I Does the *First Postulate* Prohibit different time dilations?

[Physics_Teacher]

For example, Brian Greene says in The Elegant Universe regarding special relativity and train moving with constant velocity relative to platform: By the principle of relativity or first postulate, "there is no way for an observer on this train to detect any influence of the train's motion. But if the light clock and Rolex were to fall out of synchronization, this would be a noticeable influence indeed. [So] the Rolex must slow down in exactly the same way that the light clock does."

The first postulate states that the laws of physics are the same in all inertial frames of reference. The train passenger can look out the window and conclude that train is moving relative to platform (noting distance changing). The first postulate is from Galilean relativity. It does imply that one cannot have experiments that detect absolute motion. But in arguments, such as in above book, is it not being extended to imply that one cannot have experiments that detect Relative motion? We know from experience that we CAN detect Relative motion by multiple methods, so why could such non-matching clocks not be just another method.

Note: I am asking ONLY in reference to *First Postulate being violated* if different clocks gave different time dilation, and use of THAT reasoning ALONE to conclude that all clocks must show the same time dilation. (I am aware of the Lorentz transformations and their derivation which show that all clocks have to give same time dilation).

 

[Nugatory]

We know from experience that we CAN detect Relative motion by multiple methods, so why could such non-matching clocks not be just another method.

If such non-matching clocks happened (and of course they never do) that would lead to a measurement of absolute motion, not relative motion. We could change our speed until we found some speed at which the mismatch disappeared and the light clock and the Rolex both ticked at the same rate. That would be a measurement of absolute speed: as long as the two clocks did not match we would know that we were in motion, without having to say what that motion was relative to.

 

[Orodruin]

is it not being extended to imply that one cannot have experiments that detect Relative motion?

No. The wristwatch and the light clock are not in relative motion - in fact, that is the point of the argument. The point is that if different clocks that are at relative rest would get different time dilation, then you would be able to detect an absolute motion. If you set up a device such that you place the wristwatch at one of the mirrors of a light clock and check the proper time difference it reads for consecutive bounces for the light clock, the final measurement you make must be the same regardless of whether you make the measurement in the rest frame or any other frame.

 

[Physics_Teacher]

We could change our speed until we found some speed at which the mismatch disappeared and the light clock and the Rolex both ticked at the same rate. That would be a measurement of absolute speed: as long as the two clocks did not match we would know that we were in motion, without having to say what that motion was relative to.

Two clocks in train match when train is NOT moving Relative to platform but mismatch when train is moving relative to platform. Why would mismatch disappearing be a measure of absolute speed? It would only mean that the frame we have found is one that is also NOT moving Relative to the platform.

 

[Orodruin]

Two clocks in train match when train is NOT moving Relative to platform but mismatch when train is moving relative to platform. Why would mismatch disappearing be a measure of absolute speed? It would only mean that the frame we have found is one that is also NOT moving Relative to the platform.

It would single out the platform frame as being a special frame (ie, the frame where clocks match), which violates the principle of relativity.

 

[Physics_Teacher]

It would single out the platform frame as being a special frame (ie, the frame where clocks match), which violates the principle of relativity.

The issue was the claim, such as in Brian Greene's book, that principle of relativity prohibits different clock mechanisms from having different time dilation. If different clock mechanisms had different time dilation then inertial frames where two clocks were manufactured (to be in sync) would be "special frames" to those clocks. In calling that a violation have we not moved beyond our being able to detect absolute speed as being the violation, and (arbitrarily) extended it to existence of such "special frames"?

 

[Dale]

In calling that a violation have we not moved beyond our being able to detect absolute speed as being the violation, and (arbitrarily) extended it to existence of such "special frames"?

That is the same thing. If you can detect absolute speed then the frame where the absolute speed is zero is a special frame.

 

[Physics_Teacher]

That is the same thing. If you can detect absolute speed then the frame where the absolute speed is zero is a special frame.

We cannot detect absolute speed ... that is the point ... please review my reply to Nugatory above!

 

[Orodruin]

We cannot detect absolute speed ... that is the point ... please review my reply to Nugatory above!

Please reread Dale's response. If you can define a special frame, then you can define an absolute speed. That is the point.

 

[Ibix]

Two clocks in train match when train is NOT moving Relative to platform but mismatch when train is moving relative to platform.

I think you have this backwards. Two clocks in the train always match. A clock on the train and a clock on the platform only match when the two are at relative rest.

The two clocks on the train are always at relative rest. If they don't match, then, the reason would have to be some absolute sense of motion. The principle of relativity says that this never happens and experiment agrees so far.

