Question about Brian Greene's book

[ghwellsjr]

Brian Greene has a good discussion of the light clock on pages 37-41 of his book The Elegant Universe (if you read this section on google books you may want to start on page 28 where he first outlines the basic principles of relativity).

Brian Greene does have a good discussion about a light clock but earlier he describes starting on page 34 a story about the secretary-general of the UN attempting to resolve conflicts between warring nations by having their presidents simultaneously sign peace accords when a flash of light in the center of their table is viewed by each president sitting at opposite ends of the table. It doesn't work when the signing takes place on a moving train because the residents of the two nations on the ground outside the moving train can see that the signings do not take place simultaneously.

My question: what is it that Brian Greene is claiming that the residents actually see that convinces them that the signings are not simultaneous?

 

[JesseM]

Brian Greene does have a good discussion about a light clock but earlier he describes starting on page 34 a story about the secretary-general of the UN attempting to resolve conflicts between warring nations by having their presidents simultaneously sign peace accords when a flash of light in the center of their table is viewed by each president sitting at opposite ends of the table. It doesn't work when the signing takes place on a moving train because the residents of the two nations on the ground outside the moving train can see that the signings do not take place simultaneously.

My question: what is it that Brian Greene is claiming that the residents actually see that convinces them that the signings are not simultaneous?

Since the light from the center must travel at the same speed in both directions in the frame of the residents on the ground, but the back of the train is moving towards the position the flash was set off while the front is moving away from that position, they must see (or more accurately, measure in the coordinates of their frame) that the light reached the back of the train before the front. For example, if they had synchronized clocks at various positions on the ground and took photos of each president signing the treaty as that president passed right next to one of the clocks, then the photo of the president at the back of the train would show the nearby clock displaying an earlier time than the clock in the photo of the president at the front.

 

[ghwellsjr]

Since the light from the center must travel at the same speed in both directions in the frame of the residents on the ground, but the back of the train is moving towards the position the flash was set off while the front is moving away from that position, they must see (or more accurately, measure in the coordinates of their frame) that the light reached the back of the train before the front. For example, if they had synchronized clocks at various positions on the ground and took photos of each president signing the treaty as that president passed right next to one of the clocks, then the photo of the president at the back of the train would show the nearby clock displaying an earlier time than the clock in the photo of the president at the front.

Well, yes, if they had synchronized clocks, etc, but Brian Greene specifically states that the secretary-general is "Familiar with the fact that the laws of physics take precisely the same form regardless of one's state of motion" but he apparently isn't aware of the issue of relativity of simultaneity or the need to synchronize clocks because later Brian Greene says "When CNN broadcasts the eyewitness account, the secretary-general, and the two presidents, and all the advisers [on the train] can't believe their ears". So I don't think the residents of the two warring nations are aware of the need to synchronize their clocks in order to be eyewitnesses that could claim that the two presidents signed their peace accords at different times.

Brian Greene has made no mention of the need to synchronize clocks in either frame, the train frame or the ground frame, in order to conclude that the two presidents signed at the same time in the train frame or at different times in the ground frame. In fact, earlier, he specifically states that the one-way speed of light has been measured to be a constant, as opposed to being defined as a constant in Special Relativity. He talks about measuring the speed of approaching photons as if it could actually be done. He never points out that we cannot measure or know the one-way speed of light or the time it takes for light to travel a given distance. He never points out that we can only measure the average round-trip speed of light and that Special Relativity arbitrarily defines the one-way speed of light to be equal to the average of the round-trip speed of light.

To someone already way up on the Special Relativity learning curve, Brian Greene's explanations might make sense, but to his intended audience of learners, I think he has left out some very important preliminary steps.

 

[JesseM]

Well, yes, if they had synchronized clocks, etc, but Brian Greene specifically states that the secretary-general is "Familiar with the fact that the laws of physics take precisely the same form regardless of one's state of motion" but he apparently isn't aware of the issue of relativity of simultaneity or the need to synchronize clocks because later Brian Greene says "When CNN broadcasts the eyewitness account, the secretary-general, and the two presidents, and all the advisers [on the train] can't believe their ears". So I don't think the residents of the two warring nations are aware of the need to synchronize their clocks in order to be eyewitnesses that could claim that the two presidents signed their peace accords at different times.

