to 1,000,000 km in radius, following the trend of increased time dilation difference even though the difference in acceleration between top and bottom of the tower is decreasing with the increasing radius.
How about the infinity?
The infinity is for the straight line, linear acceleration. The speed delta is 0. The time flows at the same rate at the bottom and at the top of the 10 mile tower if the Clock Postulate is true.
You cannot extend this example to infinity for a couple of reasons. The first is that one of the conditions we set for extending the radius was that the magnitude of acceleration at the base of the tower was a constant magnitude in all cases (one Earth gravity). At infinity, You are assuming linear motion, and while there is no difference in acceleration between top and bottom of the tower, this is because it will be zero at both. You can't have an infinite radius and still hold to the 1 earth gravity acceleration at the base of the tower rule. The other reason you can't is that in order to maintain that 1 Earth gravity as the radius increases, the speed has to go up. As you approach infinite radius, it approaches infinity. But Relativity restricts us to speeds less than c, and thus sets an upper limit to the radius of this experiment. ( There is a similar limit for the planetary gravity example. We can only keep increasing the mass and radius of the planet so far in our attempt to maintain a surface gravity equal to Earth's. The mass eventually reaches the point where you find that the "surface" is now within the event horizon of a black hole. Yet another example of the equivalence principle in action, both scenarios have limits.
That brings us back to my post #19 on the first page of this thread where I tried to make the following point.
Einstein/Feynman rocket thought experiment does not lead to the conclusion about the proper time delta between the bottom and the top of the rocket if the Clock Postulate is true. The CP was tested. The rocket thought experiment is flawed and it was not verified by the real experiment.
No. Again you are missing the point of the Clock postulate. The Clock postulate only applies to the difference in acceleration felt by the two clocks. As long as the acceleration experienced by the clocks > 0, then there will be a time dilation between them. What the clock postulate says in this instance is that even though there is zero difference in the acceleration between the two clocks, this does not have any effect on whether or not there is a time dilation between them. You are trying to make the Clock postulate say something it doesn't say.
The time dilation between clocks in the rocket happens according to the rules of Relativity. To deny this is to deny Relativity. Is this your purpose?
I can use a completely different approach to show that this difference in accumulated time takes place. Consider an inertial frame that the rocket is accelerating relative to. In this frame, the rocket is constantly gaining speed. As it does so, it length contracts. But this means that the distance between the tail clock and nose clock is decreasing; The tail clock is "catching up" to the nose clock. But to do this it must be moving a little faster with respect to our inertial frame than the Nose clock, and as a result, showing more time dilation and running slower. If the rocket now stops its acceleration, both frame are now inertial and there will be a fixed time difference between the clocks according to our external frame. It will also turn out that this difference will be smaller than what it should be if taking Relativity of simultaneity into account. In other words, there will be real difference between the readings of the clocks that does not transform away as you go from one frame to the other. The nose clock will be ahead of the tail clock according to both frames.
This link math.ucr .edu/home/baez/physics/Relativity/SR/clock.html
has a description of the "momentarily comoving inertial frame" (MCIF).
Let's look at the MCIF in terms of both the rotating structure and the accelerating rocket. With the rotating structure, you have a clock at the base of the tower and one at the top. The MCIF for the base clock will be different than the one for top Clock at any given moment. If I pick any inertial frame and measure the velocity of the two clocks relative to it I get a different answer for each clock, thus they have different MCIF wit different relative velocities.
With the accelerating rocket, As I pointed out above, Any inertial frame will measure the top and bottom clocks as having different velocities with respect to it at any given moment(due to length contraction), and thus the MCIF's for those clocks will have different velocities.
One centimeter in heights gives us 30nm/s^2 difference in the gravitational acceleration g on the Earth. It's like 30nm/s velocity change with every centimeter in the MCIF.
No. If you want to relate the difference in 1 cm in height on the Earth's surface to the difference in velocity between inertial frames, it would work out, to a velocity difference of 0.4427449297m/s ( the equivalent to the velocity gained by dropping an object from 1 cm above the surface of the Earth a distance of 1 cm.
On Planet X from earlier, that same 1cm height difference would result in only a difference of ~ 15/s^2. However, the potential difference Would result in an equivalent inertial frame velocity difference of 0.4427449536 m/s, just a bit larger, which goes along with a greater difference in time dilation over the 1 cm difference.
10 miles give us 0 velocity change between the bottom and the top MCIF's in the straight line linear acceleration.
As shown above, this is wrong. The two MCIFs do have a velocity difference, and thus there will be a time dilation. Again, to deny this is to deny Relativity. [/quote]
Where does it leave the Equivalence Principle?
Alive and well as long as you properly apply it and properly analyze the scenarios involved.
[/quote]
-
...
At infinity, You are assuming linear motion, and while there is no difference in acceleration between top and bottom of the tower, this is because it will be zero at both.
...
Thank you Janus,
the discussion grows like a tree. So many branches.
I'd like to address all of them and hopefully I will do that over the time. I suggest to go one by one. The linear acceleration as discussed by Einstein/Feynman.
Here is an addition to the thought experiment.
We place the identical clocks at the bottom, at the top and in the middle of the rocket. The clocks have the same ω0. We place the clock counters next to the clocks. There is a start/stop switch in the middle between the clocks, the signal travels to the bottom and the top clocks with the same delay.
We start 1g straight line acceleration and we start the clocks. We stop the clocks after one day of 1g straight line acceleration as measured by the middle clock.
Are the bottom an the top clocks going to show the same number of ticks?
-
Are the bottom an the top clocks going to show the same number of ticks?
No. For example, if the distance between the clocks when at the top and bottom is 100m, then the accumulated difference between the clocks after 1 day of acceleration will be 9.408e-10 sec.
If it were 200 meters, it would be
1.882e-9 sec.
increasing the distance in steps of 100m, gives the following results after 24 hrs of acceleration.
300m- 2.84e-9 sec
400m- 3.780e-9 sec
500m- 4.72e-9 sec
600m- 5.66e-9 sec
700m- 6.6e-9 sec
800m- 7.54e-9 sec
900m- 8.48e-9 sec
1 km - 9.42e-9 sec
The accumulated time difference between a clock sitting on the Earth's surface, and one 1km above it over the 24 hrs (as measured by the sea level clock), is:
9.41e-9 sec, a smaller difference than that between the two clocks separated by the same distance in the rocket.
-
Are the bottom an the top clocks going to show the same number of ticks?
No. For example, if the distance between the clocks when at the top and bottom is 100m, then the accumulated difference between the clocks after 1 day of acceleration will be 9.408e-10 sec.
If it were 200 meters, it would be
1.882e-9 sec.
increasing the distance in steps of 100m, gives the following results after 24 hrs of acceleration.
300m- 2.84e-9 sec
400m- 3.780e-9 sec
500m- 4.72e-9 sec
600m- 5.66e-9 sec
700m- 6.6e-9 sec
800m- 7.54e-9 sec
900m- 8.48e-9 sec
1 km - 9.42e-9 sec
The accumulated time difference between a clock sitting on the Earth's surface, and one 1km above it over the 24 hrs (as measured by the sea level clock), is:
9.41e-9 sec, a smaller difference than that between the two clocks separated by the same distance in the rocket.
Here are the equations (42.5) and (42.6).
The clock counter (the receiver) is next to the clock (at the bottom and at the top) so H=0 and it follows that (Rate at the receiver) = (Rate of emission).
The identical clocks will have the same counts at the bottom and at the top after one day of straight line 1g rocket acceleration.
I am saying no to your no unless you show us how Einstein/Feynman made mistake in this equation (42.5).
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Ftheelectromagneticnatureofthings.com%2Fimg%2Fi7%2Fep03.png&hash=fbcb6ea24f902e05b859cd01ec0a6359)
-
Here are the equations (42.5) and (42.6).
The clock counter (the receiver) is next to the clock (at the bottom and at the top) so H=0 and it follows that (Rate at the receiver) = (Rate of emission).
The identical clocks will have the same counts at the bottom and at the top after one day of straight line 1g rocket acceleration.
I am saying no to your no unless you show us how Einstein/Feynman made mistake in this equation (42.5).
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Ftheelectromagneticnatureofthings.com%2Fimg%2Fi7%2Fep03.png&hash=fbcb6ea24f902e05b859cd01ec0a6359)
There is nothing wrong with his equation. The problem is how you are interpreting it.
w0 is the frequency emitted by the source as measured at the source
w1 is the frequency measured at the receiver.
With a classical Doppler shift, you see a shift in the received vs. the transmitted frequency because the distance between you and source is changing and the propagation delay changes with it. If the source is moving towards you the distance is decreasing and the propagation delay is getting shorter which causes you to receive a higher frequency. If you were watching a clock it would also appear to tick faster. But if you account for this, you would conclude that the source is actually emitting at the lower frequency and the clock is ticking at the same rate as your own, and the the higher frequency and faster tick rate you see is an artifact caused by the decreasing distance between you.
In the accelerating rocket ship however, the distance between the top and bottom clock does not change according to anyone accelerating with the rocket. But someone at the bottom of the rocket watching the top clock will still see a higher frequency/faster tick rate for it. However, here the propagation delay is constant and not changing. There is nothing additional to account for the higher frequency/ faster tick rate he measures other than concluding that the top clock is indeed ticking faster than his own. If both clocks are stopped and brought together again, they will show a difference in elapsed time. This is consistent, as I pointed out in an earlier post, to what would happen according to an inertial frame not accelerating with the rocket and watching both clocks.
-
The point what I am trying to make is that the top clock A has its 'observer' - the counter next to it. There is no propagation delay between the clock and the observer because H=0.
The same is true for the clock B. The observer - the counter is next to the clock and H=0.
