Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: mxplxxx on 07/02/2017 23:41:29

I cannot understand how relativity/time dilation works in a very simple instance. Can someone please help me?
I have three particles A, B and C. B is moving 80% of the speed of light faster than A. C is moving 80% of the speed of light faster than B. Therefore C is moving 160% of the speed of light faster than A. Right? But according to relativity nothing moves faster than the speed of light and time dilation is what allows this to happen. How does time dilation work in the example I have just given?

I trained as a chemist (now I wish I had taken up physics) so I may not have completely understood you.
Surely B can't move faster than A and C can't move faster than B. So the situation can't occur.

I cannot understand how relativity/time dilation works in a very simple instance. Can someone please help me?
I have three particles A, B and C. B is moving 80% of the speed of light faster than A. C is moving 80% of the speed of light faster than B. Therefore C is moving 160% of the speed of light faster than A. Right? But according to relativity nothing moves faster than the speed of light and time dilation is what allows this to happen. How does time dilation work in the example I have just given?
You need to look up the relativistic addition of velocities rule, you will find some very good explanations on the web.
Come back if you have questions about what you discover.
Remember that in viewing motion in one frame from another, we are not viewing the velocity experienced by the other object, but the velocity we measure from our frame.

I cannot understand how relativity/time dilation works in a very simple instance. Can someone please help me?
I have three particles A, B and C. B is moving 80% of the speed of light faster than A. C is moving 80% of the speed of light faster than B. Therefore C is moving 160% of the speed of light faster than A. Right? But according to relativity nothing moves faster than the speed of light and time dilation is what allows this to happen. How does time dilation work in the example I have just given?
You need to look up the relativistic addition of velocities rule, you will find some very good explanations on the web.
Come back if you have questions about what you discover.
Remember that in viewing motion in one frame from another, we are not viewing the velocity experienced by the other object, but the velocity we measure from our frame.
Thx, but I am after an answer to my question on this site. You add value to the site by answering questions rather than pointing to other sites.

heh :)
Tortoise and the hare, in relativistic terms is it? A trick question? What you're asking is why matter can't go faster than light in a vacuum.
By formulating it the way you do you made me think of it as if speeds might be unlimited inside our universe, although relativity tells us the opposite. It's always a relation to energy expended, and getting to the speed of light in a vacuum would then demand you to expend a infinite 'energy'. It's tricky in more ways than one actually, if you're discussing it as a uniform motion. There is no defined way to measure a speed, other than in a comparison to something else. So what is the speed of A? You could assume them to measure their speed relative a suns 'blue shift' but to do so you also need to know how that sun is 'moving' relative you, from you or towards you. What you could do is to define all three 'test particles' relative some same sun though, and then decide that we don't care about that suns 'motion', we call it being 'still' and use it for the measurement. That's a start. then you need to define A speed relative that sun, and from that then define the speeds of B and C. Assuming A to be at rest (still) relative the sun, then 80% of that speed will be nothing for B, as well as for C :) Unless you know a way to set a 'golden standard' of motion defining the universe that is. What will happen if you accelerate a 'test particle/rocket' is that no matter how much 'energy' you put into this acceleration it always will see the light propagating away from it, as when you looking into a mirror inside the rocket seeing your reflection.

By formulating it the way you do you made me think of it as if speeds might be unlimited inside our universe, although relativity tells us the opposite.
Yep, what I want to know is how time dilation is applied to my example. And it seems to me that all particles in the universe can be tabled in terms of speed relative to each other such that there is one particle that is slower than all the rest. The slowest particle is effectively at rest since it has no other particle to compare speeds against.
It seems to me that a single particle can be considered to be at rest and all the other particles in the universe move relative to it. This seems to be similar in nature to gravity where a single particle attracts all other particles in the universe. Is there a relationship?

But yes, it's when thinking in terms of such one start to notice the importance of 'locality' for the universe. Let us assume that all three 'rockets' are at different speeds, then start to 'coast' (uniform motion). You set up a two way mirror experiment inside each one of them and all of them find 'c' to be the same relative their clock and ruler. You can now point to that sun to prove that you at least have different speeds relative it, or just use the three of you to prove that different speeds exist, but you will also see that it doesn't matter for the speed of light. It's a local constant, but so are everything else we define. The experiments done on/in those three rockets should give you a same result, and from that you then can define 'repeatable experiments'.