 

[Physics_Teacher]

Please reread Dale's response. If you can define a special frame, then you can define an absolute speed. That is the point.

I created this thread to *rigorously* examine the claim, such as in Brian Greene's book, that principle of relativity prohibits different clock mechanisms from having different time dilation. I emphasize "rigorously."

In my opinion, rigorous examination must bring in the formal principle of relativity. Principle of Relativity: (1) the laws of physics are the same in all inertial frames; (2) that means there is no preferred frame and no way to detect absolute motion.

If different clock mechanisms had different time dilation then inertial frames where two clocks were manufactured (to be in sync) could be called "special frames" to these clocks; in other inertial frames these clocks could give different amounts of time dilation and fall out of sync. But there would be infinite "special frames" and this infinite family cannot rigorously be called preferred frames in terms of violating the Principle of Relativity. If you insisted on so calling them then (1) the laws of physics would still be the same in all of these; (2) there would be no way to detect absolute motion because whichever frame you chose to manufacture two clocks in sync would be "special frames" and so all frames would be "special frames".

 

[A.T.]

If different clock mechanisms had different time dilation then inertial frames where two clocks were manufactured (to be in sync) could be called "special frames" to these clocks; in other inertial frames these clocks could give different amounts of time dilation and fall out of sync.

That would lead to paradoxes. Imagine a bomb triggered when those two clocks deviate from each other. Different frames would then disagree on whether the bomb goes off, or not. So this possibility is ruled out implicitly for consistency reasons.

 

[Vitro]

If different clock mechanisms had different time dilation then inertial frames where two clocks were manufactured (to be in sync) could be called "special frames" to these clocks; in other inertial frames these clocks could give different amounts of time dilation and fall out of sync. But there would be infinite "special frames" and this infinite family cannot rigorously be called preferred frames in terms of violating the Principle of Relativity. If you insisted on so calling them then (1) the laws of physics would still be the same in all of these; (2) there would be no way to detect absolute motion because whichever frame you chose to manufacture two clocks in sync would be "special frames" and so all frames would be "special frames".

Your assumptions do not lead to your conclusion, it would indeed be possible to detect absolute motion with your clocks working as described if they had different time dilation in different frames. Here's how:

Let's call the clocks A and B. They are made to run synchronous when at rest in some inertial frame. If time dilation was to affect these two clock differently then by taking them to rest in other inertial frames you would first discover anisotropy(*), in some frames A would run faster than B, in others B would run faster than A, and yet in others A and B would run at the same rate. So you will find a unique axis of relative motion along which the difference for the same relative speed is maximum. You then repeat the experiment in frames moving relatively along this particular axis (in both directions) and you will find an inflection point, the rate difference increases up to this point then decreases again. The frame containing this inflection point is the absolute rest frame.

Of course this does not happen in reality because all clocks are affected equally by time dilation.

EDIT: (*) If you don't find anisotropy this means the initial rest frame where you set up the synchronized clocks was already the absolute rest frame.

 

[Herman Trivilino]

I created this thread to *rigorously* examine the claim, such as in Brian Greene's book, that principle of relativity prohibits different clock mechanisms from having different time dilation. I emphasize "rigorously."

You have misunderstood one of Greene's points. This point has nothing to do with time dilation: Two clocks aboard the train -- any two clocks -- will stay in sync whether the train is moving or not. If that were not the case then the absolute motion of the train could be detected.

Now, there's another point being made, let's call it the second point, and you seem to be conflating it with the former, which we'll call the first point. Greene's second point is that one of those two clocks aboard the train will not be in sync with a clock on the platform.

He's using the first point to illustrate the first postulate. He's not using the second point to illustrate the first postulate, he's instead using it to illustrate time dilation. You seem to be saying that he's using the first point to illustrate time dilation, but he's not.

 

[Physics_Teacher]

That would lead to paradoxes. Imagine a bomb triggered when those two clocks deviate from each other. Different frames would then disagree on whether the bomb goes off, or not. So this possibility is ruled out implicitly for consistency reasons.

Google gives a lot of results when enter: "time dilation" bomb paradox

The train folks have their Rolex and Light Clock, and platform folks have their own Rolex and Light Clock. All clocks on the platform and train were in sync when train was at rest on platform.

Suppose the Rolex and Light clock follow slightly different time dilation formulas. On the moving train Rolex and LightClock would go out of sync.

It would be true that each observer would see other's clocks as ticking at a slower rate than their own clock - whether comparing their Rolex or Light Clock. But it would not be true that to each observer the other's clock is out of sync.

