Time dilation and the photon clock

[Stellar1]

Hello,
I just baught my next set of textbooks and started reading about relativity. In one of the books it uses the example of a two clocks who "tick" every time a photon it emitted hits the mirror and returns to the sensor. It demonstrated that, if the box containing this clock is moving, it will tick slower than one that is stationary. I understand this and why, but I don't understand how this is supposed to show time dilation? If I perform the same experiment but with a clock that shoots a tennis ball, while fixing the tennis ball's speed at a constant value, the moving clock, even at speeds far below the speed of light, will still tick slower than the stationary one, yet there would not really be time dilation.

 

[jcsd]

The second postulate of relativity is that the speed of light (i.e. the speed of a photon) is the same in all inertial (non-acclerated) frames of reference. There is no equivalent postulate for tennis balls :)

 

[Riogho]

Of course, the speed of a photon isn't constant :P It's just constant in a vacuum, and that is given as c

 

[Stellar1]

Yes, I know its not constant everywhere, but that's what I meant, in a vacuum.

Never the less, I still do not see how this test actually displays any time dilation.

jcsd: if the tennis ball were held at a constant speed, the speed of the tenis ball would also be the same in all inertial frames of reference.

Can anyone simply explain to me how this whole example shows time dilation, rather than the mechanism of the clock simply being affected by the movement? That's all I see happening, the mechanism of the clock is made such that the clock is only accurate when it is stationary.

 

[Doc Al]

If I perform the same experiment but with a clock that shoots a tennis ball, while fixing the tennis ball's speed at a constant value, the moving clock, even at speeds far below the speed of light, will still tick slower than the stationary one, yet there would not really be time dilation.

Why do you say that the moving tennis-ball clock will tick slower than a stationary tennis-ball clock even at speeds far below light speed?

And why do you think that with a tennis-ball clock there "would not really be time dilation"?

All moving clocks will be observed to slow down by the same factor, whether made of light beams, tennis balls, or the ticking of a human heart. Of course, analyzing the tennis-ball clock from first principles would be much harder since--as jcsd stated--there's no simple principle about the speed of a tennis ball being the same in all frames.

 

[jcsd]

Can anyone simply explain to me how this whole example shows time dilation, rather than the mechanism of the clock simply being affected by the movement? That's all I see happening, the mechanism of the clock is made such that the clock is only accurate when it is stationary.

Yes, simply put in relativity all motion is relative (whence relativity). There is no absolute way to distinguish betwen a stationery and a moving observer (assuming both observers are inertial). Someone who was moving with the 'moving' photon clock would view the same time dialtion effect on a 'stationery' photon clock.

 

[jcsd]

jcsd: if the tennis ball were held at a constant speed, the speed of the tenis ball would also be the same in all inertial frames of reference.

The speed of a tennis ball (unless they are traveling at c, which it is safe to assume they are not unless otherwise stated), cannot be the same in all inertial frames of reference.

 

[Stellar1]

Why do you say that the moving tennis-ball clock will tick slower than a stationary tennis-ball clock even at speeds far below light speed?

Because if the speed of the tennis ball is constant, then the stationary clock's tennis ball has only a vertical component for velocity. The moving clock has both a vertical and horizontal component for it's tennis ball's velocity, and the speed can not exceed that of the stationary one's vertical velocity therefore the moving clock's tennis ball's vertical velocity is slower than that of the stationary one, thus the clock ticks slower.

And why do you think that with a tennis-ball clock there "would not really be time dilation"?

Because it is moving at speeds far below that of the speed of light, yet the ticks can still differ greatly. The clocks will be far out of sync, but it isn't due to time dilation, it is due to the way the clocks were constructed.

All moving clocks will be observed to slow down by the same factor, whether made of light beams, tennis balls, or the ticking of a human heart. Of course, analyzing the tennis-ball clock from first principles would be much harder since--as jcsd stated--there's no simple principle about the speed of a tennis ball being the same in all frames.

Not at all, not if the tennis ball's speed is maintained at a constant and equal level between the two clocks. One clock's tennis ball will have a faster vertical velocity than the other, therefore the one that's moving will tick slower.

Yes, simply put in relativity all motion is relative (whence relativity). There is no absolute way to distinguish betwen a stationery and a moving observer (assuming both observers are inertial). Someone who was moving with the 'moving' photon clock would view the same time dialtion effect on a 'stationery' photon clock.

Ok, but how does this whole example prove time dilation? It simply shows the inexactitude of the mechanism of the clock, does it not?

The speed of a tennis ball (unless they are traveling at c, which it is safe to assume they are not unless otherwise stated), cannot be the same in all inertial frames of reference.

If it was constant, then why not?

 

[Doc Al]

Ah, I see what you were doing. You were assuming that the tennis ball speed would be constant in all frames (like for photons), which is not true. (Only things that move at lightspeed can have the same speed in all frames.)

An ordinary tennis ball clock (if there's such a thing) would behave like any other clock. All clocks exhibit the same "slowing down" affect due to relative motion. It has to be this way, otherwise the laws of physics would depend on one's arbitrary speed, which they do not.

The reason why the light clock is used as an example is that it is easy to analyze and deduce the time dilation factor. As I stated earlier, analyzing the behavior of the tennis ball clock to predict the time dilation factor would not be simple--but it could be done. (Since the tennis ball does not have the same speed in all frames, you would have to use the relativistic transformation for velocity to predict its speed in various frames.)