No, the slowest particle is just as arbitrarily chosen as any other. There is nothing special about it.

Now, using this we come to what physics is. It's about repeatable experiments, that's what builds the foundations for anything else. And even if the 'uniform motion' you have is relative, the experiments you do will not be so. that's also why the 'equivalence principle' makes such a eminent sense to me. It's a acceleration that becomes indistinguishable from a 'gravity', 'locally measured' which then should be read as in a 'black box scenario'. Everything we define is coming from a local measurement, using your clock and ruler, and what join it is a logic.

Let us assume that all three 'rockets' are at different speeds
Your explanation does not tell me how my example is invalid. If you don't know, say so:), otherwise this is an exercise in futility.

I cannot understand how relativity/time dilation works in a very simple instance. Can someone please help me?
I have three particles A, B and C. B is moving 80% of the speed of light faster than A. C is moving 80% of the speed of light faster than B. Therefore C is moving 160% of the speed of light faster than A. Right? But according to relativity nothing moves faster than the speed of light and time dilation is what allows this to happen. How does time dilation work in the example I have just given?
We measure velocity using light/energy that is emitted/reflected by the object. If I see you running, what reaches my brain or my camera, is the light that reflects off you as you run. I don't measure your speed with a matter trail, like scent. Instead we use light, which is energy. Light is limited to the speed of light. Therefore you can never see anything move faster than the speed of light, since the light you use to see, cannot move faster than the speed of light.
A loose analogy is a jet moving faster than the speed of sound. It will give off a sonic boom that lags behind. The sonic boom is limited to the speed of sound, and not the speed of the plane. The boom falls behind the jet, and appears after the jet passes. So whether the jet moves at Mach 1 or Mach 10, the boom always moves at the same speed of sound.
Special relativity successfully tells us how the light, which we use for seeing motion, changes between references. The speed of light does not change. What we will see are red and blue shifts, due to relativistic changes in spacetime. The sonic booms gets louder or quieter but does not change speed.
The problem with special relativity is although it tells us things about relative motion, one cannot confirm an accurate energy balance using relative motion. Einstein made a provision for this, which he called relativistic mass. This is how you close the energy balance. But relativistic mass is often ignored, since we can't measure relativistic mass very easily. It has become lumped into spacetime, which was a mistake. The result is special relativity, without relativistic mass to confirm our energy balance, allows one to create energy illusions, which can violate energy conservation. This is what creates confusion.
Let me give example. Say we had two rockets, sidebyside, one with mass M and the other with mass 2M. They start stationary, with zero relative velocity. We add energy E, to just one of the rockets, until the two rockets have a relative velocity V, between them.
If neither rocket knew who got the energy, for motion, the assumption of relative motion could result in each reference creating a different energy balance. If rocket M assumes it is the rocket in motion, it would say the total energy added was 1/2MV2, which is the kinetic energy inferred from the relative velocity. If the 2M rocket thinks it is the one with the motion, it would calculate the kinetic energy as MV2 since it has double the mass. Which of the two is right? Relative reference does not always work if we do an energy balance. The only time it works is if we have two references with the same mass, or if mass is not part of the example.
In terms of tangible relativistic affects that persist, only the rocket with the real energy will show a persistent form of time dilation, this would linger, if the two rockets were to meet at zero velocity. In the twin paradox, only the twin with the added kinetic energy; rocket fuel, ages less, even if he sees relative motion with his other twin. The twin might see what appears to be parallel time dilation in his brother, but this is illusion based on a wrong energy balance. It will not persist when they meet.
Relative reference can create sort of a mirage in the desert. A mirage can look proper and can even be photographed. But it is still an illusion, since it lacks sufficient tangible energy, to be what appears to be. You can't drink the water from a mirage. However, as long as it is in the distance, one still assume the water is real.