In fact knowing the slightly different time dilation formulas, Formula-Rolex and Formula-LightClock, the platform folks would correctly calculate that the train's clocks would be out of sync. And the train folks would indeed see their clocks out of sync. The train folks, also knowing the different formulas, and calculating using the time on their clocks, would correctly calculate that the platform's clocks would be in sync.

If both the train and the platform had a bomb triggered when their two clocks deviate from each other, then both would agree that the train blows up and not the platform.

 

[Physics_Teacher]

If time dilation was to affect these two clock differently then by taking them to rest in other inertial frames you would first discover anisotropy(*), in some frames A would run faster than B, in others B would run faster than A, and yet in others A and B would run at the same rate.

It would still be true that each observer would see other's clock as ticking at a slower rate than their own clock - whether comparing their Rolex or Light Clock. There would be slightly different time dilation formulas, Formula-Rolex and Formula-LightClock. It is not haphazard as you suggest.

 

[Physics_Teacher]

If that were not the case then the absolute motion of the train could be detected.

Please explain in detail how "absolute motion of the train could be detected" if clocks did not stay in sync.

 

[Vitro]

It would still be true that each observer would see other's clock as ticking at a slower rate than their own clock - whether comparing their Rolex or Light Clock. There would be slightly different time dilation formulas, Formula-Rolex and Formula-LightClock. It is not haphazard as you suggest.

I did not mention any other observes, comparing clocks in relative motion or any time dilation formulas. Please read again and try to follow.

My analysis includes a single observer holding two clocks in his hand, which clocks supposedly would be affected differently by time dilation. This single observer compares the rates of these two clocks which are always mutually at rest, and at rest wrt the observer. He does this in the initial rest frame where the clocks are synchronized because they were created that way. He then changes speed, together with the clocks, in steps and in different directions and compares the rates of the same two clocks side by side (always at rest wrt each other and the observer but in different inertial frames). That's all it takes, no different observers, no comparing of clocks that are moving wrt each other, no time dilation formulas.

 

[A.T.]

The train folks have their Rolex and Light Clock, and platform folks have their own Rolex and Light Clock...

You complicate the issue and confuse yourself. Keep it simple:

Consider just two clocks, Rolex and Light Clock, both at rest on the platform, sitting right next to each other, on the bomb. If they stay in sync in the platform frame, the bomb doesn't go off. Since all frames must agree that the bomb doesn't go off, all frames must agree that they stay in sync. So there is no frame where the clocks have different time dilations.

 

[martinbn]

The point is that if the time dilation was different for the light clock and the rolex, then the principle of relativity would be false. Because a pair of a light clock and a rolex next to each other not moving with respect to each other on the platform would tick at the same rate. Another pair on the train would tick at a different rate. So how do you reconcile that with the relativity principle?

 

[Physics_Teacher]

You complicate the issue and confuse yourself. Keep it simple:

Consider just two clocks, Rolex and Light Clock, both at rest on the platform, sitting right next to each other, on the bomb. If they stay in sync in the platform frame, the bomb doesn't go off. Since all frames must agree that the bomb doesn't go off, all frames must agree that they stay in sync. So there is no frame where the clocks have different time dilations.

I explained and agree with what you state: "Since all frames must agree that the bomb doesn't go off, all frames must agree that they stay in sync."
"They" refers to the clocks on the platform.
But your conclusion "So there is no frame where the clocks have different time dilations" does not follow. We have different time dilations and yet all agree that the the clocks on the platform stay in sync. I explained that.

 

[Ibix]

You complicate the issue and confuse yourself. Keep it simple:

Consider just two clocks, Rolex and Light Clock, both at rest on the platform, sitting right next to each other, on the bomb. If they stay in sync in the platform frame, the bomb doesn't go off. Since all frames must agree that the bomb doesn't go off, all frames must agree that they stay in sync. So there is no frame where the clocks have different time dilations.

...the point being that someone else in motion relative to the clocks must see them as dilated. By different amounts, according to you, @Physics_Teacher.

Unless you are proposing that "the rest frame of the clock" is clock-specific, but that just raises the question of which frame you mean. The frame I used when I synchronised the clocks? The rest frame of the clocks when they were first synchronised? Or when they were last synchronised? What about if I change the function of the clock while it's working (e.g. add weight to the pendulum) - does that reset the frame? How does the clock record which is the correct frame?

Edit: note that you dump the principle of relativity unless you can answer that last question in operational terms: two identical clocks in identical states of motion function differently - why?

Edit 2: Never mind. You lose the principle of relativity whatever you do with this scheme, because you end up with the clocks behaving differently depending on whether I change speed or the clocks do.