The clocks are identical, they have the same ω0 therefore the counters will show the same number of ticks after one day.
This is a measurement of the proper time.
The apparent/observed time, the new bottom counter of the top clock A and the new top counter of the bottom clock B is a different story and I will return to it once we agree what I said above.
-
The point what I am trying to make is that the top clock A has its 'observer' - the counter next to it. There is no propagation delay between the clock and the observer because H=0.
The same is true for the clock B. The observer - the counter is next to the clock and H=0.
The clocks are identical, they have the same ω0 therefore the counters will show the same number of ticks after one day.
This is a measurement of the proper time.
The apparent/observed time, the new bottom counter of the top clock A and the new top counter of the bottom clock B is a different story and I will return to it once we agree what I said above.
So in other words, the set up for clock A and B is such that they can record the local proper time for each. But that is just the same a clock that records its own accumulated time, and what I have been using as my definition of "Clock" rather separating it into two components.
-
The point what I am trying to make is that the top clock A has its 'observer' - the counter next to it. There is no propagation delay between the clock and the observer because H=0.
The same is true for the clock B. The observer - the counter is next to the clock and H=0.
The clocks are identical, they have the same ω0 therefore the counters will show the same number of ticks after one day.
This is a measurement of the proper time.
The apparent/observed time, the new bottom counter of the top clock A and the new top counter of the bottom clock B is a different story and I will return to it once we agree what I said above.
So in other words, the set up for clock A and B is such that they can record the local proper time for each. But that is just the same a clock that records its own accumulated time, and what I have been using as my definition of "Clock" rather separating it into two components.
Understood but when you say ...
w0 is the frequency emitted by the source as measured at the source
...
and ...
There is nothing additional to account for the higher frequency/ faster tick rate he measures other than concluding that the top clock is indeed ticking faster than his own.
...
I am still confused what you are saying. It's a contradiction.
...
If both clocks are stopped and brought together again, they will show a difference in elapsed time.
...
This can not be true.
What you are missing is that the bottom observer at the clock B is receiving the photon with 'additional velocity', with additional energy.
... but the photon travels at c so the additional energy is exhibited by higher frequency and not by the addition of c+v.
-
The point what I am trying to make is that the top clock A has its 'observer' - the counter next to it. There is no propagation delay between the clock and the observer because H=0.
The same is true for the clock B. The observer - the counter is next to the clock and H=0.
The clocks are identical, they have the same ω0 therefore the counters will show the same number of ticks after one day.
This is a measurement of the proper time.
The apparent/observed time, the new bottom counter of the top clock A and the new top counter of the bottom clock B is a different story and I will return to it once we agree what I said above.
So in other words, the set up for clock A and B is such that they can record the local proper time for each. But that is just the same a clock that records its own accumulated time, and what I have been using as my definition of "Clock" rather separating it into two components.
Understood but when you say ...
w0 is the frequency emitted by the source as measured at the source
...
and ...
There is nothing additional to account for the higher frequency/ faster tick rate he measures other than concluding that the top clock is indeed ticking faster than his own.
...
I am still confused what you are saying. It's a contradiction.
There's is no contradiction other than the one you are inventing yourself....
If both clocks are stopped and brought together again, they will show a difference in elapsed time.
...
This can not be true.
But it istrue. You are standing next to the upper clock, watching the lower clock. The frequency javascript:replaceText('%CF%89',%20document.postmodify.message); you see coming from the lower clock will be lower than the frequency of your own local clock. This means you see the lower clock accumulate ticks at a slower rate than your own. (In other words, you will also see the counter for the lower clock count up at a slower rate.)
Now assume that the lower clock stops, and it counter display freezes at that reading. Upon seeing this, you stop your own clock and counter.
Now we will assume that when we started this experiment, the reading you saw on the lower clock was identical to the one you read off your own. Thus the clocks started reading the same time, drifted apart, with the lower clock falling behind, and then stopped. Since the readings on the clocks are frozen, bringing them together has no further effect on them, and when they are brought together, they will read differently. (unless your are going to argue that a stopped clock is going to change it reading.)
Now granted, we stopped our clock when we "saw" the lower clock stop, and there will be a propagation delay between the lower clock stopping and our seeing it, so the lower clock actually stopped a hair before we stopped our clock. However, this delay is a constant. In other words, the offset in clock readings caused by this is the same whether we let the clock lower clock run for 1 day or 1 year before it stopped. The accumulative difference in the clocks we measure does differ depending on how long we run the experiment. If we run the experiment for 1 year, we get a larger difference between the clocks when they are brought back together than if we only ran it for 1 day. Th eonly conclusion we can make is that the lower clock actually ran slower than ours when it was in its lower location.
This is different from the Classical Doppler shift effect caused by a constant relative velocity.
This time imagine two clocks, that start side by side with the same reading and separate at some fixed speed. If you are watching one clock from the other, you will see it tick slower and thus accumulate time slower. If we do the same experiment, where one clock stops ticking, and we at the other clock stop our own when we see this, and then bring the clocks together again, we get the same end result, of the two clocks having different readings when brought back together. However, we would not come to the same conclusion as above. Because now, the propagation delay between the receding clock stopping and our see this does increase the longer we run the experiment, and just enough to account for the difference in the clock readings we see.(For this example we are only considering the Doppler shift effect and ignoring time dilation, which would be a separate factor.) The end conclusion is that the two clocks did not run at different rates while separating (again ignoring the time dilation factor).
What you are missing is that the bottom observer at the clock B is receiving the photon with 'additional velocity', with additional energy.
... but the photon travels at c so the additional energy is exhibited by higher frequency and not by the addition of c+v.
That higher frequency is accompanied with the fact that you would also see the upper clock ticking faster and accumulating ticks faster, you can't separate these two effects.
The shift in frequency/time rate you see at the bottom of the rocket is really just Doppler shift. Doppler shift is related to the difference in velocity of the source at emission and the receiver upon reception. Since the rocket is accelerating, and it takes some non-zero interval between emission and reception, there is a difference in velocity between the source at the moment of emission and the receiver at the moment of reception. (when the source emitted the light it was moving at a different speed than the receiver is when it receives it.) This results in an increase in the measured frequency, and an increase in the measured tick rate of a clock located at the source.
But unlike the Doppler shift caused by a constant linear velocity difference, this perceived increase in tick rate cannot be explained away by a changing propagation delay, because the propagation delay is a constant with the accelerating rocket.
This is what Relativity predicts. To say that it is not true is to deny Relativity. So I ask again: Is this your intent?
-
...
But it istrue. You are standing next to the upper clock, watching the lower clock. The frequency javascript:replaceText('%CF%89',%20document.postmodify.message); you see coming from the lower clock will be lower than the frequency of your own local clock. This means you see the lower clock accumulate ticks at a slower rate than your own. (In other words, you will also see the counter for the lower clock count up at a slower rate.)
Janus, please, let us stop for a moment.
Please, do not modify the thought experiment that I proposed. I suggest we number the modifications and all the experiment branches.
Let us use tags:
<Exp 01>
Here is an addition to the thought experiment.
We place the identical clocks at the bottom (B), at the top (A) and in the middle of the rocket. The clocks have the same ω0. We place the clock counters next to the clocks. There is a start/stop switch in the middle between the clocks, the signal travels to the bottom and the top clocks with the same delay.
We start 1g straight line acceleration and we start the clocks. We stop the clocks after one day of 1g straight line acceleration as measured by the middle clock.
Are the bottom an the top clocks going to show the same number of ticks after one day?
</Exp 01>
Having said that there is no one watching the lower clock from the top.
There is no frequency coming from the lower clock to the top.
There is no observer at the top seeing the lower clock going slower. There is only the top counter counting the top clock (H=0). The same goes for the bottom clock B as well.
Please, can you imagine what I am talking about?
There are just clocks A, B with their respective counters and the only signal that is transmitted is the start and stop.
Please, no signal transfer during the 24 hours - one day when the experiment is done.
The question stands: Are the bottom an the top clocks going to show the same number of ticks after one day?
I hope you admit that what I described is as real as it gets. It can happen, there are no additional signal transfers but the clocks run and they have to show something at the end.
Do you have any issue with the Exp 01 as it is described that there is something unrealistic?
Let us put the signal transfers into the Exp 02, 03, ... one by one.
Please, feel free to setup <Exp 02></Exp 02> with modifications of your choice.
Now assume that the lower clock stops, and it counter display freezes at that reading. Upon seeing this, you stop your own clock and counter.
Now we will assume that when we started this experiment, the reading you saw on the lower clock was identical to the one you read off your own. Thus the clocks started reading the same time, drifted apart, with the lower clock falling behind, and then stopped. Since the readings on the clocks are frozen, bringing them together has no further effect on them, and when they are brought together, they will read differently. (unless your are going to argue that a stopped clock is going to change it reading.)
Now granted, we stopped our clock when we "saw" the lower clock stop, and there will be a propagation delay between the lower clock stopping and our seeing it, so the lower clock actually stopped a hair before we stopped our clock. However, this delay is a constant. In other words, the offset in clock readings caused by this is the same whether we let the clock lower clock run for 1 day or 1 year before it stopped. The accumulative difference in the clocks we measure does differ depending on how long we run the experiment. If we run the experiment for 1 year, we get a larger difference between the clocks when they are brought back together than if we only ran it for 1 day. Th eonly conclusion we can make is that the lower clock actually ran slower than ours when it was in its lower location.
This is different from the Classical Doppler shift effect caused by a constant relative velocity.