Let us assume that all three 'rockets' are at different speeds
Your explanation does not tell me how my example is invalid. If you don't know, say so:), otherwise this is an exercise in futility.
Ok, so you pick your own numbers for a speed and plug them in into this calculator http://convertalot.com/relativistic_star_ship_calculator.html (http://convertalot.com/relativistic_star_ship_calculator.html) to see how they come out. If you complain about that too I don't know how you want it explained? Without relativity perhaps?
=
Relativity is 'c' in SR, gravity's equivalence principle in GR. I described 'c' for you the way it works. It's frame dependent so any of your particles will still see 'c' propagate away from it (the mirror), if it is the mathematics you want to question? Read this one first http://www.einsteinonline.info/elementary/specialRT/speed_of_light

Ok, so you pick your own numbers for a speed and plug them in into this calculator http://convertalot.com/relativistic_star_ship_calculator.html to see how they come out. If you complain about that too I don't know how you want it explained? Without relativity perhaps?
Thx, but sorry to say this is not an explanation of why my example is incorrect. I don't want a general description of how relativity works or a calculator, I just want an explanation of how relativity works to ensure that no particle in my example exceeds the speed of light.

Mxpllxxx, as a nonmathematician I tried many ways to get my head round this question, without going into the maths. My verdict? It probably can’t be done.
My path to, some sort of, understanding took me from the lightbox, via the time dilation equation, to the equation for relativistic addition of speeds. It does make sense, and is very satisfying if you bring yourself to the answer. I don’t know what your maths background is, but if it’s anything like mine, it involves work.
I’m in hospital at the moment, so don’t have access to the notes I wrote when I was struggling with this, but once home, I’d be happy to share anything that might help.

mxplxxx
I cannot understand how relativity/time dilation works in a very simple instance. Can someone please help me?
I have three particles A, B and C. B is moving 80% of the speed of light faster than A. C is moving 80% of the speed of light faster than B. Therefore C is moving 160% of the speed of light faster than A. Right? But according to relativity nothing moves faster than the speed of light and time dilation is what allows this to happen. How does time dilation work in the example I have just given?
Since energy is transferred at light speed, the faster an object moves, the more time required for the transfer. This prevents an object from reaching light speed.
Using the radar method A sends a signal to an object B that reflects back to A. A knows the local time of emission t1 and detection t3, but not the time of reflection t2. Since there is relative motion for A and B, one of the two (outbound and inbound) paths will be longer than the other but there is no known method of determining v in the expressions (cv) and (c+v). As part of the clock synch convention Einstein defined the paths as equal to maintain the consistent value of c. This requires assigning the reflection event halfway between emission and detection. This is not a problem if the measurement is made in a pseudo rest frame, i.e. one defined as not moving, A in this example. If the measurement is made in a moving frame, as in the case of B measuring the speed of C, the speed of B affects the result. For the example let u, v, w denote the speeds of A, B, C respectively as fractions of c with c = 1. The expression used to calculate the speed of B by A is s=(vu)/(1uv) = v (since u = 0).
In general, s is always > (vu) and <c, so the speed of C was not made by A but by B. The question for A then becomes, what value of w did B use in s=(wv)/(1vw) that results in .8c. Solving for w gives
w=(s+.8)(1+.8s) = 1.60/1.64 = .976. The composition of velocities corrects for measurements made in moving frames. Note that speed =Δx/Δ t, and x=vt, so both intervals contain t which cancels in the expression for s. I.e. measurement of speed is independent of time dilation.

Why do smileys remain when they are edited out????????

Maybe you are thinking of in terms of wanting to know why 'c' is 'c'? That's an unanswered question so far, I don't think there is a simple answer for that one, it's more of a axiom. If you can stand to read another paper I have one here that Galina Weinstein wrote, being at the Center for Einstein studies. It has annotations and references that may disturb the reading, but if one leave them be for now, one might get an idea on how he thought about it. One has to remember though that looking back at something may not be exactly the same as what one thought as 'it happened'. Memories change although logic seems to hold a little better, even when getting incorporated into some new theory, as Newtons logic into Einsteins. He also has stated that what made him wonder was Maxwells equations in where the very mathematics demands that 'c' must exist. Wish we still had JP here :) he was very knowledgeable on Maxwell. Einstein Chases a Light Beam. (https://arxiv.org/pdf/1204.1833)