 

[A.T.]

I explained and agree with what you state: "Since all frames must agree that the bomb doesn't go off, all frames must agree that they stay in sync."
"They" refers to the clocks on the platform.
But your conclusion "So there is no frame where the clocks have different time dilations" does not follow. We have different time dilations and yet all agree that the the clocks on the platform stay in sync. I explained that.

Let me rephrase for clarity:
There is no frame where the two clocks on the platform tick at different rates, compared with each other. So they must both obey the same time dilation formula in all frames.

 

[Herman Trivilino]

Please explain in detail how "absolute motion of the train could be detected" if clocks did not stay in sync.

You have two clocks on board the train. When the train is not moving the clocks stay in sync. But when the train is moving the clocks do not stay in sync.

 

[Dale]

Suppose the Rolex and Light clock follow slightly different time dilation formulas. On the moving train Rolex and LightClock would go out of sync.

It would be true that each observer would see other's clocks as ticking at a slower rate than their own clock - whether comparing their Rolex or Light Clock. But it would not be true that to each observer the other's clock is out of sync.

Do you have a reference that supports this claim? I doubt that there exist any "slightly different" time dilation formulas that satisfy the two postulates.

If different clock mechanisms had different time dilation then inertial frames where two clocks were manufactured (to be in sync) could be called "special frames" to these clocks; in other inertial frames these clocks could give different amounts of time dilation and fall out of sync. But there would be infinite "special frames" and this infinite family cannot rigorously be called preferred frames in terms of violating the Principle of Relativity.

And do you have any references supporting this claim?

 

[Physics_Teacher]

Do you have a reference that supports this claim? I doubt that there exist any "slightly different" time dilation formulas that satisfy the two postulates.
And do you have any references supporting this claim?

When I say: "Suppose the Rolex and Light clock follow slightly different time dilation formulas" I am addressing the argument (such as in Brian Greene book quoted by me) that First Postulate would be inconsistent with this case. I am not saying this IS the case - I am saying "Suppose" it was. I have never suggested that there exist "slightly different" time dilation formulas that satisfy the two postulates.

When I say "If different clock mechanisms had different time dilation..." I am again continuing discussion of whether "IF" this happened that would violate the First Postulate.

I had made it clear that I was not saying the Lorentz transformations have alternatives or suggesting that I have a reference that they do. I was discussing a narrow hypothetical situation based on "IF clocks gave different time dilation." Indeed Greene and others have discussed this, and I am addressing their discussion.

Please see my message that started this thread. There I wrote:

Note: I am asking ONLY in reference to *First Postulate being violated* if different clocks gave different time dilation, and use of THAT reasoning ALONE to conclude that all clocks must show the same time dilation. (I am aware of the Lorentz transformations and their derivation which show that all clocks have to give same time dilation).

 

[Dale]

When I say: "Suppose the Rolex and Light clock follow slightly different time dilation formulas" I am addressing the argument (such as in Brian Greene book quoted by me) that First Postulate would be inconsistent with this case. I am not saying this IS the case - I am saying "Suppose" it was.

I understand that, but even so your "suppose" needs to be self consistent. I strongly doubt that it is, hence the request for a reference. I think that your argument rests on inconsistent premises. It is common for the professional scientific literature to include suppositions, but they generally justify them carefully.

 

[Physics_Teacher]

I understand that, but even so your "suppose" needs to be self consistent. I strongly doubt that it is, hence the request for a reference. I think that your argument rests on inconsistent premises. It is common for the professional scientific literature to include suppositions, but they generally justify them carefully.

My reference is the discussion such as in the Greene book, which I quoted from. I think his suppose -- Suppose the Rolex and Light clock follow slightly different time dilation formulas -- is an acceptable suppose. I think this is a "self consistent" suppose. I don't know why you doubt it is. It is his "suppose" and not my original "suppose." I am following his "Suppose" and discussing his reasoning and the conclusion he reaches.

 

[Dale]

My reference is the discussion such as in the Greene book, which I quoted from.

This reference clearly does not support your argument. It also is not a professional scientific reference.

For clarity, I understand that you are supposing that a light clock and a Rolex may have different time dilation formulas and yet satisfy the principle of relativity. That is exactly the opposite of what Greene claims and that is what I am asking you to justify.

 

[Physics_Teacher]

This reference clearly does not support your argument. (It also is not a professional scientific reference)

I am trying to critically examine Greene's argument and reasoning that IF different clocks gave different time dilation THEN the First Postulate would be violated. Is it well-settled that it would? If so, I would appreciate a "professional scientific reference". I could ask Greene for a "professional scientific reference" but we know he does not have time to read most of the emails he gets - he said so himself.