 

[Stellar1]

Ah, I see what you were doing. You were assuming that the tennis ball speed would be constant in all frames (like for photons), which is not true. (Only things that move at lightspeed can have the same speed in all frames.)

I know that's not true, but let's make that assumption. It doesn't change the laws of physics. If need be, let's say its not a tennis ball but a device that will exert the appropriate amount of thrust in the appropriate direction in order to maintain that constant speed.

An ordinary tennis ball clock (if there's such a thing) would behave like any other clock. All clocks exhibit the same "slowing down" affect due to relative motion.

I know it will. But I'm not asking about that, I'm asking about how the experiment/example itsself shows time dilation. I don't see that it does, I just see a flawed design of the clock.

The reason why the light clock is used as an example is that it is easy to analyze and deduce the time dilation factor.

But as I see it, it is not time dilation that is occurring... time still goes by at the same rate, its just the clock that records things differently depending on how fast the clock is travelling.

As I stated earlier, analyzing the behavior of the tennis ball clock to predict the time dilation factor would not be simple--but it could be done.

But if we use a tennis ball, the time dilation, according to the clocks, will be much greater than according to the photon clocks.

 

[Janus]

I know that's not true, but let's make that assumption. It doesn't change the laws of physics. If need be, let's say its not a tennis ball but a device that will exert the appropriate amount of thrust in the appropriate direction in order to maintain that constant speed.

In order for that to work, the thrust would only be exerted as seen in one frame, and that would involve a change in the law of Physics between the two frames.

I know it will. But I'm not asking about that, I'm asking about how the experiment/example itsself shows time dilation. I don't see that it does, I just see a flawed design of the clock.

We are talking about a difference between identical clocks.

But if we use a tennis ball, the time dilation, according to the clocks, will be much greater than according to the photon clocks.

Imagine that you have a "tennis ball" clock running next to each photon clock. An observer next to each set of clocks notes that the photon clock ticks x times for every one tick of the tennis ball clock next to it. This must be true for any observer watching the pair of clocks. Thus if the photon is seen as ticking twice as slow due tot he fact that the motion of the clock, the tennis ball clock must also tick half as slow in order to maintain that x to 1 ratio. The tennis ball clock and the photon undergo the same time dilation.

 

[Stellar1]

In order for that to work, the thrust would only be exerted as seen in one frame, and that would involve a change in the law of Physics between the two frames.

How would it involve a change in the law of physics? In any case, it is irrelevant because I was just using it as an example to better convey my question "how do we know that it is time dilation that occurs rather than inaccuracy in the equipment?"

We are talking about a difference between identical clocks.

Indeed they are identical; however, the accuracy of it is dependent on the speed of the clock. It seems to me that, rather than time dilation occurring in the example, it is simply inaccuracy in the equipment that's responsible for time being different.

Imagine that you have a "tennis ball" clock running next to each photon clock. An observer next to each set of clocks notes that the photon clock ticks x times for every one tick of the tennis ball clock next to it. This must be true for any observer watching the pair of clocks. Thus if the photon is seen as ticking twice as slow due tot he fact that the motion of the clock, the tennis ball clock must also tick half as slow in order to maintain that x to 1 ratio. The tennis ball clock and the photon undergo the same time dilation.

Indeed, I understand that. My point is, however, that the time dilation measured by the difference of the clock's values for the tennisball is different than that of the photon clock...

 

[Ich]

Instead of concentrating only on the second postulate, you should remember the first.
That means that it does not matter whether the clock is moving and the observer is stationary, or the clock is stationary and the observer is moving.
This implies that the photon in a stationary clock is moving at the same speed as seen by every observer moving at arbitrary speed relative to the clock. How you achieve that with thrusters?

 

[Doc Al]

I know that's not true, but let's make that assumption. It doesn't change the laws of physics. If need be, let's say its not a tennis ball but a device that will exert the appropriate amount of thrust in the appropriate direction in order to maintain that constant speed.

Unfortunately that does require a change in the laws of physics. Unless the tennis balls are moving at light speed (not possible), they will have different speeds depending upon who's doing the observing. And there's no possible device that could ensure the same speed for all observers.

But if we use a tennis ball, the time dilation, according to the clocks, will be much greater than according to the photon clocks.

Why do you keep saying this? Time dilation measured by any kind of clock will be the same.

 

[neopolitan]

What orientation does the tennis ball clock have? That is, do the tennis balls travel parallel with the frame's velocity or transversely to that velocity.

This seems to make a difference.

Say we have two observers with a tennis ball clock each. One we consider to be stationary and the other we consider to be in motion. We set the clocks in motion when the observers are collocated. At the end of one tick and one tock, where are the tennis balls?

Doesn't it all rely on what we mean by set the "clocks in motion"? If we think that the operating speed of the tennis ball in each clock is vtb then setting the clocks in motion means bestowing enough momentum to each tennis ball such that it attains this speed. The amount of moment transferred may be lorentz invariant, but in the moving frame you have to overcome a little inertia as well as setting the tennis ball in motion (or possibly give the tennis ball insufficient momentum to account for the frame's motion, depending on the orientation of the clock, the effect is the same either way). The tennis ball in moving frame will move more slowly.