This time imagine two clocks, that start side by side with the same reading and separate at some fixed speed. If you are watching one clock from the other, you will see it tick slower and thus accumulate time slower. If we do the same experiment, where one clock stops ticking, and we at the other clock stop our own when we see this, and then bring the clocks together again, we get the same end result, of the two clocks having different readings when brought back together. However, we would not come to the same conclusion as above. Because now, the propagation delay between the receding clock stopping and our see this does increase the longer we run the experiment, and just enough to account for the difference in the clock readings we see.(For this example we are only considering the Doppler shift effect and ignoring time dilation, which would be a separate factor.) The end conclusion is that the two clocks did not run at different rates while separating (again ignoring the time dilation factor).
What you are missing is that the bottom observer at the clock B is receiving the photon with 'additional velocity', with additional energy.
... but the photon travels at c so the additional energy is exhibited by higher frequency and not by the addition of c+v.
That higher frequency is accompanied with the fact that you would also see the upper clock ticking faster and accumulating ticks faster, you can't separate these two effects.
The shift in frequency/time rate you see at the bottom of the rocket is really just Doppler shift. Doppler shift is related to the difference in velocity of the source at emission and the receiver upon reception. Since the rocket is accelerating, and it takes some non-zero interval between emission and reception, there is a difference in velocity between the source at the moment of emission and the receiver at the moment of reception. (when the source emitted the light it was moving at a different speed than the receiver is when it receives it.) This results in an increase in the measured frequency, and an increase in the measured tick rate of a clock located at the source.
But unlike the Doppler shift caused by a constant linear velocity difference, this perceived increase in tick rate cannot be explained away by a changing propagation delay, because the propagation delay is a constant with the accelerating rocket.
This is what Relativity predicts. To say that it is not true is to deny Relativity. So I ask again: Is this your intent?
-
Janus, please, let us stop for a moment.
Please, do not modify the thought experiment that I proposed. I suggest we number the modifications and all the experiment branches.
Let us use tags:
<Exp 01>
Here is an addition to the thought experiment.
We place the identical clocks at the bottom (B), at the top (A) and in the middle of the rocket. The clocks have the same ω0. We place the clock counters next to the clocks. There is a start/stop switch in the middle between the clocks, the signal travels to the bottom and the top clocks with the same delay.
We start 1g straight line acceleration and we start the clocks. We stop the clocks after one day of 1g straight line acceleration as measured by the middle clock.
Are the bottom an the top clocks going to show the same number of ticks after one day?
</Exp 01>
No.Having said that there is no one watching the lower clock from the top.
There is no frequency coming from the lower clock to the top.
There is no observer at the top seeing the lower clock going slower. There is only the top counter counting the top clock (H=0). The same goes for the bottom clock B as well.
Please, can you imagine what I am talking about?
There are just clocks A, B with their respective counters and the only signal that is transmitted is the start and stop.
Please, no signal transfer during the 24 hours - one day when the experiment is done.
Whether or not there is a signal transfer or observers at the clocks makes no difference. The end result is the same. At least when you have these factors, you have measurement upon which you can base your conclusion rather than just assuming it.
The question stands: Are the bottom an the top clocks going to show the same number of ticks after one day?
No.
I hope you admit that what I described is as real as it gets. It can happen, there are no additional signal transfers but the clocks run and they have to show something at the end.
Do you have any issue with the Exp 01 as it is described that there is something unrealistic?
Nothing unrealistic about the set up, but I said above, this set up will not produce any different result than one with information being exchanged between the clocks.
Your problem is that you are assuming that just because Clock 1 measures its tick rate as javascript:replaceText('%CF%89',%20document.postmodify.message); locally, and clock 2 measures its tick rate as having the same javascript:replaceText('%CF%89',%20document.postmodify.message); locally, that the two clocks are ticking at the same rate globally. This is not an assumption you can make under Relativity.
By claiming that the clocks will not show different times when brought together you are assuming the end result of your thought experiment from the very start rather arriving at it from actual measurements.
-
...
Your problem is that you are assuming that just because Clock 1 measures its tick rate as javascript:replaceText('%CF%89',%20document.postmodify.message); locally, and clock 2 measures its tick rate as having the same javascript:replaceText('%CF%89',%20document.postmodify.message); locally, that the two clocks are ticking at the same rate globally. This is not an assumption you can make under Relativity.
By claiming that the clocks will not show different times when brought together you are assuming the end result of your thought experiment from the very start rather arriving at it from actual measurements.
The Relativity is built on the Principle of locality. I do not understand, what is the global ticking rate? How does it work?
The counter next to the clock is doing the actual local measurement. What do I miss?
What would be the cause for the delta in the count?
If the rocket is in the intergalactic space with the gravitational field g around the rocket almost zero, the A and B clocks have the same speed so how is the Clock postulate going to fit in?
Where is the delta in speed that would cause delta in the tick count?
-
The Relativity is built on the Principle of locality. I do not understand, what is the global ticking rate? How does it work?
There isn't one, and that's the point. When you assume that if clock 1 ticks at javascript:replaceText('%CF%89',%20document.postmodify.message); measured locally and Clock 2 ticks a tjavascript:replaceText('%CF%89',%20document.postmodify.message); measured locally, that they tick at the same rate when compared to each other, you are tacitly assuming global time. That the same measurement of time applies to both clocks. The counter next to the clock is doing the actual local measurement. What do I miss?
According to each clock, it ticks at javascript:replaceText('%CF%89',%20document.postmodify.message);, But clocks at other positions do not. A clock closer to the nose of the rocket ticks faster than javascript:replaceText('%CF%89',%20document.postmodify.message); and one closer to the tail ticks slower. What would be the cause for the delta in the count?
It's built into the very nature of space and time itself. Its not something you can directly visualize. The best that I can say is that time itself is different for the clock at the nose than it is for the clock at the tail. [/quote]
If the rocket is in the intergalactic space with the gravitational field g around the rocket almost zero, the A and B clocks have the same speed so how is the Clock postulate going to fit in?
[/quote] The clock postulate holds. Remember, the clock postulate says that the difference in locally measured acceleration creates no difference in clock rate, but it also goes the other way, no difference in locally measured acceleration does not mean that there cannot be a difference in clock rate. The rocket scenario is an example of the second case. The clocks measure the same local acceleration but still exhibit different tick rates when compared to each other.Where is the delta in speed that would cause delta in the tick count?
The difference is between the speed of clock1 when it has a certain time reading locally, and the speed of clock 2 at a different point of the rocket when it locally measures that reading for clock 1.
Or you can consider it from an inertial frame that does not share the rocket's acceleration. In this frame, the nose does travel at a different speed than the tail to account for decreasing length of the rocket due to length contraction. If we stop the clocks and bring them both to the center of the rocket, this frame will note a difference in the readings on the clocks. This is a end result that all frames (accelerating or not) must agree on.
The point is that this is how time and space work under Relativity. Much of it is counter-intuitive, But counter-intuitive javascript:replaceText('%E2%89%A0',%20document.postmodify.message); wrong.
Maybe someday you will "get it" as to why there is a time difference between the clocks in the Rocket, but I can only lead you along that path so far. You are going to have to make that last step yourself.
But whether or not you personally "get it" or not has no bearing on the fact that there is a time difference.
-
Janus,
the <Exp 01> and the clock postulate.
What is the reference frame that determines the speed required by the clock postulate in order to identify how fast the clocks are ticking?
-
Janus,
the <Exp 01> and the clock postulate.
What is the reference frame that determines the speed required by the clock postulate in order to identify how fast the clocks are ticking?
The clock postulate doesn't require a speed. Again, The postulate merely states that that the difference in magnitude of acceleration felt locally by two clocks is not a determining factor as far as their relative tick rate is concerned. In one example, the centrifuge test, we do compare the time dilation to that expected for something traveling at the tangential speed relative to the non-rotating lab frame, but speed is not a general requirement for the Clock postulate.( It holds for clocks stationary in a gravitational field also).
-
Janus,
the <Exp 01> and the clock postulate.
What is the reference frame that determines the speed required by the clock postulate in order to identify how fast the clocks are ticking?
The clock postulate doesn't require a speed. Again, The postulate merely states that that the difference in magnitude of acceleration felt locally by two clocks is not a determining factor as far as their relative tick rate is concerned. In one example, the centrifuge test, we do compare the time dilation to that expected for something traveling at the tangential speed relative to the non-rotating lab frame, but speed is not a general requirement for the Clock postulate.( It holds for clocks stationary in a gravitational field also).
Well, I don't know how it follows that the speed is not required. Please, see the bold text.
The clock postulate can be stated in the following way. First, we take the rate that our frame's clocks count out their time, and compare that to the rate that a moving clock counts out its time. Before the clock postulate was ever thought of, all that was known was that when the moving clock has a constant velocity and speed v (measured relative to the speed of light c), this ratio of rates is the "gamma factor"
γ = (1 − v^2)^(−1/2)
The clock postulate generalises this to say that even when the moving clock accelerates, the ratio of the rate of our clocks compared to its rate is still the above quantity. That is, this ratio depends only on v, and does not depend on any derivatives of v, such as acceleration. So this says that an accelerating clock will count out its time in such a way that at any one moment, its timing has slowed by a factor (γ) that depends only on its current speed; its acceleration has no effect at all.
From http://math.ucr.edu/home/baez/physics/Relativity/SR/clock.html (http://math.ucr.edu/home/baez/physics/Relativity/SR/clock.html)
Please, do you have a source to back up your claim?
If you claim that there is a time dilation then we need a reference frame for the velocity in the gamma factor γ.
-
Janus,
the <Exp 01> and the clock postulate.
What is the reference frame that determines the speed required by the clock postulate in order to identify how fast the clocks are ticking?