I cannot understand how relativity/time dilation works in a very simple instance. Can someone please help me?
I have three particles A, B and C. B is moving 80% of the speed of light faster than A. C is moving 80% of the speed of light faster than B. Therefore C is moving 160% of the speed of light faster than A. Right? But according to relativity nothing moves faster than the speed of light and time dilation is what allows this to happen. How does time dilation work in the example I have just given?
In relativity, one of the main precepts is that the speed of light is invariant. What this means is that each of your particles measures light as moving at c relative to themselves.
So imagine that the three particles start at the same point, and at the moment they are together a flash of light is emitted from the same spot. What does each particle see?
We'll start with particle B: It sees itself at the center of a sphere of light expanding outward from it at c(invariant speed of light). Particle A is traveling away from it at 0.8c in one direction, and particle C at 0.8c in the other, both remaining in the sphere of light at all times.
Particle A also sees itself at the center of the sphere of light expanding at c. It sees particle B traveling away from it at 0.8c and remaining in the sphere. It sees particle C moving away from it faster than particle B but still less than c, also remaining within the sphere of light.
Finally, particle C also sees itself at the center of the sphere of light expanding at c. It sees particle B traveling away from it at 0.8c and remaining in the sphere. It sees particle A moving away from it faster than particle B but still less than c, also remaining within the sphere of light.
The point is that each particle sees itself at the center of the sphere and thus remaining in the sphere at all times, and therefore all of the particles must see all three as remaining in the sphere, which means that none of the particles can measure the other as moving at greater than c relative to itself since none of the particles can measure the sphere as expanding away from itself at anything but c.
You can't have A see itself and B as remaining in the sphere and C leaving the sphere, while C and B both say that C remains in the sphere. This leads to a physical contradiction.
To analyze this a bit deeper, you can't apply time dilation, you have to include length contraction and the relativity of simultaneity also.
To explain, lets set this up a bit differently. We'll start with two spaceships with a relative velocity of 0.8c. In one of the ships(B) we have clocks at the front and back which are synchronized according to anyone on the ship. A bullet is fired from the back to the front of this ship and the time on the respective clocks are noted upon firing and arrival. The difference in time reading is taken and divided into the length of the ship(as measured by the ship) to get the speed of the bullet relative to the ship. We will assume that an answer of 0.8c is arrived at.
What does the other ship(A) see. Well, first off, both clocks on B will be running slow by a factor of 0.6 (time dilation). Secondly, the length of B (and thus the distance between the clocks) will be shortened by a factor of 0.6 (length contraction.). Finally the clocks at the front and back of B will not be in sync with each other. The rear clock will read some fixed time ahead of the front clock (relativity of simultaneity), by how much depends on the actual distance between the clocks.
The result is that Ship A will see the bullet leave the rear clock when that clock reads the same time as Ship B said it read when the bullet left, and will arrive at the front clock when that clock reads the same as Ship B said it read upon the bullet's arrival. By noting how much time elapses on his own clock between these two events, the length contracted distance between the clocks, and the distance Ship B moved in that time period, ship A can calculate how fast the bullet was moving with respect to him. He will come up with an answer of ~0.9756c.
We can set up the same bullet and clock arrangement in Ship A, and get like results. Ship A measures the speed of the bullet as being 0.8c relative to itself and ship B measures it as having a speed of 0.9756c relative to itself.
Neither ship can tell which one is "really" moving as they get identical results when measuring each other. You could even consider a frame which measures the velocities of both ships being equal in magnitude, but in opposite directions. In this case, the ship's would have a speed of 0.5c relative to the frame, and each bullet would be moving at 0.92857c relative to the frame we are measuring from.
In essence, Relativity is based on two ideas:
1.The invariant speed of light
2.The consistency of events between frames. ( If an event (such as a bullet being fired from a gun) happens at the same location as clock reading a certain time, then all frames of references will agree that that event occurred at the same location as the clock when that clock read that time.)
Everything else, time dilation, length contraction, and relativity of simultaneity follows.
So for example if you have two men with hammers, each standing by a clock and they are separated by some distance, and they then each hit their clock breaking it and stopping it from running, everyone will agree what time was on each clock when it stopped running. However, depending on their relative motion with respect to the men and clocks, they may not agree on the distance between the clocks, whether or not the clocks were stopped simultaneously, and if not how much time elapsed between each clock stopping.
I cannot understand how relativity/time dilation works in a very simple instance. Can someone please help me?
I have three particles A, B and C. B is moving 80% of the speed of light faster than A. C is moving 80% of the speed of light faster than B. Therefore C is moving 160% of the speed of light faster than A. Right? But according to relativity nothing moves faster than the speed of light and time dilation is what allows this to happen. How does time dilation work in the example I have just given?