It doesn't seem valid to compare this to the operation of a light clock (where we don't actually need to provide the photon with momentum, we just release it).

That said, the light clock derivation has its own problems, specifically when you orient the clock such that the photon travels parallel with the frame's motion.

cheers,

neopolitan

 

[Janus]

Indeed they are identical; however, the accuracy of it is dependent on the speed of the clock. It seems to me that, rather than time dilation occurring in the example, it is simply inaccuracy in the equipment that's responsible for time being different.

As Ich has already pointed out, you are missing an important part of this whole scenerio.

It doesn't matter which photon clock is considered as "moving". You have two identical photon clocks, each with an observer at rest with repect to it. The photon clocks have a relative velocity to each other. Each observer notes that his clock ticks once every sec. Each observer will also note that the other clock will take longer than one sec between ticks. IOW, the two observers do not measure the same amount of time as elapsing between two given events (such as the ticking of one particular clock).

 

[Doc Al]

That said, the light clock derivation has its own problems, specifically when you orient the clock such that the photon travels parallel with the frame's motion.

Nonsense. When the light clock is oriented parallel to the direction of motion the derivation is a bit different, but it still works just fine.

 

[Stellar1]

Hmm, let me start this from scratch.
Forgetting about the whole tennis ball clock analogy, what is it about the photon-clock that proves time dilation? Maybe that's the fundamental point I'm missing.

 

[Stellar1]

Alright, one sec. I just lied down in bed for a while and just thought about the whole situation. So I see what you are saying now and what you mean by the tennis ball not being the same speed between the two inertial frames of reference.

So, what you are saying is that, since the speed of light is maxed at c, the stationary clock's photons are moving vertically at c. From the perspective of the moving clock, however, the photons of the stationary clock would also have a horizontal component for velocity, which would put their speed above c, which is impossible, therefore it is time that must slow down to maintain the speed at c, correct?

 

[paw]

...which would put their speed above c, which is impossible, therefore it is time that must slow down to maintain the speed at c, correct?

Bingo. That's the whole point.

IF we lived in a universe where tennis balls always moved at a specific speed in a vacuum AND if the speed they move was always the same for all inertial observers THEN the tennis ball clock would also demonstrate time dilation in exactly the same manner.

Since we don't live in a universe where tennis balls behave this way the tennis ball clock cannot demonstrate time dilation. It will, of course, slow down like any other mechanical clock when viewed from a different inertial frame but because tennis balls can have any velocity < c there's no way to calculate delta t using tennis balls.

 

[Stellar1]

So my next question is this, what experiments have shown that this is the case? In other words, how do we know that it is time dilation that occurs rather than speed of the photon relative to the moving clock being greater than c?

 

[Janus]

Okay you have two photon clocks, A and B. Each is uses light which bounces back a forth between two mirrors placed a tad under 150,000 km apart, such that if the two clocks were sitting right next to each other they would both tick at 1 sec intervals.

Now we add two observers, one by each clock and at rest with respect to it and put the clocks in motion with respect to each other along a line at a right angle to the photons of either clock as seen by that clocks observer.

According to each observer, he and his clock is at rest, and the other observer and their clock is in motion. Thus each observer measures his clock as ticking once every second.

When they measure the other clock's ticks however they note otherwise. In the time it takes for his clock to tick off on second, the other clock has moved some distance along its line of motion. The photons for that other clock must travel a diagonal path to bounce between the mirrors, and this diagonal path will be longer than the 150,000 km separation between the mirrors. Since the photons must travel at c according to our observer, it must take longer for the photons of the other clock to complete the round trip. For instance, if the relative velocity between the two clocks is 0.866c, then he will measure 2 ticks of his clock for every 1 tick of the other clock.

This is true whether is is is observer A looking at clock B or observer B is looking at clock A. Each will see the other clock as ticking slow. This is what time dilation is.
And each is equally justified in saying that his own clock is ticking at one sec per sec.

IOW, time is not an absolute measurement and there is no one true rate at which time can be said to pass.

 

[Doc Al]

So, what you are saying is that, since the speed of light is maxed at c, the stationary clock's photons are moving vertically at c. From the perspective of the moving clock, however, the photons of the stationary clock would also have a horizontal component for velocity, which would put their speed above c, which is impossible, therefore it is time that must slow down to maintain the speed at c, correct?

Something like that. Here's how I would phrase it. In a frame in which the light clock is stationary, the photons move vertically the length of the clock. Since photons move at speed c, it takes them a certain amount of time to move across that distance. Now from a frame in which the light clock is moving sideways, the photons move through a greater distance (since they move horizontally as well as vertically). If they move through a greater distance it must take more time, since photons move at the same speed c in any frame. So if the clock is built such that one "tick" takes 1 second when it's stationary, that same tick will take longer than 1 second when viewed from a moving frame. That's how you can deduce that moving clocks run slow compared to stationary clocks.

 

[Stellar1]

Ok, so, what experiments have shown this to be the case, rather than the relative velocity beingg reater than c?

 

[paw]

So my next question is this, what experiments have shown that this is the case? In other words, how do we know that it is time dilation that occurs rather than speed of the photon relative to the moving clock being greater than c?