The clock postulate doesn't require a speed. Again, The postulate merely states that that the difference in magnitude of acceleration felt locally by two clocks is not a determining factor as far as their relative tick rate is concerned. In one example, the centrifuge test, we do compare the time dilation to that expected for something traveling at the tangential speed relative to the non-rotating lab frame, but speed is not a general requirement for the Clock postulate.( It holds for clocks stationary in a gravitational field also).
Well, I don't know how it follows that the speed is not required. Please, see the bold text.
The clock postulate can be stated in the following way. First, we take the rate that our frame's clocks count out their time, and compare that to the rate that a moving clock counts out its time. Before the clock postulate was ever thought of, all that was known was that when the moving clock has a constant velocity and speed v (measured relative to the speed of light c), this ratio of rates is the "gamma factor"
γ = (1 − v^2)^(−1/2)
The clock postulate generalises this to say that even when the moving clock accelerates, the ratio of the rate of our clocks compared to its rate is still the above quantity. That is, this ratio depends only on v, and does not depend on any derivatives of v, such as acceleration. So this says that an accelerating clock will count out its time in such a way that at any one moment, its timing has slowed by a factor (γ) that depends only on its current speed; its acceleration has no effect at all.
From http://math.ucr.edu/home/baez/physics/Relativity/SR/clock.html (http://math.ucr.edu/home/baez/physics/Relativity/SR/clock.html)
Please, do you have a source to back up your claim?
If you claim that there is a time dilation then we need a reference frame for the velocity in the gamma factor γ.
Later in that same article, he states the the clock postulate generalizes to General Relativity, which deals with gravity. General Relativity has time dilation without a difference in velocity. In the passage you quote, he is merely talking about how the Clock postulate applies to accelerating clocks in order to point out that the time dilation that you(in an inertial frame) measure for the clock is only related to the relative speed the clock has to you at that moment, and is independent of the magnitude of the acceleration it is undergoing at that moment.
Relative velocity will produce time dilation, this does not mean that time dilation is only produced by relative velocity (if A then B does not automatically mean if B then A. for example, with the equation x^2+2x-3=y, if x=1 then y = 0, however if y=0 then x = 1 orx = -3)
In an accelerating frame, or a gravitational field, you can have time dilation without any relative velocity difference between the clocks in that frame.
The rules used to deal within non-inertial frames are not the same as those that deal within inertial frames.
Now If you want to, you can examine the relative tick rates of the clocks in the nose and tail of the rocket from a inertial frame, and I've done this twice already in this thread. Such an examination leads to the same conclusion; the nose clock accumulates time faster than the tail clock and if brought together will read differently. What is it about this analysis that you find unsatisfactory?
-
Later in that same article, he states the the clock postulate generalizes to General Relativity, which deals with gravity. General Relativity has time dilation without a difference in velocity. In the passage you quote, he is merely talking about how the Clock postulate applies to accelerating clocks in order to point out that the time dilation that you(in an inertial frame) measure for the clock is only related to the relative speed the clock has to you at that moment, and is independent of the magnitude of the acceleration it is undergoing at that moment.
Relative velocity will produce time dilation, this does not mean that time dilation is only produced by relative velocity (if A then B does not automatically mean if B then A. for example, with the equation x^2+2x-3=y, if x=1 then y = 0, however if y=0 then x = 1 orx = -3)
In an accelerating frame, or a gravitational field, you can have time dilation without any relative velocity difference between the clocks in that frame.
The rules used to deal within non-inertial frames are not the same as those that deal within inertial frames.
Now If you want to, you can examine the relative tick rates of the clocks in the nose and tail of the rocket from a inertial frame, and I've done this twice already in this thread. Such an examination leads to the same conclusion; the nose clock accumulates time faster than the tail clock and if brought together will read differently. What is it about this analysis that you find unsatisfactory?
Janus, good question, what is unsatisfactory.
Let us set up another experiment.
<Exp 02>
There are two spaceships in the intergalactic space where the gravitational acceleration is close to zero.
The spaceship A (SA), the spaceship B (SB), each spaceship flying at constant velocity 5km/s towards each other, the relative velocity is 10km/s.
Both spaceships have identical clocks A, B the same ω0 and two counters.
SAC counting local clock (proper time) of the SA and SABC counter counting the light (apparent/observed time) from SB.
SBC counting local clock (proper time) of the SB and SBAC counter counting the light (apparent/observed time) from SA.
At time T0 the spaceships are 1000000km apart and at T0 a switch right in the middle between the spaceships sends light signal towards the spaceships to clear all counters and to start counting.
At time T1=100000s the spaceships meet in the middle and during the flyby they exchange the information about their counts.
Questions:
1. SAC = SBC?
2. SABC = SBAC?
3. SAC = SBAC?
4. SBC = SABC?
</Exp 02>
In other words is the apparent/observed time going to agree with the proper time?
Another interesting question is SAC>SABC or SAC<SABC?
-
Here is another example.
An experiment from http://math.ucr.edu/home/baez/physics/Relativity/SR/clock.html
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Ftheelectromagneticnatureofthings.com%2Fimg%2Fi7%2Fep10.png&hash=d5a1360504715aa38692f37294910bee)
<Exp 03>Modified train experiment.
There is a train A clock (TAC) - torch, mirror and we change the platform observer for an observer on a train B that has own torch mirror clock (TBC).
When the trains pass each other they observe the clock on the other train.
Trains can have different velocities, TA moving and TB standing, TA standing and TB moving, TA and TB moving, ...
but the conclusion is that the apparent/observed time of the other train is slower and it depends on the relative velocity.
What does the apparent time say about the proper time on the other train?
<Exp 03>
This is the same issue as with the spaceships in the <Exp 02>.
-
Later in that same article, he states the the clock postulate generalizes to General Relativity, which deals with gravity. General Relativity has time dilation without a difference in velocity. In the passage you quote, he is merely talking about how the Clock postulate applies to accelerating clocks in order to point out that the time dilation that you(in an inertial frame) measure for the clock is only related to the relative speed the clock has to you at that moment, and is independent of the magnitude of the acceleration it is undergoing at that moment.
Relative velocity will produce time dilation, this does not mean that time dilation is only produced by relative velocity (if A then B does not automatically mean if B then A. for example, with the equation x^2+2x-3=y, if x=1 then y = 0, however if y=0 then x = 1 orx = -3)
In an accelerating frame, or a gravitational field, you can have time dilation without any relative velocity difference between the clocks in that frame.
The rules used to deal within non-inertial frames are not the same as those that deal within inertial frames.
Now If you want to, you can examine the relative tick rates of the clocks in the nose and tail of the rocket from a inertial frame, and I've done this twice already in this thread. Such an examination leads to the same conclusion; the nose clock accumulates time faster than the tail clock and if brought together will read differently. What is it about this analysis that you find unsatisfactory?
Janus, good question, what is unsatisfactory.
Let us set up another experiment.
<Exp 02>
There are two spaceships in the intergalactic space where the gravitational acceleration is close to zero.
The spaceship A (SA), the spaceship B (SB), each spaceship flying at constant velocity 5km/s towards each other, the relative velocity is 10km/s.
Both spaceships have identical clocks A, B the same ω0 and two counters.
SAC counting local clock (proper time) of the SA and SABC counter counting the light (apparent/observed time) from SB.
SBC counting local clock (proper time) of the SB and SBAC counter counting the light (apparent/observed time) from SA.
At time T0 the spaceships are 1000000km apart and at T0 a switch right in the middle between the spaceships sends light signal towards the spaceships to clear all counters and to start counting.
At time T1=100000s the spaceships meet in the middle and during the flyby they exchange the information about their counts.
Questions:
1. SAC = SBC?
2. SABC = SBAC?
3. SAC = SBAC?
4. SBC = SABC?
</Exp 02>
In other words is the apparent/observed time going to agree with the proper time?
Another interesting question is SAC>SABC or SAC<SABC?
5 km/sec is just too low a velocity for this type of exercise, in that to get any type of accurate answer you have to carry your calculations out to too many significant digits. For example, at 5 km/sec each, with A coming at you from the Right and B from the Left and you try to work out what velocity they have with respect to each other as measured by either, you need to use the addition of velocities equation. But if you plug those values in to a standard hand-held calculator, it will give you a result of 10 km/s, which is wrong (the correct answer is close to 9.9999999999999972 km/sec.) Now while my desktop calculator will handle this many decimals, it has only 1 memory cache. This means recording each intermediate result to use later and hoping you don't make a mistake somewhere along the line.
It is much better to use velocities where you don't have to carry things out to such a ridiculous number of decimals.
Thus, The same example with velocities of 0.25c gives an answer of 0.47c with the velocity addition theorem, a difference that is much easier to deal with. Also, such a scenario is much easier to work with in the form of Space-Time diagrams.
I am including the diagrams from the rest frame of the midpoint and the rest frames of both A and B with the 0.25c velocity( as measured from the midpoint)
First the rest frame of the midpoint
javascript:replaceText(' [ Invalid Attachment ] ',%20document.postmodify.message);
The circles mark the recorded times by SAC and SBC
The yellow lines represent the light carrying information about the reading of Clock A to Clock B and vice-versa. The "+"'s mark when either A or B records a particular tick from the other. In your set up you had SABC and SBAC starting when they get the signal from the midpoint. This does not really work because then neither records the first tick of the other clock until after the local clock has ticked of ~3, and then records the remaining ticks as arriving faster than the local clock. It makes more sense to have the length of the first tick as being recorded as the time between when the counter sees the light start the other clock. Then all the recorded ticks will be equally spaced.
You will note that all the counters will read the same time when A and B meet up.
Next we look at the rest frames of A and B (the left and right images below)
javascript:replaceText(' [ Invalid Attachment ] ',%20document.postmodify.message);
Please note that this is the exact same set up as the last image, just according to different inertial frames.
