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Author Topic: Will a photon clock run at a different rate from an atomic clock under gravity?  (Read 45632 times)

Offline amrit

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Graham,

“time dilatation” means only that the velocity of clock slows down.
Not as a result time running slower, because there is no time as a 4-th dimension of space.
Physical time is “ticking” if clock in space that itself is timeless.
Velocity of photon clock is equal in all inertial systems because light has same speed in all inertial systems.
More than that:
By photon clock “time dilatation” is in contradiction with “length contraction”
   We have a photon clock in a fast airplane.  Mirrors are fixed in a way that photon moves along the direction of motion of the airplane. Distance between the mirrors is shortened by the length contraction. Because of the shorter distance between mirrors a path for the photon is shorter and so photon clock on the airplane “ticks” faster than same construction photon clock on the surface of the earth.
Experimental data show that atom clock in a fast airplane ticks slower than atom clock on the earth. Solution of this contradiction is in a preposition that photon clock in the airplane do not shorten. “Length contraction” is only a mathematical calculation that has no correspondence to the physical world. “Time dilatation” has also no correspondence in the physical world. What really happens by “time dilatation” is that velocity of material change velocity of clocks including slows down. Material change clocks run included run in space only and not in time.

Experimental data shows that velocity of atom clocks change. So relativity of velocity of material change starts above photon scale.

See my last article:
http://www.fqxi.org/data/forum-attachments/Relativistic_effects_of_felative__velocity__vixra.pdf
« Last Edit: 24/05/2010 11:32:47 by amrit »
 

Offline graham.d

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By photon clock “time dilatation” is in contradiction with “length contraction”
   We have a photon clock in a fast airplane.  Mirrors are fixed in a way that photon moves along the direction of motion of the airplane. Distance between the mirrors is shortened by the length contraction.
OK

Quote
Because of the shorter distance between mirrors a path for the photon is shorter and so photon clock on the airplane “ticks” faster than photon clock on the surface of the earth.


No. Firstly the photon has a short path because the mirror is approaching it but then it has a long path because the front mirror is receding from it. As the plane approaches lightspeed this long path dominates and the time to get there will tend to infinity. The length contracts, but not so much that the time delay for the photon to travel in both directions gets shorter. See the maths I took the time to work out for you. The time for the photon travel is not the same in each direction.
Quote
We know that atom clock in a fast airplane ticks slower than atom clock on the earth.
Yes, and there is no contradiction as I have shown.
 

Offline amrit

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By photon clock “time dilatation” is in contradiction with “length contraction”
   We have a photon clock in a fast airplane.  Mirrors are fixed in a way that photon moves along the direction of motion of the airplane. Distance between the mirrors is shortened by the length contraction.
OK

Quote
Because of the shorter distance between mirrors a path for the photon is shorter and so photon clock on the airplane “ticks” faster than photon clock on the surface of the earth.


No. Firstly the photon has a short path because the mirror is approaching it but then it has a long path because the front mirror is receding from it. As the plane approaches lightspeed this long path dominates and the time to get there will tend to infinity. The length contracts, but not so much that the time delay for the photon to travel in both directions gets shorter. See the maths I took the time to work out for you. The time for the photon travel is not the same in each direction.
Quote
We know that atom clock in a fast airplane ticks slower than atom clock on the earth.


Yes, and there is no contradiction as I have shown.



Graham, in SR length is getting shorter into direction of motion. Suppose our photon clock is 5 cm long. Because of the “length contraction” our clock will shrink a bit.
So is will “tick” faster.
But we know atom clocks run slower.
So there is a mistake here. Solution is: C is constant and there is no length contraction in material universe
« Last Edit: 24/05/2010 11:41:10 by amrit »
 

Offline graham.d

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Amrit you are missing the point. You have to follow the events very carefully. The light gets from the front to the back mirror quickly because the mirror is coming towards it (time t1 in the maths). But it then takes a long time to get to the front mirror which is receding from it (time t2). The sum of these two times (t1+t2) is longer, as seen from the stationary observer, than the proper time (observer on the plane). Even though the plane is Lorentz contracted the net result is still that the time is longer. You have to follow the maths carefully. If you can find an error then please point it out.
 