There are many experiments confirming time dilation. Check out http://en.wikipedia.org/wiki/Time_dilation#Experimental_confirmation" for some of them.

 

[neopolitan]

Nonsense. When the light clock is oriented parallel to the direction of motion the derivation is a bit different, but it still works just fine.

There is a bit of bootstrapping required. To the best of my knowledge, you can't use the light clock oriented parallel to the direction of motion to derive the equation for time dilation. The standard approach, the only one I have ever seen, is to do time dilation with a transverse orientation and then do spatial contraction with a parallel orientation and knowledge of time dilation.

I am willing to stand corrected if you can derive the equation for time dilation without assuming spatial contraction using nothing more than a light clock aligned parallel to the direction of motion. Note that I am not talking about bootstrapping, I am talking about first principles. No reference to Lorentz boosts, no reference to spatial contraction, no reference to anything that comes after you have established time dilation to derive time dilation. You can't use more advanced concepts to prove this simple one either, so no tensors, no geodesics.

I am willing to make an exception, if you can establish spatial contraction using nothing more than the light clock on the side, you can then use that to establish time dilation.

Anyone may take up the challenge. Just remember - first principles, no "well, I use 4-vector notation to describe Minkowski space, that's good enough for me".

cheers,

neopolitan

 

[Doc Al]

Ok, so, what experiments have shown this to be the case, rather than the relative velocity beingg reater than c?

Special relativity has tons of experimental support.

One famous demonstration of time dilation itself was done with mu-mesons back in the 40s: http://www.egglescliffe.org.uk/physics/relativity/muons1_.html"

Here's another reference for experimental evidence: http://www2.corepower.com:8080/~relfaq/experiments.html"

 

[Janus]

So my next question is this, what experiments have shown that this is the case? In other words, how do we know that it is time dilation that occurs rather than speed of the photon relative to the moving clock being greater than c?

For one thing, if the speed of light varied with relative motion, we would have measured such a variation.

Also, we have measured the effects of time dilation directly. A famous example is the Muon Experiment. Muons are subtomic particles that are created by cosmic ray hitting the upper atmosphere. The muons are created we a velocity of a good fraction of c. Muons also have a short half-life; they don't exist very long before they decay into other particles.

We know that the muons are created 40 miles up, we know how fast they are moving when they are created, and how long they should last. Given these facts, it can be calculated that very few muons created in the upper atmosphere should last long enough to reach the surface of the Earth. But many more muons are measured as reaching the Surface, the reason being that due to the fact that they are traveling so close to c, time dilation slow their aging and allows them to reach the surface before they decay.

 

[Doc Al]

There is a bit of bootstrapping required. To the best of my knowledge, you can't use the light clock oriented parallel to the direction of motion to derive the equation for time dilation. The standard approach, the only one I have ever seen, is to do time dilation with a transverse orientation and then do spatial contraction with a parallel orientation and knowledge of time dilation.

So what would be your point? How does that invalidate the standard light clock demonstation of time dilation? Where's the "problem"?

 

[neopolitan]

So what would be your point? How does that invalidate the standard light clock demonstation of time dilation? Where's the "problem"?

The problem is that as an expounder of SR are, on one hand, saying any clock, irrespective of make, model, mode of operation or orientation, in an inertial frame which has a velocity relative to a "stationary" reference frame will run slower than an identical clock at rest in the reference frame. Then you go to prove it and say, we must have a specific orientation to prove this. This seems to be a problem. Perhaps it is a philosophic bagatelle, but it is one which you can dismiss if you can do the derivation that you said you do and I challenged you to produce.

Can you provide the derivation? You don't need to provide it immediately, it may take you some time.

cheers,

neopolitan

 

[robphy]

Try out my page of visualizations:
http://physics.syr.edu/courses/modules/LIGHTCONE/LightClock/
which links to my article:
http://arxiv.org/abs/physics/0505134, which was later published.

In the above, I have tried to address possible complaints or confusions I have encountered in the literature or in discussions with others.

 

[Doc Al]

The problem is that as an expounder of SR are, on one hand, saying any clock, irrespective of make, model, mode of operation or orientation, in an inertial frame which has a velocity relative to a "stationary" reference frame will run slower than an identical clock at rest in the reference frame.

And that's still as true as ever.

Then you go to prove it and say, we must have a specific orientation to prove this. This seems to be a problem. Perhaps it is a philosophic bagatelle, but it is one which you can dismiss if you can do the derivation that you said you do and I challenged you to produce.

Again I ask: Where's the problem? If you understand the principle of relativity, and how to construct the standard light clock thought experiment, you can immediately prove that any sort of clock must be affected in the same way. You certainly don't need to explore the detailed mechanism of every possible clock!

Can you provide the derivation? You don't need to provide it immediately, it may take you some time.

You may find the book "It's About Time", a pedagogical work on basic relativity by N. David Mermin, interesting. He derives the relativistic addition of velocities, clock desynchronization, length contraction, and time dilation through a series of clever thought experiments without once using the traditional "light clock". In all of his examples, everything travels parallel to the direction of motion. (My copy is packed away, so I hope I am remembering correctly.)