All three counters still read the same when they meet. The relative timing between seeing ticks from the other clock and their local clock is the same. However, the timing of the start of the clocks and their counters no longer match up. According to A, SBC starts counting before SAC does, and according to B, SAC starts counting before SBC. The same offset occurs for SABC and SBAC.
So even though Clock A ticks slower than Clock B according to Frame B, it starts ticking earlier and the clocks end up reading the same when they meet. In frame A, it is clock B that started earlier and runs slower, but you still end up with the same result.
-
This should complement what Janus has posted.
The scale is 1 ct=1 x.
On the left, A and B are in fixed positions within a space can, accelerating in the x direction. A photon of 1 wave length is exchanged between them. Its length is exaggerated for clarity. The closing speed for B is >c, thus the A photon is absorbed in less than .50, and blue shifted. The closing speed for A is <c, thus the B photon is absorbed in more than .50, and red shifted. Time dilation has not been applied, and would not change the relative doppler effects. As the can accelerates, length contraction reduces the space between A and B, with the A path having less curvature than the B path. This translates to a stronger equivalent g-field for B than for A, corresponding to a lower frequency for B than for A.
It's accelerating the objects vs accelerating the light.
-
Thank you Janus,
The logical question is do the space time diagrams change when one of the spaceships does not move?
For example if the spaceship A did not move, the spaceship B would move at 0.47c and the mid point at the half of that velocity; would the second diagram on the left look the same?
Would you apply the same logic in diagrams to the train experiment?
-
Thank you Janus,
The logical question is do the space time diagrams change when one of the spaceships does not move?
For example if the spaceship A did not move, the spaceship B would move at 0.47c and the mid point at the half of that velocity; would the second diagram on the left look the same?
Would you apply the same logic in diagrams to the train experiment?
Since there is no absolute frame by which to measure motion, The question is pretty meaningless.
Which ship is "moving" or "not moving" simply depends on the frame of reference it's being it being measured from. So the left diagram is what things looks like when Ship A is not moving. As far as the midpoint goes. In the present scenario, the relative velocity between A and the midpoint is 0.25c As measured by A or the midpoint. Consequently, the velocity difference between B and the midpoint as measured by A is 0.22c. The relative velocity of A with respect to the midpoint as measured by B will be 0.22c and its and Both the midpoint and B measure their relative velocities as being 0.25c.
If you want to change the scenario so that A and the Midpoint measure their relative velocity as being 2/.47c, but without changing the relative velocity of B to A, then according to A, its relative velocity to the midpoint is 0.235c, B is moving at 0.235c with respect to the "midpoint", the "midpoint" and B measure their relative velocity as being .264 c. and B measures the difference in velocity of A and the midpoint as being 0.206c.
Thus in the frame of the midpoint, A is approaching at 0.235c and B is approaching at .264c, and if A and B are to meet at the "midpoint", The "midpoint" can't be halfway between A and B at the start in its own frame. Nor will the signal it sends start SAC and SBC simultaneously in this frame. The clocks won't read the same when they meet in any of the frames.
You can arrange things so that any one frame will measure the A-midpoint and B-midpoint respective velocities as being equal, but then they won't be equal according to the other frames.
-
Since there is no absolute frame by which to measure motion, The question is pretty meaningless.
Which ship is "moving" or "not moving" simply depends on the frame of reference it's being it being measured from. So the left diagram is what things looks like when Ship A is not moving.
...
From Hafele-Keating experiment: https://en.wikipedia.org/wiki/Hafele%E2%80%93Keating_experiment
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Ftheelectromagneticnatureofthings.com%2Fimg%2Fi7%2Fep04.png&hash=e764263ff20c56efee38625c8937a33e)
How we would calculate the SR time dilation between a point on the Earth and a spaceship flying around the Sun at 0.5AU from the Earth, the spaceship has an elliptical orbit around the Sun, but the spaceship does not move in the center of Earth inertial reference system.
The center of the Earth inertial reference system is good for H-K experiment calculation. Would it be good for the above?
It follows from the H-K experiment that the same logic that was applied for the spaceships in the intergalactic space can not be used for the two trains in the <Exp 03>. The SR time dilation depends on the direction of the train velocity in the Earth inertial reference frame system.
-
What is missing from post 128.
A and B are moving at constant speeds of .3c and .6c respectively. The hyperbolic curves are lines of equal time, aka calibration curves. Passive observation by A and B of each others clock will see doppler shifts, since clocks are frequencies. Each perceives the other clock running, slower when diverging and faster when converging. To test for time dilation each needs to poll the other clock for a time value.
A sends a signal at .46, receives a value of .68 at 1.00. A assigns the clock event (.68) to her clock event (.73). A concludes the B clock is running slower than hers.
B sends a signal at .68, receives a value of 1.00 at 1.47. B assigns the clock event (1.00) to his clock event (1.08). B concludes the A clock is running slower than his.
The distant clock events are assigned to the local clock using the axis of simultaneity (red) per the SR clock synch convention. The assigned times are therefore always later than the clock values, thus the time dilations are fictional.
-
Timey is right. SR can't explain Doppler shift. This means we need to take in consideration absolute time. For example, 1 absolute true second can be equal to 2 seconds in a certain reference frame. We've been all, explaining different aspects of relativity, but relativity seems to be wrong.
-
Since there is no absolute frame by which to measure motion, The question is pretty meaningless.
Which ship is "moving" or "not moving" simply depends on the frame of reference it's being it being measured from. So the left diagram is what things looks like when Ship A is not moving.
...
From Hafele-Keating experiment: https://en.wikipedia.org/wiki/Hafele%E2%80%93Keating_experiment
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Ftheelectromagneticnatureofthings.com%2Fimg%2Fi7%2Fep04.png&hash=e764263ff20c56efee38625c8937a33e)
How we would calculate the SR time dilation between a point on the Earth and a spaceship flying around the Sun at 0.5AU from the Earth, the spaceship has an elliptical orbit around the Sun, but the spaceship does not move in the center of Earth inertial reference system.
From your description above, we have a modified version of the rotating space colony scenario. For the space ship to circle the Sun at 0.5 AU and maintain a constant position with respect to the Earth, it would have to have a period of one year. This is basically the same as having a space colony of radius 1 AU with the Earth at the "floor", and your spaceship at the top of a 0.5 AU tower, except you also have the additional factor of the Sun and its gravity at the center of the Colony.( your spaceship would have hang on to the top of the tower or provide constant thrust to stay on the top of the tower, and the Earth would be weightless on the floor.)
There would be some small variation due to the present eccentricity of the Earth's orbit, but these will be small enough that we can safely treat both paths as circular.
In this case, we use 1/sqrt(1-3GM/rc^2)[/tex] To find the time dilation for the Earth, and 1/sqrt(1-17GM/4rc^2)[/tex] to find the time dilation for the ship. where M is the mass of the Sun and r = 1 AU and you can use this to find the time difference between the Earth and spaceship.
The center of the Earth inertial reference system is good for H-K experiment calculation. Would it be good for the above?
In the H-K experiment they were comparing the respective rates of three clocks each in a different non-inertial frame, the Earth surface clock was traveling in a circle with the surface of the Earth due to the Earth's rotation. The East bound clock was traveling in circle at that speed plus its speed with respect to the Earth, and the West bound clock was travel at Earth surface speed minus its speed relative to the surface. The center of the Earth inertial reference system is at the center of these circular paths.
You can use any reference system you want, It is just that it's simpler to work starting from certain frames and then transforming to the frame you are interested in rather than trying to work it out directly from that frame.
For example, if we change your earlier scenario so that the Spaceship is in orbit at 0.5 AU, and I want to work out the difference in time between the Earth clock and the space ship clock over the period between the two lining up, it's much easier to work from a Sun centered inertial frame than from the Earth frame because, as measured from the Earth frame, the ship would be constantly changing relative speed.
It follows from the H-K experiment that the same logic that was applied for the spaceships in the intergalactic space can not be used for the two trains in the <Exp 03>. The SR time dilation depends on the direction of the train velocity in the Earth inertial reference frame system.
Only because, due to to the Earth's rotation, even if you neglect gravity, the Earth's surface is not an inertial frame of reference. the Train experiment is done assuming IFR's for everything involved. In real life experiments Such as the H-K experiment you have to account for all pertinent factors that might have an effect on the outcome to check your prediction against measured results. In thought experiments, like the train experiment, you have the luxury of stripping things down to just those factors you wish to examine. Thus while on the real Earth's surface you can't escape the effects to the Earth's gravity and the rotation of the Earth, you can frame a thought experiment which doesn't include them.
-
Timey is right. SR can't explain Doppler shift.
This is completely and absolutely wrong.
Consider the following animation. You have a source, emitting light waves outward spherically at c relative to itself and relative to two red and blue dots. Note how the waves hit the red and blue dots at the same frequency as they are emitted by the source.
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fhome.earthlink.net%2F%7Eparvey%2Fsitebuildercontent%2Fsitebuilderpictures%2Fdoppler1.gif&hash=485f4dc879a4e2bbb6572b72c596b3bf)
Now imagine that the source has a relative velocity with respect to the other dots.