 

[Ibix]

The principle of relativity says that the laws of physics are the same in any inertial frame. That means that a clock moving at half light speed in some frame must operate the same regardless of why it's traveling at half light speed - i.e., whether it accelerated or I did.

Have a rolex and a light clock on the platform, synchronised in that frame. Rig a bomb so that they explode if they are out of sync. Observed from this frame, then, they do not explode.

Now observe them from the train frame. If there is a different time dilation formula for the two clocks they now tick at different rates. They explode.

The proposal is inconsistent with the principle of relativity since different frames analysing the same system see different outcomes.

I think this is the full version of the argument A.T. has made several times.

 

[Herman Trivilino]

I am trying to critically examine Greene's argument and reasoning that IF different clocks gave different time dilation THEN the First Postulate would be violated. Is it well-settled that it would?

Yes. See Post #24. It's the direct response to the question you asked. Until you can understand that, or explain what it is about it that you don't understand, you'll never be satisfied with any of the responses you're getting here.

 

[Dale]

I would appreciate a "professional scientific reference".

Sure. Here is a college lecture where the argument is used:
https://www.coursera.org/learn/einstein-relativity/lecture/qRmOC/time-dilation

Here is a textbook where it uses the argument even before deriving time dilation in order to justify the use of a light clock in the first place
*link deleted, possible copyright violation*

And of course the Greene book which is not a professional source, but clearly makes the argument.

Now, please do not continue without posting references supporting your argument.

Edit: also
https://newt.phys.unsw.edu.au/einsteinlight/jw/module4_time_dilation.htm
http://faculty.tnstate.edu/louyang/teach/Phys2020/ppt/Walker3_Lecture_Ch29.ppt

 

[Physics_Teacher]

Sure. Here is a college lecture where the argument is used:
https://www.coursera.org/learn/einstein-relativity/lecture/qRmOC/time-dilation

Here is a textbook where it uses the argument even before deriving time dilation in order to justify the use of a light clock in the first place
http://web.pdx.edu/~pmoeck/books/Tipler_Llewellyn.pdf

And of course the Greene book which is not a professional source, but clearly makes the argument.

Dale, appreciate the effort you made. Will look at these carefully and post here whether all is now clear or will specify I have further doubt regarding the arguments they make. As per our correspondence, I want to keep within the rules of the forum.

 

[Physics_Teacher]

Sure. Here is a college lecture where the argument is used:
https://www.coursera.org/learn/einstein-relativity/lecture/qRmOC/time-dilation

Here is a textbook where it uses the argument even before deriving time dilation in order to justify the use of a light clock in the first place
http://web.pdx.edu/~pmoeck/books/Tipler_Llewellyn.pdf

And of course the Greene book which is not a professional source, but clearly makes the argument.

Now, please do not continue without posting references supporting your argument.

Edit: also
https://newt.phys.unsw.edu.au/einsteinlight/jw/module4_time_dilation.htm
http://faculty.tnstate.edu/louyang/teach/Phys2020/ppt/Walker3_Lecture_Ch29.ppt

I have looked over the links. I did not find anywhere an argument that IF clocks have different time dilation THEN one would be able to Detect Absolute Motion. Absolute Motion (to me at least, see my post #11) is needed to violate the First Postulate.
(There never was a doubt that "motion" could be detected if clocks have have different time dilation)
I will leave it at that, given the rules imposed against my making further argument that the First Postulate is not violated in this situation.

I was never attempting an argument against time dilation being same for all clocks - was only examining the claim that First Postulate would be violated it were not.

 

[Herman Trivilino]

(There never was a doubt that "motion" could be detected if clocks have have different time dilation)

If it's possible to detect motion then it's possible to detect the absence of motion. For example, if you can detect that the train is moving then you can, by definition, determine when it's not moving. Otherwise your detection of it moving is meaningless and not physical. Having an ability to detect motion and its absence is what is meant by the detection of absolute motion.

 

[Dale]

I did not find anywhere an argument that IF clocks have different time dilation THEN one would be able to Detect Absolute Motion.

Are you looking for exactly that phrasing? Sorry, that is silly. Whether they express it as "if ... then ..." or otherwise, or if they call it "the first postulate" or the "principle of relativity" is simply a matter of style. Please read and understand the substance of the argument and don't require other authors to make exactly the same stylistic choices you would make.

Can you yet present an author who agrees with the substance of your argument?