Offline Farsight

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If you note, Farsight, I positioned both clocks in a near zero gravitational field. The only difference is gravitational potential so I am not sure how the issue of orientation is relevant.
In SR the length contraction is in the direction of motion, and in GR via the principle of equivalence it's radial. The local strength of the gravitational field indicates the rate of change of gravitational potential at this location.

I am not sure whether is is possible to determine whether there is length change or lightspeed lowering. A proper GR treatment would simply give the result that the spacetime interval was agreed by all observers. As I said previously, the remote measurement of time intervals for light travelling has to be thought out carefully. It is necessary to define the events of emission and detection with care.
It's tricky to say what the proper GR treatment is. When you read the original it is different to what's in modern textbooks, and that brings us back to the conflict between interpretations again.  

You quote Baez who says "[...] a more modern interpretation is that the speed of light is constant in general relativity", but contradict this statement, so I don't follow your reasoning.
Einstein's interpretation was that the speed of light varies, but the modern interpretation is that it's constant. I side firmly with Einstein because IMHO this is backed up by evidence like the Shapiro delay.

You seem very definite but there seems varying opinions.
I am. Einstein started with the constant speed of light as a postulate in 1905, but in 1911 he wrote On the Influence of Gravitation on the Propagation of Light, where he gives the expression c = c0(1 + Φ/c²). Here c is varying with gravitational potential. Then in 1912 he said "On the other hand I am of the view that the principle of the constancy of the velocity of light can be maintained only insofar as one restricts oneself to spatio-temporal regions of constant gravitational potential". He repeated this in 1913 when he said this: "I arrived at the result that the velocity of light is not to be regarded as independent of the gravitational potential. Thus the principle of the constancy of the velocity of light is incompatible with the equivalence hypothesis". There it is again in 1915 when he says " the writer of these lines is of the opinion that the theory of relativity is still in need of generalization, in the sense that the principle of the constancy of the velocity of light is to be abandoned."  That’s on page 259 of Doc 21, sorry, I’m not sure what the original paper is called. He says it again in late 1915, on page 150 of Doc 30, within The Foundation of the General Theory of Relativity. Einstein says "the principle of the constancy of the velocity of light in vacuo must be modified.". He spells it out in section 22 of the 1916 book Relativity: The Special and General Theory where he says this:

"In the second place our result shows that, according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity and to which we have already frequently referred, cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with position. Now we might think that as a consequence of this, the special theory of relativity and with it the whole theory of relativity would be laid in the dust..."

People see the word velocity in the translations without seeing the context and without noticing that he’s repeatedly referring to “the principle” and "one of the two fundamental assumptions". That's the SR postulate, which is the constant speed of light. And it's important to note that what he actually said was in German. it was die Ausbreitungsgeschwindigkeit des Lichtes mit dem Orte variiert. It translates into the speed of light varies with the locality. The word “velocity” in the 1920 Methuen translation was the common usage, as in “high velocity bullet”, not the vector quantity that combines speed and direction. He was saying the speed varies with position, and it causes the curvilinear motion. It causes the light to follow a curved path, like a car veers when the near-side wheels encounter mud at the side of the road.

If you read my lengthy description of a local and distant observer measuring the photon clock, I would be interested to know if you see anything wrong in the reasoning.
I read your post. What's wrong with it is that the Lorentz contraction in SR corresponds to the radial length contraction in GR. If you say your distant observer up in space isn't moving with respect to your observer at the centre of the earth, and if both observers hold their clocks flat, there is no length change. You can then remove redshift with a single observer who leaves a light-clock in space and takes another synchronised light-clock down to the centre of the earth for a while. When he goes back up into space the clocks are no longer synchronised. So the speed must be different.    

A light pulse going around lots of coils of fibre optic might be a practical photon clock too. With enough coils the time delay can be significant and measurable with low errors.
Sounds good to me graham.
 