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fhome.earthlink.net%2F%7Eparvey%2Fsitebuildercontent%2Fsitebuilderpictures%2Fdoppler2.gif&hash=15cb984e7e8317c7608a2b8afab4fb99)
As each wave or part of a wave is emitted, it still expands outward at c from the point of emission as measured by the red and Blue dots as per SR and the invariant nature of light speed. But the source is moving away from the Red Dot and towards the blue dot. The center of each expanding sphere is shifted, Though as you can see still remain spherical. As a result each successive wave has a slightly shorter distance to travel to reach the Blue dot and a slightly longer distance to reach the red dot. Thus the wave peaks are spaced both closer together in time and distance for the Blue dot than for the Red. The blue dot measures a Doppler shift towards a higher part of the spectrum and the red a Doppler shift to a lower part of the spectrum. The red dot sees a red shift and the blue dot see and blue shift. The only other factor in SR is time dilation. According to the Red and Blue dots, the source is actually emitting at a slower frequency than that measured by the source itself. This adds an additional factor to what the red and Blue dots see. This results in the Relativistic Doppler shift equation: Fo Sqrt((1+v/c)(1-v/c))fs
where fo is the observerd frequency at the receiver, fs the frequency measured by the source and v the relative velocity between source and receiver (positive when they are approaching each other). So SR does give an explanation for Doppler shift, And not only that, it gives us a formula for Doppler shift that should be correct if SR holds.
This formula actually was tested in a solving a practical problem. There was a communication problem between a surface probe and its orbiting counter part with a mission to one of the outer planet's moons. It was caused by a frequency difference in the communication protocol. They solved the problem by adjusting the orbiter's velocity with respect to the surface probe so that Doppler shift compensated for the Difference and it worked. They used the Relativistic Doppler shift formula to do this. If this SR based equation had been incorrect, they would not have gotten the results they did. (For example Classical Doppler shift depends on the Motion of the receiver and senders with respect to the medium carrying the signal. If this had been the case, they would have had to account for the motion of the Moon and its planet etc, in order to get the right solution to their problem and it would keep changing depending upon the Moon's position in its orbit. As it was, using the Relativistic Doppler shift formula, all they had to deal with was the relative motion between orbiter and surface probe.
-
I understand SR adds the time dilation factor for both observers and they get a lower emmited frequency. But thre observer in the right "sees" the source comming at a speed v and pulses comming at a speed c. At the same time it sees the difference between the source and the pulses also c. This is not clear for me.
The animation you have presented shows a classincal Doppler effect in an absolute reference frame and I think this is exactly what happens to light in reality, except that the moving source will emit at a lower absolute frequency than the stationary one. Is it a coincidence that it can give the same relativistic formula ?
Here is how. You first calculate Classical Dopplet effect, then if the source is moving the clocks that move with the source show a distorted time by gamma factor and the same mechanism will make the sources send pulses at a lower rate. This gives the relativistc Doppler effect which is SR if it is not wrong after all, it is not very clear.
-
I understand SR adds the time dilation factor for both observers and they get a lower emmited frequency. But thre observer in the right "sees" the source comming at a speed v and pulses comming at a speed c. At the same time it sees the difference between the source and the pulses also c.
No it doesn't, it sees the difference between source and pulses as being c-v. The source will measure the pulses as moving at c relative to it and the difference between pulses and the receiver as being c+v. The invariant measurement of light speed refer to the speed relative to the measuring frame, it doesn't apply to the measured "closing" speed between things moving relative to the measurement frame.
The animation you have presented shows a classincal Doppler effect in an absolute reference frame and I think this is exactly what happens to light in reality, except that the moving source will emit at a lower absolute frequency than the stationary one. Is it a coincidence that it can give the same relativistic formula ?
The animation shows exactly what you should see according to SR and an invariant speed of light. To explain the difference between this and classical Doppler shift, you will have to imagine three more scenarios. The first would show what happens if we view the source as being stationary and the dots moving to the left. The blue dot, rushes to meet the expanding waves and red one runs away, thus we still see a blue shift at the blue dot and a red shift at the Red dot. This is also pretty much we expect to see under SR if we were moving with the Source under SR.
However, this is not what we would expect to see with classical Doppler shift if the Source was moving and we were moving with the Source. In this case we would would see the centers of the Circular waves moving to left along with the Two dots. It would be like looking at the second animation while moving to the right with the source.
Now we have to imagine what happens if consider things from the perspective of the Dots, if they are the ones moving and the Source is stationary. Now the Dots will see the spherical waves a shifting to the right (and always centered on the source). It would be like you took my first animation and moved everything to the right while the read dots remained stationary.
Thus with Classical Doppler shift you have to consider 4 different Viewpoints:
1.From the Source with source stationary and Dots moving
2.From the Dots with Source stationary and Dots moving
3.From the Source with source moving and dots stationary
4.From the Dots with Source moving and Dots stationary.
In SR you only need to consider two viewpoints:
1. From the Source with a relative velocity between Source and Receiver.
2. From the Receiver with a relative velocity between Source and Receiver.
With the First 4, 1 and 2 give the same answer and 3 and 4 given the same answer for the perceived Doppler shifts, But the first pair do not give the same answer as the second pair. In Other words you get different answers if you consider the Source as moving from what you get if you consider the Receiver as moving.
With the second 2, you get the same answer for both. It makes no difference which one you consider as "moving".
-
Timey is right. SR can't explain Doppler shift. This means we need to take in consideration absolute time. For example, 1 absolute true second can be equal to 2 seconds in a certain reference frame. We've been all, explaining different aspects of relativity, but relativity seems to be wrong.
Yes Nilak - that is more or less what I am saying only I wish to be a little more complex.
A clock being subject to 'only' a higher gravity potential difference is increasing in frequency relative to the lower clock, and a clock that is moving at a greater speed relative to the stationary clock in the same gravity potential will experience an addition of kinetic energy...
My point of dissatisfaction lies in the fact that an increase in kinetic energy for the moving clock will 'increase' the moving clocks frequency relative to the stationary clock - at least it will if we follow the rules of kinetic energy and relativistic mass for light - but the moving clocks frequency is observed to be decreased...
...Now this is where relativistic mass steps in to save the day, I guess... More kinetic energy causes more mass, more mass causes a greater gravity field, and a greater gravity field slows time down...
But if time is slowed down for the moving clock due to an increase in relativistic mass, isn't the speed the clock is travelling at also slowed as a result of this slower time? Is this a case of tautology?
Faster speed = more mass, more mass = slower time, slower time = slower speed, slower speed = less mass, less mass = faster time, faster time = faster speed, faster speed = more mass...
Ok - back to a universe comprised of variable times versus an absolute time. I do not see any reason why there cannot be both!
(My model states a universal present. ie: that everywhere in the universe experiences a common 'now', and that variable rates of time are occurring simultaneously - but that an observation of a reference frame experiencing a rate of time differing from the observation points rate of time will be in some manner proportional to the difference in rate of time being experienced by both reference frames. ie: what my model terms as an "observational time frame dependancy")
Edit: I was actually replying to another post of yours, but I can't find it and my reply is also fitting to this very similar post of yours that I could find.
-
Sorry Timey , I forgot you also said that a moving clock frequency should also increase which semms to be against the ecperimental results. However I support the idea of true absolute time. However my model shows the moving clocks slow down without forcing things at all. Basically The atom inner frequency (de Broglie) increases or decreases due to Doppler shift but the tick rate being the revolution motion decreases. The increase / decrease in frequency is exactly as to light only when atoms are oriented along the traveling axis. At c it can't revolve anymore. Regarding mass, mass particles have only relativistic mass just like photons, because the revolving motion keeps them moving at c even though center of rotation is at rest.
-
No - I most certainly did not say that a moving clocks frequency should increase. What I said was that if one follows the current physics mathematical rules for an increase in kinetic energy for light, that a moving clocks frequency should increase as per those rules.
The difference here is that in implementing those kinetic energy, relativistic mass rules for light, one is not doing so with the viewpoint of lights experience of its own time, but as a mathematical means of explaining the phenomenon of how light travels across space.
When applying relativistic mass to a moving clock, the experimental observation is that the clock has a decreased frequency relative to the stationary clock in the same gravity potential. The only means (that I can see, please someone point out to me if I have gone astray), of describing this decrease in frequency observed of the moving clock is to state that the greater gravity field caused by the addition of relativistic mass has caused the decrease in frequency of the moving clock.
But then one gets into a tautology problem, as I explained in last post, where adding kinetic energy increases mass, increasing mass slows time, and a constant speed in a slower time will reduce speed, which will reduce kinetic energy, which will reduce mass...
There is no means of avoiding this inherent seesaw action. This being my point of dissatisfaction in the current physics remit.
(these considerations being based on the concept of people ageing at differing rates in reference frames of dilated or contracted rates of time, as per NIST and NASA seem to purport. Which is directly contradictory to the notion that a clock only 'appears' dilated or contracted from another reference frame, and that the clock in the other reference frame will be running at the same frequency as the observation points clock is, if you were to be in that other reference frame with the other clock)
-
Oh, I need to apologize again, Timey, I understand your point now. You trust the evidence but not the explanation. If added kinetic energy increases mass and decreases time rate, you say the decrease in time should counteract the kinetic energy increase. I will confront this to my model which uses your idea of a variable second ( I use absolute time) to see what I get. At the moment it seesm that my model says that kinetic energy is constant in the absolute frame no matter of how the particle travels so time dilation indeed counters the increase of mass. It only changes shape and becomes more elongated until it mimics a photon. The tick rate is correct. This means you also seem to be correct. But I have to study more aspects of my model.
-
Yes, Janus, I thought I saw something wrong but I understand now, the Doppler shift seems to be correct.
The point at the right sees the source comming at v and light at c. Drawing this on a spacetime chart shows the speed difference. I don't see any issues anymore with regard to Doppler Effect. Thanks.
-
javascript:replaceText(' [ Invalid Attachment ] ',%20document.postmodify.message);
All three counters still read the same when they meet.
The left diagram shows the spaceship A not moving and the spaceship B moving.
Where is the aging coming from in the twin paradox then if all counters show the same time when they meet?
-
javascript:replaceText(' [ Invalid Attachment ] ',%20document.postmodify.message);
All three counters still read the same when they meet.