 

[robphy]

You may find the book "It's About Time", a pedagogical work on basic relativity by N. David Mermin, interesting. He derives the relativistic addition of velocities, clock desynchronization, length contraction, and time dilation through a series of clever thought experiments without once using the traditional "light clock". In all of his examples, everything travels parallel to the direction of motion. (My copy is packed away, so I hope I am remembering correctly.)

Mermin is essentially using the invariance of a certain area in Minkowskian spacetime (abstracted from a radar measurement which could have been associated with a light-clock mirror).
Jacobson and Brill also make use of this area (the corrected url is http://arxiv.org/abs/gr-qc/0407022 ) from my earlier post
https://www.physicsforums.com/showthread.php?p=747083#post747083
See also Liebscher's new book (details in above URL).

My animations also exploit this area in the "Longitudinal Light Clock".

This invariance of this area isn't new...(It's in Bohm's book, for example.) ..it just hasn't been used to teach relativity.

 

[neopolitan]

Can you provide the derivation? You don't need to provide it immediately, it may take you some time.

You may find the book "It's About Time", a pedagogical work on basic relativity by N. David Mermin, interesting. He derives the relativistic addition of velocities, clock desynchronization, length contraction, and time dilation through a series of clever thought experiments without once using the traditional "light clock". In all of his examples, everything travels parallel to the direction of motion. (My copy is packed away, so I hope I am remembering correctly.)

I am sure I may well find the book interesting, but you have strayed from the challenge entirely. I can derive all the SR equations without reference to the light clock too. (All you need to do is start with Gallilean boosts and then systematically remove the assumptions, do this in a structured way and you end up with Lorentz transformations and relativistic effect equations.)

The issue was that the light clock is problematic when used as a tool for introducing SR.

Cheers,

neopolitan

 

[Doc Al]

I am sure I may well find the book interesting, but you have strayed from the challenge entirely. I can derive all the SR equations without reference to the light clock too. (All you need to do is start with Gallilean boosts and then systematically remove the assumptions, do this in a structured way and you end up with Lorentz transformations and relativistic effect equations.)

The issue was that the light clock is problematic when used as a tool for introducing SR.

I didn't stray from the challenge, I rejected it as bogus! You have yet to offer an argument as to why it matters. I repeat: What's the problem?

Why does it matter that one makes use of length contraction in the typical analysis of the longitudinal light clock?

You make it sound like you've uncovered some flaw in the way the light clock is typically used. Well, where's the flaw?

 

[neopolitan]

I didn't stray from the challenge, I rejected it as bogus!

Okay, I understand.

 

[neopolitan]

You make it sound like you've uncovered some flaw in the way the light clock is typically used. Well, where's the flaw?

I am going to be Socratean here. I know Socrates was annoying and eventually the Atheans persuaded him to kill himself, but if I give you the answer, you won't own it. If you work it out yourself, you might just decide to give me a hand rather than fight me every step of the way.

I am going to ask you to provide for me four equations. The first two are simple: the equation for time dilation (in terms of t, c and v) and the equation for length contraction (in terms of x, c and v).

For the third and fourth equations, consider this scenario. K' knowingly travels for an extremely long time away from K at a rather slow speed of v, relative to K. Then, in an extremely short period of time, K' changes direction 180 degress and then travels back to K at a speed of v, relative to K. According to K, K' has been away for a period of t and therefore traveled (approximately) a total distance of v.t = x

Equation three: How long has K' been away, according to K', in terms of t, c and v?

Equation four: How far did K' travel, according to K', in terms of x, c and v?

I will continue the discussion once you have written up the equations. You may care to discuss them in your answer. But until you, or someone else, presents those four equations, there really is nothing to discuss. Until then, it's nothing more than opinions.

cheers,

neopolitan

 

[JesseM]

Equation three: How long has K' been away, according to K', in terms of t, c and v?

This is a well-defined question, since K' can carry a watch and measure how much time has elapsed between first passing K and then later passing K again after the turnaround (according to K' the time would be t * \sqrt{ 1 - v^2/c^2}, if t is the time measured by K between their two meetings, and K is an inertial observer).

Equation four: How far did K' travel, according to K', in terms of x, c and v?

This is not a well-defined question, since K' does not have a single inertial rest frame. You could ask how far K' traveled in the inertial frame where K' was at rest during the outbound leg, or how far K' traveled in the inertial frame where K' was at rest during the inbound leg (in both cases K' would travel zero distance during the phase where K' was at rest, and during the other phase of the trip, K' would be moving at velocity 2v/(1 + v^2/c^2) in this same frame according to the velocity addition formula, while K would be moving away at v in this frame, so the time for K' to catch up with K should be \frac{x * \sqrt{1 - v^2/c^2}}{(2v/[1 + v^2/c^2]) - v}, so to get the distance K' moved you'd multiply by the velocity of K', which was 2v/[1 + v^2/c^2], giving an answer of \frac{x * (2v/[1 + v^2/c^2]) * \sqrt{1 - v^2/c^2}}{(2v/[1 + v^2/c^2]) - v} =
\frac{x * (2v/[1 + v^2/c^2]) * \sqrt{1 - v^2/c^2}}{(v*[1 - v^2/c^2]/[1 + v^2/c^2])} = \frac{2x}{\sqrt{1 - v^2/c^2}}), or how far K' traveled in a non-inertial frame where K' was at rest during the entire trip (of course in this last case, since K' is always at rest, the distance traveled by K' is zero!).