Offline amrit

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Amrit you are missing the point. You have to follow the events very carefully. The light gets from the front to the back mirror quickly because the mirror is coming towards it (time t1 in the maths). But it then takes a long time to get to the front mirror which is receding from it (time t2). The sum of these two times (t1+t2) is longer, as seen from the stationary observer, than the proper time (observer on the plane). Even though the plane is Lorentz contracted the net result is still that the time is longer. You have to follow the maths carefully. If you can find an error then please point it out.

Graham

GPR corrections of velocity are equal for all observers.
There is no such a thing as “proper time”.
There is only a change of velocity of clock on the orbit that is valid for the observer on the orbit and for the observer on the surface of the earth.

In classical example of SR clock run slower on the fast train for the observer on the station and for the observer in the train. This is what shows experimental data.

In Relativity is relative velocity of material change and velocity of clocks and is valid for all observers.  Observer is not even necessary. Clock runs slower on the orbit without watching it.

Relativity is a very nature of the universe. Just it starts above photon size. Constancy of c point that out clearly.

Yours amrit
PS read my article on
http://www.vetrnica.net/index.php?option=com_content&view=article&id=21&Itemid=23
 

Offline amrit

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If you note, Farsight, I positioned both clocks in a near zero gravitational field. The only difference is gravitational potential so I am not sure how the issue of orientation is relevant.
In SR the length contraction is in the direction of motion, and in GR via the principle of equivalence it's radial. The local strength of the gravitational field indicates the rate of change of gravitational potential at this location.

I am not sure whether is is possible to determine whether there is length change or lightspeed lowering. A proper GR treatment would simply give the result that the spacetime interval was agreed by all observers. As I said previously, the remote measurement of time intervals for light travelling has to be thought out carefully. It is necessary to define the events of emission and detection with care.
It's tricky to say what the proper GR treatment is. When you read the original it is different to what's in modern textbooks, and that brings us back to the conflict between interpretations again.  

You quote Baez who says "[...] a more modern interpretation is that the speed of light is constant in general relativity", but contradict this statement, so I don't follow your reasoning.
Einstein's interpretation was that the speed of light varies, but the modern interpretation is that it's constant. I side firmly with Einstein because IMHO this is backed up by evidence like the Shapiro delay.

You seem very definite but there seems varying opinions.
I am. Einstein started with the constant speed of light as a postulate in 1905, but in 1911 he wrote On the Influence of Gravitation on the Propagation of Light, where he gives the expression c = c0(1 + Φ/c²). Here c is varying with gravitational potential. Then in 1912 he said "On the other hand I am of the view that the principle of the constancy of the velocity of light can be maintained only insofar as one restricts oneself to spatio-temporal regions of constant gravitational potential". He repeated this in 1913 when he said this: "I arrived at the result that the velocity of light is not to be regarded as independent of the gravitational potential. Thus the principle of the constancy of the velocity of light is incompatible with the equivalence hypothesis". There it is again in 1915 when he says " the writer of these lines is of the opinion that the theory of relativity is still in need of generalization, in the sense that the principle of the constancy of the velocity of light is to be abandoned."  That’s on page 259 of Doc 21, sorry, I’m not sure what the original paper is called. He says it again in late 1915, on page 150 of Doc 30, within The Foundation of the General Theory of Relativity. Einstein says "the principle of the constancy of the velocity of light in vacuo must be modified.". He spells it out in section 22 of the 1916 book Relativity: The Special and General Theory where he says this:

"In the second place our result shows that, according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity and to which we have already frequently referred, cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with position. Now we might think that as a consequence of this, the special theory of relativity and with it the whole theory of relativity would be laid in the dust..."

People see the word velocity in the translations without seeing the context and without noticing that he’s repeatedly referring to “the principle” and "one of the two fundamental assumptions". That's the SR postulate, which is the constant speed of light. And it's important to note that what he actually said was in German. it was die Ausbreitungsgeschwindigkeit des Lichtes mit dem Orte variiert. It translates into the speed of light varies with the locality. The word “velocity” in the 1920 Methuen translation was the common usage, as in “high velocity bullet”, not the vector quantity that combines speed and direction. He was saying the speed varies with position, and it causes the curvilinear motion. It causes the light to follow a curved path, like a car veers when the near-side wheels encounter mud at the side of the road.