 

[Physics_Teacher]

Are you looking for exactly that phrasing? Sorry, that is silly. Whether they express it as "if ... then ..." or otherwise, or if they call it "the first postulate" or the "principle of relativity" is simply a matter of style. Please read and understand the substance of the argument and don't require other authors to make exactly the same stylistic choices you would make.

I was never worrying about phrasing such as "if ... then ..." or otherwise, or if they call it "the first postulate" or the "principle of relativity." Quoting what I said: "I did not find anywhere an argument that IF clocks have different time dilation THEN one would be able to Detect Absolute Motion."

Can you yet present an author who agrees with the substance of your argument?

The first postulate is from Galilean relativity. All physics authors over the centuries have talked of First Postulate and preferred frames strictly in terms of experiments that can Detect Absolute Motion; the exceptions are a handful recent authors today, such as Brian Greene, who say knowing just that a train is in "motion" (not specifying Absolute Motion) would violate First Postulate. I believe Einstein would never have agreed with such reduction of the First Postulate, and the second postulate is needed to establish (Lorentz transformations derivation) that all clocks must have same time dilation.

 

[Ibix]

I believe Einstein would never have agreed with such reduction of the First Postulate, and the second postulate is needed to establish (Lorentz transformations derivation) that all clocks must have same time dilation.

No, for reasons already stated.

 

[Dale]

knowing just that a train is in "motion" (not specifying Absolute Motion)

Again, this is a stylistic choice. Saying that something is "in motion" without a specified reference frame or reference object is the same as "Absolute Motion". Why should you demand that he use your words?

 

[Justintruth]

The classical laws of mechanics define an inertial frame of reference as one where Newtons law of inertia holds.

The classical transformation laws show that any frame of reference moving relative to an inertial frame of reference with constant velocity will also be an inertial frame of reference.

The classical laws of electromagnetism (Maxwell's equations) predict that electromagnetic waves (light) moves at c relative to any inertial frame of reference.

So we have a contradiction because if I take the velocity of a light pulse relative to some inertial frame of reference, and apply the classical transformation equations to transform the speed of light to another inertial frame moving relative to the first, I get a speed of the light wave relative to the second that is different than c as measured relative to the first.

But Maxwell's equations predict that the speed of the light will be c relative to both frames. That is the contradiction.

This can easily be solve by asserting that Maxwell's equations apply only in one frame and that in all others they do not apply. We call the frame in which they apply "privileged".

Einstein showed that if, instead of assuming that the classical laws of electromagnetism are wrong, and there are privileged frames, you assume they are right, at least as far as they predict that light will travel at c relative to any frame moving at constant velocity relative to some frame of reference where it travels at c, then you get transformation equations that contradict the classical transformation laws, and you get the rest of the theory.

You cannot take the principle of relativity to imply that light moves relative to any frame at c. For example you can have a world in which there are two photons, one at rest in one frame, and the other at rest relative to some other inertial frame. The first photon moves in the second frame and the second photon moves relative to the first. That is a consistent theory in which the principle of relativity holds because the laws are the same in both frames, but the principle of the constancy of the speed of light does not hold, because for either single photon the velocity relative to each of the two frames is different. But in fact the first principle does not even imply constant velocity of light, or even the existence of light.

I think that Greene meant that if you use classical theory then you cannot base a clock on the motion of light (say one second is *defined* to be the time light takes to cover 186,000 miles) because if you measure two such clocks, they will disagree depending on the different light velocities in a given frame. By classical *definition* two clocks must agree.

The principle of relativity does not imply any set of physical laws.

Orodruin wrote: "I created this thread to *rigorously* examine the claim, such as in Brian Greene's book, that principle of relativity prohibits different clock mechanisms from having different time dilation. I emphasize "rigorously."" [Mentor's note: Orodruin didn't write that, the original poster did]

Rigorously the principle of relativity does not prohibit different clock mechanisms from having different time dilation. The definition of a "clock" in classical mechanics does. It does by definition. Time is absolute by assumption and clocks by definition measure it so if one clock has any dilation of any kind relative to another then one of them is wrong. Not so in Einstein's theory. If you have a theory that allows time dilation of one class of clocks over another and this theory holds in each frame then you are consistent with the principle of relativity. If for example you take two different frequencies of photons and define time by them and assume either classical or relativistic Doppler effect then you have a consistent theory in which the laws are the same in each frame but clocks disagree with each other. There is dilation of one set relative to the first and contraction otherwise. Then you just make the laws of physics depend on which type of clock you have and you have a consistent theory. It fails because of it's complexity but it is logically rigorous.