 

[rbj]

The second postulate of relativity is that the speed of light (i.e. the speed of a photon) is the same in all inertial (non-acclerated) frames of reference.

doesn't the second postulate regarding the constancy of the speed of light really mean the wavespeed of propagation of E&M, what comes out as 1/\sqrt{\epsilon_0 \mu_0} in the solution of Maxwell's Eqs. (with no mention of the concept of photons)? That E&M has particle-like properties (besides the wave-like properties) and that the particle speed is the same as the wavespeed, is another issue. There have been some propositions that the rest mass of photons are not precisely zero and might have something like 10^-56 kg of mass which means that they do not move at precisely the same as the wavespeed c.

 

[jcsd]

doesn't the second postulate regarding the constancy of the speed of light really mean the wavespeed of propagation of E&M, what comes out as 1/\sqrt{\epsilon_0 \mu_0} in the solution of Maxwell's Eqs. (with no mention of the concept of photons)? That E&M has particle-like properties (besides the wave-like properties) and that the particle speed is the same as the wavespeed, is another issue. There have been some propositions that the rest mass of photons are not precisely zero and might have something like 10^-56 kg of mass which means that they do not move at precisely the same as the wavespeed c.

Strictly it's the propagation speed and that assumes that photons have zero rest mass.

 

[rbj]

Strictly it's the propagation speed and that assumes that photons have zero rest mass.

i don't know why it has to assume anything about the rest mass of photons. you can have a concept of a "light clock" without any notion of photons bouncing up and down (or back and forth, whatever the orientation).

 

[jcsd]

i don't know why it has to assume anything about the rest mass of photons. you can have a concept of a "light clock" without any notion of photons bouncing up and down (or back and forth, whatever the orientation).

The rest mass of photons must me zero, assuming that they travel at c (defining c as being the all important 'Eisntein constant' in relatvity, rather than defiening it as the speed of light). Otherwise their momentum would be infinite, which it isn't.

 

[rbj]

The rest mass of photons must me zero, assuming that they travel at c (defining c as being the all important 'Eisntein constant' in relatvity, rather than defiening it as the speed of light). Otherwise their momentum would be infinite, which it isn't.

i know that. that's not the point.

you can have a notion of a light clock, discuss the principles of its operation, show that if the wavespeed of propagation remains the same speed c then time gets dilated, all without any notion of a photon. so whether not photons have no rest mass (i actually think that is the case) or that they must always travel at speed c (from the perspective of any inertial observer) is not needed to deal with this at all. a "light clock" need not be a "photon clock" and yet we can still arrive at the conclusions Einstein did a century ago.

 

[neopolitan]

K' ___knowingly___ travels for an extremely long time away from K at a rather slow speed of v, relative to K.

...

Equation three: How long has K' been away, according to K', in terms of t, c and v?

Equation four: How far did K' travel, according to K', in terms of x, c and v?

... (according to K' the time would be t * \sqrt{ 1 - v^2/c^2}, if t is the time measured by K between their two meetings, and K is an inertial observer).

You failed to provide equations 1, 2 and 4. (Equation 1, time dilation in terms of t, c and v. Equation 2, length contraction in terms of x, c and v.) Note:

According to K, K' has been away for a period of t and therefore traveled (approximately) a total distance of v.t = x

--------------
Provide all four equations together in the same post please, then we can continue.

cheers,

neopolitan

 

[JesseM]

Why did you highlight the word "knowingly" like that? The time measured on a clock carried along by K' will not depend on what he knows or doesn't know.

You failed to provide equations 1, 2 and 4. (Equation 1, time dilation in terms of t, c and v. Equation 2, length contraction in terms of x, c and v.) Note:

--------------
Provide all four equations together in the same post please, then we can continue.

cheers,

neopolitan

Equations 1 and 2 are just the standard time dilation and length contraction equations, which I made use of in my answers--if a clock moves at speed v for time t in some inertial frame (such as the frame of K), it will only elapse a time of t * \sqrt{1 - v^2/c^2} in that time (so if K' is moving at the same speed v in opposite directions both before and after the turnaround in the frame of K, and the turnaround is negligibly short, then if the time between K' passing K the first and second time is t according to K, then the clock of K' will elapse the shorter time given by the time dilation equation above). And if the distance between two fixed objects at rest in a given frame (like K's own position and a space station at the position where K' turns around) is x, then the distance between them in a frame moving at speed v relative to the objects is x * \sqrt{1 - v^2/c^2}

As for equation 4, didn't you read my response? I said that your question as stated was not well-defined, since you didn't specify what sort of frame you wanted to use for K' to answer the question "how far did K' travel". I did point out that if we use an inertial frame where K' is at rest for one phase of the trip and moving at speed 2v/(1 + v^2/c^2) for the other phase of the trip (either the frame where K' is at rest before the turnaround and moving after, or the frame where K' is moving before the turnaround and at rest after), then the distance traveled by K' during the moving phase will be \frac{2x}{\sqrt{1 - v^2/c^2}}. And I also pointed out that if we use a non-inertial frame where K' is at rest the whole time, both before and after the turnaround, the distance traveled by K' is of course zero (but you can't use the usual equations of special relativity in this non-inertial frame, like the equations for time dilation and length contraction above).