If you read my lengthy description of a local and distant observer measuring the photon clock, I would be interested to know if you see anything wrong in the reasoning.
I read your post. What's wrong with it is that the Lorentz contraction in SR corresponds to the radial length contraction in GR. If you say your distant observer up in space isn't moving with respect to your observer at the centre of the earth, and if both observers hold their clocks flat, there is no length change. You can then remove redshift with a single observer who leaves a light-clock in space and takes another synchronised light-clock down to the centre of the earth for a while. When he goes back up into space the clocks are no longer synchronised. So the speed must be different.    

A light pulse going around lots of coils of fibre optic might be a practical photon clock too. With enough coils the time delay can be significant and measurable with low errors.
Sounds good to me graham.

Farsight gravitational red shift shows light velocity c is constant. Only frequency changes. If c is not constant connection betwen SR and GR is broken. This would be a bit to much....I do not think in Relativity there is a mistake....Relativity is perfect. The case is that there is no time there. With clocks we measure numerical order only...
http://www.vetrnica.net/index.php?option=com_content&view=article&id=21&Itemid=23
yours amrit
« Last Edit: 24/05/2010 12:38:16 by amrit »
 

Offline Farsight

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An oscillator produces microwave energy that causes the caesium to fluoresce. The detector measures the amount of fluorescence. Maximum fluorescence (photon emissions I suppose) is achieved when the microwave energy is tuned to 9.1xxx GHz. The clock makes very small adjustments to the oscillator to maintain maximum photon emission.
Noted Geezer, but remember that this is defining the second. Hertz is cycles per second, so we're finding the maximum then defining the frequency to be 9.192631770 GHz.

The clock is really comparing the natural oscillation of the caesium atom with the frequency of a microwave resonator and adjusting the resonator to match the frequency of the caesium. So, it's not really measuring a property of light at all.
The oscillation is a hyperfine transition, and electron spin-flip. The event is electromagnetic, as is the emitted light. If the gravitational potential is lower, all electromagnetic phenomena occur at a slower rate. We call it time dilation, but that rather misses the obvious fact that electromagnetic spin flips are happening slower and the emitted light is moving slower too.
 

Offline Farsight

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Farsight gravitational red shift shows light velocity c is constant. Only frequency changes. If c is not constant connection betwen SR and GR is broken.
This isn't true I'm afraid, amrit. The frequency of the light isn't relevant. Start with two synchronised light clocks, leave one up in space, take the other down to the planet for a while taking care to avoid radial length contraction, then take it back up to space. The two clocks are no longer synchronised. Yes, the local speed of light is always measured to be 299,792,458 metres per second, but those two different clock readings tell you that 299,792,458 metres per second up in space is not the same as 299,792,458 metres per second down on the planet. People say the difference is because of "time dilation", but you and I know that clocks clock up motion rather than "the flow of time". Hence we know that a light clock clocks up the motion of light. Those two different readings are crystal-clear evidence that down on the planet, the light goes slower.   
 

Offline amrit

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An oscillator produces microwave energy that causes the caesium to fluoresce. The detector measures the amount of fluorescence. Maximum fluorescence (photon emissions I suppose) is achieved when the microwave energy is tuned to 9.1xxx GHz. The clock makes very small adjustments to the oscillator to maintain maximum photon emission.
Noted Geezer, but remember that this is defining the second. Hertz is cycles per second, so we're finding the maximum then defining the frequency to be 9.192631770 GHz.

The clock is really comparing the natural oscillation of the caesium atom with the frequency of a microwave resonator and adjusting the resonator to match the frequency of the caesium. So, it's not really measuring a property of light at all.
The oscillation is a hyperfine transition, and electron spin-flip. The event is electromagnetic, as is the emitted light. If the gravitational potential is lower, all electromagnetic phenomena occur at a slower rate. We call it time dilation, but that rather misses the obvious fact that electromagnetic spin flips are happening slower and the emitted light is moving slower too.