The left diagram shows the spaceship A not moving and the spaceship B moving.
Where is the aging coming from in the twin paradox then if all counters show the same time when they meet?
The counters reading the same when they meet up is a consequence of how you set up your experiment. You started the counters at the same time while they were an equal distance from the midpoint and traveling at equal speeds as measured by the midpoint frame. It is obvious that they will read the same when they meet in this frame. And if they do in one frame they have to in all frames. The other frames disagreed as to whether the counters started simultaneously, were an equal distance from the midpoint when they started or traveled at the same speed with respect to the Midpoint.
The twin paradox is a different set up. Here we have two clocks starting at the same point and initially synchronized to each other. Since they are at the same point when synced they both agree that they started synced. Then the two clocks separate at some speed v, and then one of the clocks changes velocity so that it rejoins the other. We now compare clock when they met up again to find that the one that changed velocities midway through has accumulated less time.
Here are the space-time diagrams for this.
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fhome.earthlink.net%2F%7Ejparvey%2Fsitebuildercontent%2Fsitebuilderpictures%2Fst3.1.gif&hash=550afab355a23139abe9d4eaf84fa3e9)
First we have things according to the frame of our "Stay at Home" twin. Again, the yellow lines represent clock tick info being exchanged between twins.
His twin travels away at some relative speed, stops, reverses direction and returns at the same speed. during this whole time his twin's clock runs slow compared to his. What he sees via light information is his twin aging slow for a long time and then aging fast for a short time. Both lead to the conclusion that his twin's net age will be less than his own when they meet up.
For the traveling twin we have to consider two different diagrams, the first is for his outbound leg. and second for his return leg. First, we we examine what he sees happening to his brothers clock. For the Outbound trip he sees it as running slow by a factor of ~0.577, and on the return he sees it run fast by a factor of ~1.732. Both legs take the same time, ~3.5, so the total time he sees pass on the stay at home twins clock is 3.5 x 0.577+3.5 x 1.732 = ~8 for the 7 he measures by his own clock.
What actually is happening to the stay at home clock according to our traveler during both legs is that it is running slow. But how can it run slow for both legs and yet show more time has past when they meet up. The answer is in what happens when our traveler transitions from outbound to inbound legs. Looking at the middle image (out bound leg, when he reaches the turnaround point, he is just getting the image of the stay at home clock reading 2, And at that moment the stay at home clock is just about reading three ,while his own reads ~3.5. Now we look at the third image, which just after he has made his velocity change. He is still seeing the same image of the stay at home clock, but at that moment it is actually reading ~5. His transition from going from traveling in one direction to the other causes the stay at home clock to jump forward by 2.
Now what physical change could his velocity change have on the operation of the Stay at home clock? None. But that is not a problem, because, as I've said before, Relativity is not about outside physical influences effecting how clocks tick, but about the nature of time and space and its measurement.
Think of space-time as a map that you use to plot events with respect to you in space and time. (for instance, I had lunch two hrs ago and 20 feet from where I am now).
But here is the strange thing about this map. Unlike a typical map, which mark out defined directions that everyone agrees upon (everyone agrees on the North-South direction for example.) Your map is marked out left-right, forward-backward. If you turn, your map turns with you. For example, if you start with an object 3 feet to your left and 4 feet to the front of you, and you turn, it is no longer 3 feet to your left and 4 feet to the front of you.
Now replace one of the spatial dimension with time. If an event took place 3 sec ago and 4 meters from me by my measurement, and I change my velocity, it will no longer have happened 3 sec ago and 4 meters from me by my measurement. By changing my velocity, I have changed how I measure the time and spatial separation between my here and now and the event.
Relativity forces us to rethink our notions of time and space.
Either you are willing and capable of this, or you will forever flounder in trying to understand Relativity.
-
Hi Janus,
your last space diagram does not show up properly. I cannot see it.
Is it possible you can fix it?
Thanks.
-
Here is a food for thought why the straight linear acceleration is not equivalent to the rotational acceleration.
Rotational includes gravity of a curved spacetime.
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Ftheelectromagneticnatureofthings.com%2Fimg%2Fi7%2Fep11.png&hash=04bd06cddc94b9c09c7518a64d9628f2)
Figure 1: The pendulum, a simple harmonic motion (a clock), in the straight line accelerated frame of reference.
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Ftheelectromagneticnatureofthings.com%2Fimg%2Fi7%2Fep12.png&hash=1d08421e0279f50f2455c39e00301f8e)
Figure 2: The pendulum, a simple harmonic motion (a clock), in the rotationally accelerated frame of reference.
The pendulum in the rotational frame of reference is being accelerated by additional Coriolis’ acceleration that comes from dR therefore we can see that even though point B is being accelerated by the acceleration of the same magnitude 'a' in both scenarios the magnitude of point A acceleration is different for the straight line acceleration and the rotational acceleration.
This is a very simple but a major reason why the Equivalence principle cannot hold.
The accelerated rocket has Figure 1 'pendulum-clock-harmonic motion' at the bottom and at the top of the rocket.
The gravity field has Figure 2 'pendulum-clock-harmonic motion' at the bottom and at the top with different R and dR between the bottom and the top.
-
Thanks Janus, I can see the diagram now.
I wonder is there a scenario with a different planet with more mass that the twin traveling away at 0.6c and coming back would return older than the twin that stayed on the planet?
-
...
Since there is no absolute frame by which to measure motion, The question is pretty meaningless.
Which ship is "moving" or "not moving" simply depends on the frame of reference it's being it being measured from.
...
If they have the same time when they meet and the clock postulate is true then both spaceships have to have the same speed in clock postulate frame of reference. The "momentarily comoving inertial frame" (MCIF) of both spaceships have to move at the same speed in the CP frame. There is only one type of CP frame where this can be true.
If we move the CP frame to the spaceship A then SA MCIF is not moving and SB MCIF is moving fast.
If the CP is true then SBC counter should be less then SAC when they meet.
If SAC=SBC then there are two options how this can happen.
Either the CP is false or the CP frame cannot be moved to SA.
Either we deny the experiments that support CP or we say there is only one proper CP frame.
-
No - I most certainly did not say that a moving clocks frequency should increase. What I said was that if one follows the current physics mathematical rules for an increase in kinetic energy for light, that a moving clocks frequency should increase as per those rules.
Remember,light speed is independent of its source.
If light does not acquire the speed of the source, then it does not acquire additional ke.
-
Granted, if you look at a light source as being velocity red shifted or velocity blue shifted instead of the light being shifted via the gravitational shift equation (a notion which in itself raises more questions than it answers), then your comment has logic...
BUT... is it actually physically possible to separate the notion of light having an association with the electron?
http://physics.bu.edu/~duffy/PY106/Potential.html
-
No - I most certainly did not say that a moving clocks frequency should increase. What I said was that if one follows the current physics mathematical rules for an increase in kinetic energy for light, that a moving clocks frequency should increase as per those rules.
Remember,light speed is independent of its source.
If light does not acquire the speed of the source, then it does not acquire additional ke.
Light can acquire energy. When it is being blue-shifted it is increasing frequency/energy.
Light can not travel faster then c but it can increase the frequency and that's how it gains energy.
Just check the second image of the Janus' post #136.
That's how the kinetic energy of the source is added to the light - increased frequency.
-
Here is a food for thought why the straight linear acceleration is not equivalent to the rotational acceleration.
Rotational includes gravity of a curved spacetime.
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Ftheelectromagneticnatureofthings.com%2Fimg%2Fi7%2Fep11.png&hash=04bd06cddc94b9c09c7518a64d9628f2)
Figure 1: The pendulum, a simple harmonic motion (a clock), in the straight line accelerated frame of reference.
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Ftheelectromagneticnatureofthings.com%2Fimg%2Fi7%2Fep12.png&hash=1d08421e0279f50f2455c39e00301f8e)
Figure 2: The pendulum, a simple harmonic motion (a clock), in the rotationally accelerated frame of reference.
The pendulum in the rotational frame of reference is being accelerated by additional Coriolis’ acceleration that comes from dR therefore we can see that even though point B is being accelerated by the acceleration of the same magnitude 'a' in both scenarios the magnitude of point A acceleration is different for the straight line acceleration and the rotational acceleration.
This is a very simple but a major reason why the Equivalence principle cannot hold.
The accelerated rocket has Figure 1 'pendulum-clock-harmonic motion' at the bottom and at the top of the rocket.
The gravity field has Figure 2 'pendulum-clock-harmonic motion' at the bottom and at the top with different R and dR between the bottom and the top.
Coriolis effect is a second order effect that diminishes as R increases relative to the pendulum length. Or put another way, If you continue to shrink our pendulums in both the linearly and rotational accelerated frames, they converge towards each other in how they behave and the pendulum in the rotating frame acts more and more like the one in under linear acceleration.
The equivalence principle applies locally, or over a "sufficiently small" region. Your objection to it is based on applying it in a way it is not meant to be applied. The fact that a linearly accelerated object does not behave exactly like a rotating accelerated object in all respects does not invalidate the equivalence principle. ( I mean really, if it was that easy to invalidate the Equivalence principle, it would not have made it past the first peer review let alone till now.)
-
Coriolis effect is a second order effect that diminishes as R increases relative to the pendulum length. Or put another way, If you continue to shrink our pendulums in both the linearly and rotational accelerated frames, they converge towards each other in how they behave and the pendulum in the rotating frame acts more and more like the one in under linear acceleration.
The equivalence principle applies locally, or over a "sufficiently small" region. Your objection to it is based on applying it in a way it is not meant to be applied. The fact that a linearly accelerated object does not behave exactly like a rotating accelerated object in all respects does not invalidate the equivalence principle. ( I mean really, if it was that easy to invalidate the Equivalence principle, it would not have made it past the first peer review let alone till now.)