 

[neopolitan]

Why did you highlight the word "knowingly" like that? The time measured on a clock carried along by K' will not depend on what he knows or doesn't know.

Because K' knows he is travelling, he knows that he has traveled for a set period (according to himself), he knows he had a speed of v. Knowing that he can calculate how far he has gone (according to himself). He will not calculate what you provided as the staff answer.

Please provide all four equations together please. You seem set on refusing to do so. Unfortunately this is a common response, many forum posters are quick to write up complex equations but leery of writing four rather simple equations together in the one place. I would love to know why.

If this is not an article of faith for you, please write all four equations together in one post. If this is an article of faith for you, just acknowlege it and I will accept that.

cheers,

neopolitan

 

[JesseM]

Because K' knows he is travelling, he knows that he has traveled for a set period (according to himself), he knows he had a speed of v.

But speed is relative, he doesn't know he has a speed of v in any absolute sense, only a speed of v in the rest frame of K. K' can certainly calculate what the time will be in the rest frame of K, but this will not be the same as the time according to his own clocks. Are you in fact asking what time K' calculates has elapsed in the frame of K? If so then of course the answer is just t.

Knowing that he can calculate how far he has gone (according to himself).

What frame do you mean when you say "according to himself"? The notion of "distance travelled" has no frame-independent meaning in relativity. If you don't explicitly say what frame you're asking for a given answer in, your questions are meaningless.

Please provide all four equations together please. You seem set on refusing to do so.

I'm not "set on refusing to do so", I figured you would have the reading comprehension necessary to put together the answers I gave in different posts, and I also requested that you clarify what frame you were asking for the calculations to be in. The answers I have already given so far (although I am not sure if they are in the frames you're thinking of, since you haven't answered my questions about this) were:

1. "if a clock moves at speed v for time t in some inertial frame (such as the frame of K), it will only elapse a time of t * \sqrt{1 - v^2/c^2} in that time"

2. "And if the distance between two fixed objects at rest in a given frame (like K's own position and a space station at the position where K' turns around) is x, then the distance between them in a frame moving at speed v relative to the objects is x * \sqrt{1 - v^2/c^2}"

3. "K' can carry a watch and measure how much time has elapsed between first passing K and then later passing K again after the turnaround (according to K' the time would be t * \sqrt{1 - v^2/c^2}, if t is the time measured by K between their two meetings, and K is an inertial observer)."

4. "if we use an inertial frame where K' is at rest for one phase of the trip and moving at speed 2v/(1 + v^2/c^2) for the other phase of the trip (either the frame where K' is at rest before the turnaround and moving after, or the frame where K' is moving before the turnaround and at rest after), then the distance traveled by K' during the moving phase will be \frac{2x}{\sqrt{1 - v^2/c^2}}."

If this is not an article of faith for you, please write all four equations together in one post. If this is an article of faith for you, just acknowlege it and I will accept that.

Please drop the accusations of dogma, they are insulting and nothing I have said justifies this sort of accusation, I am perfectly willing to answer any well-defined question you have, and I had no way of knowing that you wouldn't consider your question answered unless I put the equations in an easy-to-read list as opposed to putting each one in different paragraphs of two different posts. And since I have answered your questions as best I could given the ambiguity in the way you stated them, I would appreciate it if you would address my requests for clarification about which frame you're asking about in each one, I may have to modify the equations depending on your answer (note that I clearly stated what frame or clock I was talking about in each of my answers).

 

[neopolitan]

JesseM,

I am willing to accept that you are not deliberately muddying the waters. So I will present the answers. You can argue them to your heart's content.

1. Time dilation: t&#039; = t / \sqrt{1 - v^2/c^2}

2. Length contraction: x&#039; = x * \sqrt{1 - v^2/c^2}

3. Time elapsed for K', according to K', since K' carries a watch and measures how much time has elapsed: t&#039; = t * \sqrt{1 - v^2/c^2}

4. Distance traveled by K', as calculated by K, given that he knows he has a speed of v: x&#039; = x * \sqrt{1 - v^2/c^2}

Note that 2 and 4 are the same. Note that 1 and 3 are not the same.

This is the problem.

Let's save some time. You will argue that this is not a problem. I will argue that not only is it a problem, but you can actually derive the last two equations as the correct equations for relativistic effects in at least four different ways, even if you use the light clock (correctly). You will argue that I don't know what I am talking about and that I must go to four years of physics studies to understand these things properly. I will argue that four years of engineering studies plus many years of application have give me more than enough mathematics to work these things out and that the only difference I can possibly see that physics studies might make involves indoctrination, rather than better mathematics skills to be applied to what mathematicians consider "trivial". You will consider that offensive but you will, in the same breath, refuse to take an open-minded look at what I have to say, which will (in my frame of reference) prove what I had just said.

Can you prove me wrong on the last step in this process?

cheers,

neopolitan

By the way, I was not accusing you of being dogmatic. I just didn't assume it wasn't the case and gave you the opportunity to clarify one way or the other. You have to admit that it did work as an incentive to write all four equations together. Being polite sure wasn't working.

 

[Doc Al]

I am going to be Socratean here. I know Socrates was annoying and eventually the Atheans persuaded him to kill himself, but if I give you the answer, you won't own it. If you work it out yourself, you might just decide to give me a hand rather than fight me every step of the way.