I don't think Green meant that the principle of relativity prohibits different clock mechanisms from having different time dilation. It does not. It is silent on the definition of time and on clocks. However, if you use the classical definition of time and clocks then you cannot have time dilation of one clock relative to another when measured in the same units. If you add the Newtonian transformations and ask where can Maxwell's laws hold you get the answer "only in one class of frames (stationary relative to each other, inertial, etc)" and you can call these frames "privileged".

 

[Dale]

If you have a theory that allows time dilation of one class of clocks over another and this theory holds in each frame then you are consistent with the principle of relativity.

I will ask the same thing of you that I asked of the OP. Do you have a reference that supports this claim (that this set of premises is self consistent)? I do not think this is a self consistent premise.

 

[Herman Trivilino]

Time is absolute by assumption and clocks by definition measure it

Metrologists don't assume clocks measure time, they demonstrate it. The amount of time measured by clocks will differ, but the smaller the amount they differ by the better the demonstration of their validity. Currently the best clocks differ by a second in several billion years. This amount that they differ by doesn't change when they don't move relative to each other, but it does change when they do.

 

[Herman Trivilino]

Metrologists don't assume clocks measure time, they demonstrate it. The amount of time measured by clocks will differ, but the smaller the amount they differ by the better the demonstration of their validity. Currently the best clocks differ by a second in several billion years. This amount that they differ by doesn't change when they don't move relative to each other, but it does change when they do.

So if you have two clocks on a moving train, they stay in sync with each other (within that one second per a few billions of years) because they are not moving relative to each other. When we compare them to a stationary clock on the platform they therefore show the same amount of time dilation. That is the point made by Greene that was mentioned in the original post.

There is nothing more to it and I don't understand why it's such a big deal to some people to learn that absolute motion can't be detected. This has been known and well-understood for more than a century. If our understanding of it were incorrect many of our modern technologies wouldn't work, the most outstanding example being the global positioning system (GPS).

 

[Nugatory]

You cannot take the principle of relativity to imply that light moves relative to any frame at c.

Which is to say that Einstein's second postulate is necessary. We've had a number of threads on this question over the years. However...

For example you can have a world in which there are two photons, one at rest in one frame, and the other at rest relative to some other inertial frame. The first photon moves in the second frame and the second photon moves relative to the first. That is a consistent theory in which the principle of relativity holds because the laws are the same in both frames,

How are the laws the same in both frames? Maxwell's laws of electrodynamics cannot hold in both frames, because they they have no solution in which a flash of light in vacuum is moving at any speed except $c$. To maintain consistency with the principle of relativity you would have to propose some other laws of electromagnetism, ones that are consistent with a frame-dependent speed of light.

 

[Herman Trivilino]

How are the laws the same in both frames? Maxwell's laws of electrodynamics cannot hold in both frames, because they they have no solution in which a flash of light in vacuum is moving at any speed except $c$. To maintain consistency with the principle of relativity you would have to propose some other laws of electromagnetism, ones that are consistent with a frame-dependent speed of light.

To qualify as laws they'd have to explain Nature's behavior. Makes me wonder why anyone would bother proposing explanations of Nature's behavior that are inconsistent with the way Nature behaves. Seems torturous, or at the very least uncomfortable.

 

[Justintruth]

I will ask the same thing of you that I asked of the OP. Do you have a reference that supports this claim (that this set of premises is self consistent)? I do not think this is a self consistent premise.

Which is to say that Einstein's second postulate is necessary. We've had a number of threads on this question over the years. However...
How are the laws the same in both frames? Maxwell's laws of electrodynamics cannot hold in both frames, because they they have no solution in which a flash of light in vacuum is moving at any speed except $c$. To maintain consistency with the principle of relativity you would have to propose some other laws of electromagnetism, ones that are consistent with a frame-dependent speed of light.

From Einstein's paper "The Foundation of the General Theory of Relativity" 1916

http://hermes.ffn.ub.es/luisnavarro/nuevo_maletin/Einstein_GRelativity_1916.pdf

"If a system of co-ordinates K is chosen so that, in relation to it, physical laws hold good in their simplest form, the same laws also hold good in relation to any other system of co-oordinates K’ moving in uniform translation relatively to K. This postulate we call the “special principle of relativity”"

The principle of relativity, as stated above by Einstein, is silent on optics. You cannot derive from the principle of relativity anything about optics, electricity and magnetism, or clocks other than if you have a theory of them valid in one frame then it must be valid in other frames.