Farsight,

I’m not expert for clocks. As far as I know atomic clock works on atom frequency. Photon clock works on photon motion in space. Difference is quite clear. I’m emotionally tuned with c as a constant. It has its own elegance this idea. As far no experiment will prove opposite I stay with it.

 

Offline amrit

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Farsight gravitational red shift shows light velocity c is constant. Only frequency changes. If c is not constant connection betwen SR and GR is broken.
This isn't true I'm afraid, amrit. The frequency of the light isn't relevant. Start with two synchronised light clocks, leave one up in space, take the other down to the planet for a while taking care to avoid radial length contraction, then take it back up to space. The two clocks are no longer synchronised. Yes, the local speed of light is always measured to be 299,792,458 metres per second, but those two different clock readings tell you that 299,792,458 metres per second up in space is not the same as 299,792,458 metres per second down on the planet. People say the difference is because of "time dilation", but you and I know that clocks clock up motion rather than "the flow of time". Hence we know that a light clock clocks up the motion of light. Those two different readings are crystal-clear evidence that down on the planet, the light goes slower.  

Farsight I do not buy that.
yours amrit
 

Offline graham.d

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Amrit, "proper time" has a specific definition to be just that of an observer comoving with the moving frame. Your link does not work properly by the way.

I appreciate English is not your first language, but however hard I try, I cannot understand the sense of what you are saying. Perhaps you could show me where my maths is at fault?
 

Offline Farsight

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We'll have to agree to differ, amrit. Sorry I couldn't help.
 

Offline graham.d

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Farsight, I understand Einstein's view on this but note he was uncomfortable with this view. And I take your point about the clocks being "flat" which I take to mean parallel to a circumference as opposed to in-line and parallel to a radius. I don't think you can conclude that this removes the difference that may occur between remote length measurements although I admit that the maths is sufficiently hard that I could not show it would produce the same quantitative result. For example you could imagine a distant observer receiving signals from the mirrors at each end of the apparatus which were set up to send beams outward exactly parallel, but because they are in a divergent field they will follow geodesics that would have them diverge such that when they reached the distant observer they would show a bigger gap between the mirrors. Now it is very hard to say that this would yield the same value as the simpler calculation for the mirrors in line, but is, nonetheless, possible. The maths to calculate this is a bit hard.

I will give this a little more thought. A tenet of GR is that the all observers should agree on the spacetime interval. I am not sure that it is necessarily possible to resolve the meaning in term of just space and just time in this case. As the modern view is, as you say, that lightspeed is constant, how would these physicist view this scenario?
 

Offline imatfaal

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A light pulse going around lots of coils of fibre optic might be a practical photon clock too. With enough coils the time delay can be significant and measurable with low errors.

3 coils at 90 degrees to each other would nicely (after serious number crunching) allow dilation from varying gravitational potential and dilation from relative velocities to be separated - I think...
 

Offline JP

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Actually, I'm not sure that there's any contradiction between the idea that the speed of light might not seem constant over large distances and the speed of light being constant locally in a vacuum.  From what I understand of it, you can think of it like traveling on the earth.  Say it takes me 4 hours to travel from Paris to Los Angeles.  I could calculate my average speed by taking the distance between them in 3D space (which is the length straight line through the globe divided by 4 hours) or I could measure my speed at every instant as I fly around the globe and average that.  The path through the globe will be far shorter than the actual speed I was traveling.  I think it's a similar case with GR and the speed of light.  If you look at lengthy paths and just try to calculate the speed of light based on what you'd expect if space-time were flat and the light moves at c, you find that it takes longer.  However, if you look at the light at every instant, it's moving at the speed c--it just takes a curved path, so the total time is longer.

Or put another way, if you look locally enough so that you're calculating instantaneous speed, space-time is flat and SR holds.  It's when you look over large enough regions of curved space-times that you get these deviations.  (I guess even if you're comparing two flat regions--which is what this discussion is about--measurements can differ because space-time can be stretched, but not curved.  Using the rulers and clocks of one region to measure the other will also cause the speed of light to appear to be slowed.)  In fact, I think you can go further and say that if the speed of light wasn't constant locally, the geometrical interpretation of general relativity would fail.  