I am going to ask you to provide for me four equations. The first two are simple: the equation for time dilation (in terms of t, c and v) and the equation for length contraction (in terms of x, c and v).

For the third and fourth equations, consider this scenario. K' knowingly travels for an extremely long time away from K at a rather slow speed of v, relative to K. Then, in an extremely short period of time, K' changes direction 180 degress and then travels back to K at a speed of v, relative to K. According to K, K' has been away for a period of t and therefore traveled (approximately) a total distance of v.t = x

Equation three: How long has K' been away, according to K', in terms of t, c and v?

Equation four: How far did K' travel, according to K', in terms of x, c and v?

I will continue the discussion once you have written up the equations. You may care to discuss them in your answer. But until you, or someone else, presents those four equations, there really is nothing to discuss. Until then, it's nothing more than opinions.

Seems to me that you've dodged or abandoned the light clock issue and have decided to divert this thread into yet another discussion of your "no twin paradox" stuff. Which seems, despite your "calculations", to be "nothing more than opinion".

And what gives with the bogus "challenges"?

 

[JesseM]

JesseM,

I am willing to accept that you are not deliberately muddying the waters. So I will present the answers. You can argue them to your heart's content.

1. Time dilation: t&#039; = t / \sqrt{1 - v^2/c^2}

This is correct if t represents the time measured on the moving clock, and t' is the time between these same two readings as measured in the frame where the clock is moving at speed v. My equation assumed t was the time in the frame where the clock was in motion, so these are equivalent.

2. Length contraction: x&#039; = x * \sqrt{1 - v^2/c^2}

Same as my equation, so presumably x is the distance between ends of the moving object in its own frame, x' is the distance between the ends of the same object in the frame where it's moving at speed v.

3. Time elapsed for K', according to K', since K' carries a watch and measures how much time has elapsed: t&#039; = t * \sqrt{1 - v^2/c^2}

Same as my equation, so again, I presume that here you are assuming t is the time as measured in the K rest frame where K' is moving at speed v, while t' is the time elapsed on the clock of K' (this is the opposite of the convention in equation 1).

4. Distance traveled by K', as calculated by K, given that he knows he has a speed of v: x&#039; = x * \sqrt{1 - v^2/c^2}

Meaningless unless you specify which frame you are doing the calculation in. K' does not have a speed of v in his own rest frame during either phase of the trip, obviously. K' has a velocity of v in the rest frame of K, but if you're using the rest frame of K, then there is no need to apply length contraction, since x was already supposed to be the distance in the frame of K.

From your answer here, and your unwillingness to answer my repeated requests for clarification about what frame you're using, I gather you are fairly confused about frame-dependent vs. frame-independent quantities in relativity, and the fact that claims about distance (unlike time) are always specific to a particular frame.

Note that 2 and 4 are the same. Note that 1 and 3 are not the same.

1 and 3 are only "not the same" because you have switched the meaning of t and t'. In 1 you seem to be using t to represent the time elapsed on the clock of K', and t' to represent the corresponding time elapsed in the K frame; but in 3 you seem to be doing the opposite, with t as the time in the K frame, and t' as the time elapsed on the clock of K' during this time.

Let's save some time. You will argue that this is not a problem. I will argue that not only is it a problem, but you can actually derive the last two equations as the correct equations for relativistic effects in at least four different ways, even if you use the light clock (correctly). You will argue that I don't know what I am talking about and that I must go to four years of physics studies to understand these things properly.

Again with the thinly-veiled accusations of dogma. I would not answer your questions by saying something like that, since it would be little more than an appeal to authority and would show that I was not able to find any specific fault in your analysis; in fact the problem is just that you are making some rather simple conceptual errors, which I tried to explain above.

the only difference I can possibly see that physics studies might make involves indoctrination

More accusations of dogma! You seem to be supremely confident that you are right without even waiting for my response, and you seem to totally discount the possibility that you might be making some errors in your analysis. This is a terrible way to approach any intellectual subject! Unless one is open to the possibility that they may have made a mistake when they reach a conclusion that seems to differ from what the experts say, then any initial misconceptions they may have when starting to study a subject will become ossified, and they will invent grand theories of collective delusions throughout the community of experts in order to preserve the ego-gratifying certainty that they are right and everyone else is wrong.

Can you prove me wrong on the last step in this process?

Your last step is wrong because you have not specified what frame you are using, and your answer wouldn't be right in either the rest from of K' or the rest frame of K. If you have a ruler moving inertially, then whether it is at rest relative to K' (during one phase of the trip) or at rest relative to K, in neither case will the difference between the initial position and the final position of K' be equal to x * \sqrt{1 - v^2/c^2}. If you think there is some other physically meaningful way to define "distance travelled" besides difference in starting and ending position on some ruler, please specify it.

By the way, I was not accusing you of being dogmatic. I just didn't assume it wasn't the case and gave you the opportunity to clarify one way or the other. You have to admit that it did work as an incentive to write all four equations together. Being polite sure wasn't working.

Jeez, nice rationalization for rude behavior! You never even asked politely that I group them all together, you just jumped directly into trying to provoke me. Like I said, I had already provided all four equations, how was I supposed to know that you wouldn't consider the request answered unless I put them all in one place?