Orodruin wrote: "I created this thread to *rigorously* examine the claim, such as in Brian Greene's book, that principle of relativity prohibits different clock mechanisms from having different time dilation. I emphasize "rigorously."" [Mentor's note: Orodruin didn't write that, the original poster did]

The principle of relativity as quoted above does not prohibit different clock mechanisms from having different time dilation:

Consider two clock mechanisms C1 and C2 and assume that relative to a system of co-ordinates K there is some law that says that the time dilation of clocks of type C1 is some function f() and the the time dilation of clocks of type C2 is some function g() such that f() is not equal to g(). Suppose further that both f'() and g'() are the functions that govern the dilation in some frame K'. Further suppose f()=f'() and g()=g'(). Then these laws are consistent with the special principle of relativity and they predict that time dilation be different for different clock mechanisms. As a concrete example let f()=2*g() and let delta t'=v * delta t.

In theoretical work it is important to trace logically to the assumptions involved. Orodruin wanted a "rigorous" examination of a certain claim that the principle of relativity prohibits different clock mechanisms from having different time dilation. As long as you propose a theory that says that if different clock mechanisms do have different time dilation in one frame, and that same situation is present relative to all frames moving with constant velocity relative to the first, then the principle of relativity holds.

So the principle of relativity as stated by Einstein does not prohibit different clock mechanisms from having different time dilation.

A more interesting question is whether the meaning of time itself prohibits it. Certainly if all mechanisms had different dilation then the notion of time itself would not be very useful. One might say of such a world, that clocks don't exist. However, setting optics aside, if all mechanisms operated according to Newtonian mechanics except one then the concept of time would be useful and a theory could be constructed that was consistent with the principle of relativity.

That this world is counterfactual is not a problem as it is only being cited to illustrate the absence of logical dependence of conclusions about clocks (or optics, or electromagnetism) on the principle of relativity as stated by Einstein. Counterfactual arguments are routinely used to illustrate lack of logical dependence.

As a historical note, the principle of relativity in Einstein's 1903 paper was restricted to electricity and magnetism. So in a sense he generalized the principle in 1917 not only by making laws invariant relative to more general coordinate transformations, but technically he also expanded the principle to apply to physical laws in general.

 

[Justintruth]

To qualify as laws they'd have to explain Nature's behavior. Makes me wonder why anyone would bother proposing explanations of Nature's behavior that are inconsistent with the way Nature behaves. Seems torturous, or at the very least uncomfortable.

The reason that it is neither "torturous nor uncomfortable" is that it is only being used to show an absence of logical dependence. It is not being proposed as a candidate for experimental confirmation.

If I were to say, "All women wear dresses. This person is wearing a dress. Therefore this person is a woman". You might be inclined to say "What if your father wore a dress?" without even blushing over the fact that he never did. It illustrates the flaw in the derivation.

 

[Ibix]

Consider two clock mechanisms C1 and C2 and assume that relative to a system of co-ordinates K there is some law that says that the time dilation of clocks of type C1 is some function f() and the the time dilation of clocks of type C2 is some function g() such that f() is not equal to g(). Suppose further that both f'() and g'() are the functions that govern the dilation in some frame K'. Further suppose f()=f'() and g()=g'(). Then these laws are consistent with the special principle of relativity and they predict that time dilation be different for different clock mechanisms. As a concrete example let f()=2*g()

What, exactly, does that mean? The time dilation factor at rest must be 1 or else the clock is time dilated at rest. In this scheme, assuming that $f$ and $g$ are playing the role of a generalisation of Lorentz's $\gamma$, one or other clock is time dilated at rest. Unless you mean that $f$ and $g$ are the decrease in clock rate? That is, assuming $f$ in vanilla special relativity would be $1/\gamma-1$. But in that case this scheme is inconsistent with the principle of relativity since it's trivial to set up a scheme where the clocks continue to work in their rest frame but fail in any moving frame.

 

[Dale]

You cannot derive from the principle of relativity anything about optics, electricity and magnetism, or clocks

This is not true.

The principle of relativity as quoted above does not prohibit different clock mechanisms from having different time dilation:

This is precisely the point that you were asked to support with a reference. I do not think this is true, and I have not seen any reference supporting this claim.

the time dilation of clocks of type C1 is some function f() and the the time dilation of clocks of type C2 is some function g() such that f() is not equal to g(). Suppose further that both f'() and g'() are the functions that govern the dilation in some frame K'. Further suppose f()=f'() and g()=g'().

I doubt that all of these "suppose"s are self consistent.

That this world is counterfactual is not a problem ... Counterfactual arguments are routinely used to illustrate lack of logical dependence.

Agreed. But even a counterfactual argument must be self consistent. Despite the routine use of counterfactual arguments in the literature, this specific argument does not appear, leading me to believe it is not merely counterfactual but is not even self consistent.