Is there an equally valid model that allows the speed of light to vary locally and produces identical results (at least within the regimes we've tested)?  I don't know.  
 

Offline graham.d

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Paris to LA in 4 hours - I didn't think the Ramjet was flying yet!

It is interesting to think of two regions that are both essentially flat regions of Minkowski space where they have different degrees of Stretched Space-Time. There would seem to be no way of determining the degree of "Stretchedness" from inside such a region because all the physical laws would work fine in both regions. So if one region is open to investigation from the other (as in the case postulated previously) it seems odd that the observed behaviour would depend on the spacetime between the two regions. I think this is what you are saying JP. I could easily imagine that you could measure the temporal and spatial difference but it is hard to believe that these would be different depending on the route your information traveled to get to you.

I think that Farsight was alluding to the idea that the velocity of light being a tensor field (rather than a scalar field) in having different radial and tangential values in a schwartzchild metric. It still seems odd that the intervening space would affect what should be scalar measurements in flat space though. Any ideas? I may be missing some key points here.
 

Offline Farsight

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Farsight, I understand Einstein's view on this but note he was uncomfortable with this view.
It's an interesting one Graham. One day when the dust has settled somebody will write an authorative narrative on the long and tortuous trail, and it will be fascinating reading.

And I take your point about the clocks being "flat" which I take to mean parallel to a circumference as opposed to in-line and parallel to a radius.
Thanks, sorry if I didn't make it clear.   

I don't think you can conclude that this removes the difference that may occur between remote length measurements although I admit that the maths is sufficiently hard that I could not show it would produce the same quantitative result.
I think you can actually, very simply. If you go along with GR radial length contraction, and Einstein, and the Occam's razor direct evidence that says the light is moving slower rather than "time runs slower", you can see it. The metre is defined as "the distance travelled by light in a complete vacuum in 1⁄299,792,458th of a second". Hence the bigger second and the slower light cancel each other out. The metre is unchanged.   

For example you could imagine a distant observer receiving signals from the mirrors at each end of the apparatus which were set up to send beams outward exactly parallel, but because they are in a divergent field they will follow geodesics that would have them diverge such that when they reached the distant observer they would show a bigger gap between the mirrors. Now it is very hard to say that this would yield the same value as the simpler calculation for the mirrors in line, but is, nonetheless, possible. The maths to calculate this is a bit hard.
Sorry, I'm not keen on this because it seems to go against the grain of general relativity regardless of which interpretation one prefers. 

I will give this a little more thought. A tenet of GR is that the all observers should agree on the spacetime interval. I am not sure that it is necessarily possible to resolve the meaning in term of just space and just time in this case. As the modern view is, as you say, that lightspeed is constant, how would these physicist view this scenario?
I'm not sure graham. But I'd say that to fix the speed of light as an absolute constant, one has to elevate time to something above and beyond the experimental and observational evidence, and say "time runs slower". The trouble is, when you look at a clock, you don't see time running at all. All you see is cogs moving, or a crystal oscillating, or a caesium atom oscillating, or light moving. It always comes down to motion one way or another. Clocks clock up motion, that's all they ever do, that's why in The Foundation of the General Theory of relativity Einstein gave us the equations of motion. And when the clock runs slower, it isn't really time running slower, it's the motion going slower. Have a google on "Farsight" and "Time Explained" for my take on this.
 

Offline Farsight

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..I think that Farsight was alluding to the idea that the velocity of light being a tensor field (rather than a scalar field) in having different radial and tangential values in a schwartzchild metric.
I wasn't, I was just trying to keep things simple and focus on what we actually observe, which is two different readings from two identical parallel-mirror light-clocks at different locations where the gμv gravitational potential is different. 