Here is a chapter from the same Feynman book, this one precedes the rocket and the clocks chapter.
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Ftheelectromagneticnatureofthings.com%2Fimg%2Fi7%2Fep13.png&hash=ece246f698bd08d9f40692f63f4d3924)
I'll repeat the last paragraph.
To be strictly correct, that is true only for one point inside the ship. The gravitational field of the earth is not precisely uniform, so a freely falling ball has a slightly different acceleration at different places—the direction changes and the magnitude changes. But if we imagine a strictly uniform gravitational field, it is completely imitated in every respect by a system with a constant acceleration. That is the basis of the principle of equivalence.
The Equivalence principle stands on imaginary, unrealistic uniform gravitational field.
I am just a messenger here, please don't shoot. :)
How is this possible? Unbelievable!!!
So yes, it passed the peer review.
I guess that's why Einstein never got the Nobel prize for the Relativity.
-
Jaaanosik
Light can acquire energy. When it is being blue-shifted it is increasing frequency/energy.
Light can not travel faster then c but it can increase the frequency and that's how it gains energy.
Just check the second image of the Janus' post #136.
That's how the kinetic energy of the source is added to the light - increased frequency.
Post 136 concerns doppler shift. This is a changed perception of the base/original frequency by the receiver due to relative motion between emitter and receiver.
-
Coriolis effect is a second order effect that diminishes as R increases relative to the pendulum length. Or put another way, If you continue to shrink our pendulums in both the linearly and rotational accelerated frames, they converge towards each other in how they behave and the pendulum in the rotating frame acts more and more like the one in under linear acceleration.
The equivalence principle applies locally, or over a "sufficiently small" region. Your objection to it is based on applying it in a way it is not meant to be applied. The fact that a linearly accelerated object does not behave exactly like a rotating accelerated object in all respects does not invalidate the equivalence principle. ( I mean really, if it was that easy to invalidate the Equivalence principle, it would not have made it past the first peer review let alone till now.)
Here is a chapter from the same Feynman book, this one precedes the rocket and the clocks chapter.
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Ftheelectromagneticnatureofthings.com%2Fimg%2Fi7%2Fep13.png&hash=ece246f698bd08d9f40692f63f4d3924)
I'll repeat the last paragraph.
To be strictly correct, that is true only for one point inside the ship. The gravitational field of the earth is not precisely uniform, so a freely falling ball has a slightly different acceleration at different places—the direction changes and the magnitude changes. But if we imagine a strictly uniform gravitational field, it is completely imitated in every respect by a system with a constant acceleration. That is the basis of the principle of equivalence.
The Equivalence principle stands on imaginary, unrealistic uniform gravitational field.
I am just a messenger here, please don't shoot. :)
How is this possible? Unbelievable!!!
So yes, it passed the peer review.
I guess that's why Einstein never got the Nobel prize for the Relativity.
All theories rest on postulates that are accepted on faith until an exception is discovered.
At least the article cited includes the restriction regarding applicability. For nonuniform g-fields that converge, such as a spherical body, other effects (tidal forces) show up.
For practical applications there are no significant differences.
-
...
Since there is no absolute frame by which to measure motion, The question is pretty meaningless.
...
There is an island on the equator with a 122.5m hill, the open ocean to the east and to the west. The observer shoots projectiles horizontally to the east and to the west at the same time with a velocity v=465m/s, we will ignore the air resistance. What is the time of the falling till the projectiles hit the ocean surface?
The Earth equatorial radius: 6,378.1km
The Earth equatorial rotation velocity: 1,674.4km/h →1674400/3600=465m/s
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Ftheelectromagneticnatureofthings.com%2Fimg%2Fi7%2Fep14.png&hash=1cc2beeb96ffe90825fd2eb9c39b9c25)
The g = 9.814m/s2 for non-rotating Earth. The centrifugal acceleration for v=465m/s is acf = v2/r =4652/6378100=0.0339m/s2.
The rotating Earth gravitational acceleration is g =9.814−0.0339=9.781m/s2. The projectile that was shot to the west is not moving horizontally in the gravitational field therefore it’s going to be falling down with the gravitational acceleration approximately g =9.814m/s2. The projectile that was shot to the east is moving horizontally in the gravitational field with the velocity v=930m/s. The centrifugal acceleration for v = 930m/s is acf = v2/r = 9302/6378100 = 0.1356m/s2 therefore it’s going to be falling down with the gravitational acceleration approximately g=9.814−0.1356=9.678m/s2.
What are the times of falling? The westward projectile falls 5s so h=0.5gt2=0.5*9.814*25=122.675m The eastward projectile falls from the same height in t=sqrt(2h/g)=sqrt(2*122.675/9.678)=5.035s.
The conclusion is that the eastward projectile will be falling 0.035s longer than the westward projectile due to the difference in g.
The inertial reference frame at the top of the hill is an approximation only, it is not accurate for the above calculation. The reference frame that is ’linked’ to the gravitational field background is preferred one for more accurate calculation. Here is a grid of the gravitational field.
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Ftheelectromagneticnatureofthings.com%2Fimg%2Fi7%2Fep15.png&hash=37fb60c198c10019e30cdb5adc3faf7f)
The horizontal lines are the gravity equipotential lines and the vertical lines are the gravity field lines. There are two reference frames. The first reference frame, the gravity field frame, has [0,0] at the sea level, straight below the observer that is on the hill at the time T0=0s when the observer shoots the projectiles. This frame is linked to the non-rotating gravitational field. The x-axis values are labelled in blue. The second reference frame, the Earth frame, has [0,0] at the sea level, straight below the observer that is on the hill at the time T0=0s when the observer shoots the projectiles but this frame rotates with the Earth at v=465m/s. The x-axis values are labelled in red.
The position of the projectiles at T1 = 1s where fallen height for the blue projectile falling straight down in the gravity field reference frame is hb=0.5gt2=0.5*9.814*12=4.907m and for the red projectile flying eastward and falling down is hr=0.5gt2=0.5*9.678*12 =4.839m.
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Ftheelectromagneticnatureofthings.com%2Fimg%2Fi7%2Fep16.png&hash=74767c28566d1b6370302660fc443fae)
The position of the projectiles at T2 = 2s where fallen height for the blue projectile falling straight down in the gravity field reference frame is hb=0.5gt2=0.5*9.814*22=19.628m and for the red projectile flying eastward and falling down is hr=0.5gt2=0.5*9.678*22 =19.356m.
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Ftheelectromagneticnatureofthings.com%2Fimg%2Fi7%2Fep17.png&hash=e345da4b7f0f5211057bbb19e1358446)
The position of the projectiles at T3 = 3s where fallen height for the blue projectile falling straight down in the gravity field reference frame is hb=0.5gt2=0.5*9.814*32=44.163m and for the red projectile flying eastward and falling down is hr=0.5gt2=0.5*9.678*32 =43.551m.
The position of the projectiles at T4 = 4s where fallen height for the blue projectile falling straight down in the gravity field reference frame is hb=0.5gt2=0.5*9.814*42=78.512m and for the red projectile flying eastward and falling down is hr=0.5gt2=0.5*9.678*42 =77.424m.
The position of the projectiles at T5 = 5s where fallen height for the blue projectile falling straight down in the gravity field reference frame is hb=0.5gt2=0.5*9.814*52=122.675m and for the red projectile flying eastward and falling down is hr=0.5gt2=0.5*9.678*52 =120.975m.
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Ftheelectromagneticnatureofthings.com%2Fimg%2Fi7%2Fep18.png&hash=2541c3ea42d9b9853f3b2bc08998105b)
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Ftheelectromagneticnatureofthings.com%2Fimg%2Fi7%2Fep19.png&hash=aa9446b05ff7e1ae01c6d6ca00621fdc)
There is the International Space Station flying with the velocity v=7.67km/s at about h=400km above the Earth and g=8.682m/s2 at that height. Let us shoot a projectile in the direction of the ISS velocity vector with v=7.67km/s and in the opposite direction of the ISS velocity vector with v=7.67km/s. Now based on what we learned above we know that the projectile in the direction of the ISS velocity vector will fly away with 2v=15.34km/s velocity, acf=v2/r=153402/6778100=34.717m/s2, the proper centrifugal acceleration needs to be adjusted by subtracting the gravitational acceleration acf−adj=34.717−8.682=26.035m/s2. The projectile in the opposite direction of the ISS velocity vector will be falling straight down because its velocity is v=0m/s in the gravity field reference frame. The ISS 'inertial reference frame' comes short in predicting what happens to the projectiles but we are being taught by the General Relativity that there is no force acting on a free falling body. We are left with a conclusion that a free falling reference frame is an approximation only at some velocities.
We are left with a conclusion that a free falling reference frame is an approximation only at some velocities.
It appears the gravitational field reference frame is a preferred one. It provides better prediction of the projectile fall within the gravity field. The question might arise why not to use the reference frame at the center of the gravity field, the Earth center?
The issue is that the locality of the gravitational field determines the gravitational acceleration g. We ignored the influence of the Moon in our calculations, but if we want to be accurate we would need to account for the gravitational field coming from the Moon as well, and the Sun, ...
Now before saying anything about the tidal effect and the size/length of the experiment let us think about a hollow ring of 1m radius on the ISS. It is in a horizontal position, the z axis going straight through the ring points to the center of the Earth.
There are 2 (4, 6, ... ) evenly distributed through the ring friction less balls with accelerometers in the balls moving at 7.67km/s inside of the ring.
Are the accelerometers going to report different instantaneous accelerations in z direction when flying in ISS direction (2v) and the opposite one (0v)?