In relativity, one of the main precepts is that the speed of light is invariant. What this means is that each of your particles measures light as moving at c relative to themselves.
So imagine that the three particles start at the same point, and at the moment they are together a flash of light is emitted from the same spot. What does each particle see?
We'll start with particle B: It sees itself at the center of a sphere of light expanding outward from it at c(invariant speed of light). Particle A is traveling away from it at 0.8c in one direction, and particle C at 0.8c in the other, both remaining in the sphere of light at all times.
Particle A also sees itself at the center of the sphere of light expanding at c. It sees particle B traveling away from it at 0.8c and remaining in the sphere. It sees particle C moving away from it faster than particle B but still less than c, also remaining within the sphere of light.
Finally, particle C also sees itself at the center of the sphere of light expanding at c. It sees particle B traveling away from it at 0.8c and remaining in the sphere. It sees particle A moving away from it faster than particle B but still less than c, also remaining within the sphere of light.
The point is that each particle sees itself at the center of the sphere and thus remaining in the sphere at all times, and therefore all of the particles must see all three as remaining in the sphere, which means that none of the particles can measure the other as moving at greater than c relative to itself since none of the particles can measure the sphere as expanding away from itself at anything but c.
You can't have A see itself and B as remaining in the sphere and C leaving the sphere, while C and B both say that C remains in the sphere. This leads to a physical contradiction.
To analyze this a bit deeper, you can't apply time dilation, you have to include length contraction and the relativity of simultaneity also.
To explain, lets set this up a bit differently. We'll start with two spaceships with a relative velocity of 0.8c. In one of the ships(B) we have clocks at the front and back which are synchronized according to anyone on the ship. A bullet is fired from the back to the front of this ship and the time on the respective clocks are noted upon firing and arrival. The difference in time reading is taken and divided into the length of the ship(as measured by the ship) to get the speed of the bullet relative to the ship. We will assume that an answer of 0.8c is arrived at.
What does the other ship(A) see. Well, first off, both clocks on B will be running slow by a factor of 0.6 (time dilation). Secondly, the length of B (and thus the distance between the clocks) will be shortened by a factor of 0.6 (length contraction.). Finally the clocks at the front and back of B will not be in sync with each other. The rear clock will read some fixed time ahead of the front clock (relativity of simultaneity), by how much depends on the actual distance between the clocks.
The result is that Ship A will see the bullet leave the rear clock when that clock reads the same time as Ship B said it read when the bullet left, and will arrive at the front clock when that clock reads the same as Ship B said it read upon the bullet's arrival. By noting how much time elapses on his own clock between these two events, the length contracted distance between the clocks, and the distance Ship B moved in that time period, ship A can calculate how fast the bullet was moving with respect to him. He will come up with an answer of ~0.9756c.
We can set up the same bullet and clock arrangement in Ship A, and get like results. Ship A measures the speed of the bullet as being 0.8c relative to itself and ship B measures it as having a speed of 0.9756c relative to itself.
Neither ship can tell which one is "really" moving as they get identical results when measuring each other. You could even consider a frame which measures the velocities of both ships being equal in magnitude, but in opposite directions. In this case, the ship's would have a speed of 0.5c relative to the frame, and each bullet would be moving at 0.92857c relative to the frame we are measuring from.
In essence, Relativity is based on two ideas:
1.The invariant speed of light
2.The consistency of events between frames. ( If an event (such as a bullet being fired from a gun) happens at the same location as clock reading a certain time, then all frames of references will agree that that event occurred at the same location as the clock when that clock read that time.)
Everything else, time dilation, length contraction, and relativity of simultaneity follows.
So for example if you have two men with hammers, each standing by a clock and they are separated by some distance, and they then each hit their clock breaking it and stopping it from running, everyone will agree what time was on each clock when it stopped running. However, depending on their relative motion with respect to the men and clocks, they may not agree on the distance between the clocks, whether or not the clocks were stopped simultaneously, and if not how much time elapsed between each clock stopping.

We measure velocity using light/energy that is emitted/reflected by the object. If I see you running, what reaches my brain or my camera, is the light that reflects off you as you run. I don't measure your speed with a matter trail, like scent. Instead we use light, which is energy. Light is limited to the speed of light. Therefore you can never see anything move faster than the speed of light, since the light you use to see, cannot move faster than the speed of light.
Absolutely, 100% wrong.
The time dilation of special relativity works even if we perfectly and ideally measure the location and times of events, it does not depend on the need to see things with light.
The speed of light comes into play when we assume that we can use light to synchronize clocks stationary relative to one another.