It still seems odd that the intervening space would affect what should be scalar measurements in flat space though. Any ideas? I may be missing some key points here.
The intervening space isn't relevant. You could run the clocks for years and see the discrepancy grow ever larger. Redshift and signal time becomes increasingly inconsequential. Like you say, the spacetime is flat at both locations. There is no discernible curvature out in space or at the centre of the earth, because there is no detectable gμv gradient. The different measurements are because the space itself is different at those two locations.
 

Offline Geezer

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An oscillator produces microwave energy that causes the caesium to fluoresce. The detector measures the amount of fluorescence. Maximum fluorescence (photon emissions I suppose) is achieved when the microwave energy is tuned to 9.1xxx GHz. The clock makes very small adjustments to the oscillator to maintain maximum photon emission.
Noted Geezer, but remember that this is defining the second. Hertz is cycles per second, so we're finding the maximum then defining the frequency to be 9.192631770 GHz.

The clock is really comparing the natural oscillation of the caesium atom with the frequency of a microwave resonator and adjusting the resonator to match the frequency of the caesium. So, it's not really measuring a property of light at all.
The oscillation is a hyperfine transition, and electron spin-flip. The event is electromagnetic, as is the emitted light. If the gravitational potential is lower, all electromagnetic phenomena occur at a slower rate. We call it time dilation, but that rather misses the obvious fact that electromagnetic spin flips are happening slower and the emitted light is moving slower too.

Er, well the second is defined as the interval for a certain number of the atomic events. The number was chosen to line up with more traditional definitions for the second. As you point out, the fundamental "tick" is an electromagnetic event with the atom.

The light output could be delayed in a very variable fashion, but it would have no effect on the frequency of the microwave resonator. The light output is only sampled periodically to make very infrequent and very minute adjustments to the frequency of the microwave resonator. I believe the detector only responds to the number of photons that reach it. I'm not sure how they know to adjust up or down because I would assume that the light output will diminish if the resonator is slow or fast relative to the caesium events.

Being pedantic, you can't really say that the events are happening at a "slower rate", because that seems to suggest that time itself is invariant.
 

Offline graham.d

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Both spaces are flat Minkowski space and I think we are assuming that the physical laws are the same, as measured locally, at each location and that it would be expected that the gravitational potential is purely relative and has no meaning in absolute terms. Are these correct assumptions to work with? If, then, the only difference is that space is "stretched" more in one region than the other then this "scaling" must apply to (x,y,x,-ct) equally mustn't it? If not what coordinate transformation would apply? In SR the basis for the Lorentz transformation is the constancy of c to all observers. Is the only effect of gravitational potential (Φ) that c is a function of Φ and that this would be the basis of any coordinate transformation?

This seems reasonable but is it all consistent with observation or gedanken experiments?
 

Offline JP

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Paris to LA in 4 hours - I didn't think the Ramjet was flying yet!

Heh.  I'm riding in my photon jet.  It would be faster, but it slowed down a bit because it's so close to the earth.
 ;)
 

Offline Geezer

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Heh.  I'm riding in my photon jet.  It would be faster, but it slowed down a bit because it's so close to the earth.
 ;)


Yes, but I'm sure you'll arrive in no time at all.
 

Offline amrit

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Amrit, "proper time" has a specific definition to be just that of an observer comoving with the moving frame. Your link does not work properly by the way.

I appreciate English is not your first language, but however hard I try, I cannot understand the sense of what you are saying. Perhaps you could show me where my maths is at fault?

Graham with your math all is fine. Just be aware clocks tick in space only and not in time. Time dilatation means that clocks run slower in a timeless space. You think in math terms, think in physical terms and you will discover universe is timeless. In the universe there is only motion, time belongs to the mind. Time is a mind frame through which we experience motion, read ma article below:
http://www.vetrnica.net/index.php?option=com_content&view=article&id=21&Itemid=23
yours amrit
 

Offline Geezer

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In the universe there is only motion, time belongs to the mind. Time is a mind frame through which we experience motion, read ma article below:

Amrit,

I have tried to persuade the molecules that make up my body that time is only a state of mind, but they won't listen.

Isn't it high time we move this topic to New Theories?

 

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