It's a humorous illustration of how simultaneity differs in a frame-dependent way, it would simply become more confusing and pedantic if he gave the exact details of how the ground observers measured simultaneity. You're free to also imagine they had a camera whose position coincided with the midpoint of the train at the moment the light from the president at the back signing the document reached the camera, for example.

In fact, earlier, he specifically states that the one-way speed of light has been measured to be a constant, as opposed to being defined as a constant in Special Relativity.

And that's true, it has. You can test it by using the slow transport method of clock synchronization, see my comment [post=2936648]here[/post]--if the laws of physics weren't Lorentz-symmetric this could lead to an observation of an asymmetry in the one-way speed even if the two-way speed were constant.

He never points out that we can only measure the average round-trip speed of light and that Special Relativity arbitrarily defines the one-way speed of light to be equal to the average of the round-trip speed of light.

Not arbitrary, it's the only way to get a set of coordinate systems where the equations of the laws of physics are the same in each one, reflecting the physical fact that the laws of physics are Lorentz-symmetric.

 

[Saw]

And that's true, it has. You can test it by using the slow transport method of clock synchronization, see my comment [post=2936648]here[/post]--if the laws of physics weren't Lorentz-symmetric this could lead to an observation of an asymmetry in the one-way speed even if the two-way speed were constant.

Not arbitrary, it's the only way to get a set of coordinate systems where the equations of the laws of physics are the same in each one, reflecting the physical fact that the laws of physics are Lorentz-symmetric.

Let me check first if I understand well what is meant when the SCT method is invoked:

- To synchronize two distant clocks what you do is (i) synchronizing them when they are together and (ii) then moving one of them away, either slowly or quickly.
- No matter the speed of the transportation, the result is always, according to experiments, the same as if the clocks had been always apart from each other and had been synchronized through light signals, through the Einstein convention. In their rest frame, the clocks are deemed to be synched and in all others they are deemed to be out-of-sync by the factor predicted by SR. Likewise, clocks synchronized this way measure the speed of light to be c.
- What is meant by “slow” is that even if the transportation were extremely slow, with the speed of the clock approaching zero, there would still exist some minimal time dilation which –extended over the almost infinite time required for the operation- would account for the above mentioned result.

Is this correct?

Anyhow…

It's a humorous illustration of how simultaneity differs in a frame-dependent way, it would simply become more confusing and pedantic if he gave the exact details of how the ground observers measured simultaneity. You're free to also imagine they had a camera whose position coincided with the midpoint of the train at the moment the light from the president at the back signing the document reached the camera, for example.

Still, with all respect for Brian Greene, I think that ghwellsjr is right in his criticism.

Ok, your comment is that “how simultaneity is measured” is indifferent in the sense that it must always give the same result, whether you use a round trip of light (like in Einstein convention) or SCT method or any other. Agreed. Yet to specify that the result is what it is because of the need to carry out some physical procedure, whatever it is, to synchronize clocks is not redundant. Maybe the detailed development is not necessary, but to mention this principle would not be “pedantic”. On the contrary, it is a must to make the illustration useful instead of misleading.

Greene’s illustration is not good because it does not make the meaning of SR shine up and easier to understand, instead it obscures such meaning: he gives the impression that the two frames can be right in giving two dissenting solutions to the practical problem at hand, which is absurd.

I have little physics (and I had even less when I read the similar “duel example” that Greene uses in his other book, The Fabric of the Cosmos) but his approach immediately struck me as unacceptable.

This made suspicious of SR until I read the direct sources (Einstein himself) and I realized that what he did was advocating that concepts (like simultaneity) be built, precisely, not in an “a priori” way, but based on the actual physical method used for their construction and on its empirical outcome. If we do this, we notice that whatever the method used for making a judgment about simultaneity (Einstein synch convention, SCT or whatever), the result is different in each frame, because it is conditioned by its physical “perspective” (in this case, its state of motion), but of course that only means what it means: different frames make different descriptions because they describe different things! However, when they try to describe the same thing, they must agree. Otherwise one of them is wrong.

In the Elegant Universe’ example, ground and train frame should of course dissent as to whether the signatures were simultaneous, but they should both admit that this disagreement is, for practical purposes, irrelevant. Alternatively, Greene could have made a much better (and still amusing) illustration of SR by pointing out, that in spite of their discrepancy on an instrumental concept (simultaneity), both frames should agree on the solution to the ultimate practical problem.

What is the problem here? The example chosen by Greene is not very fortunate, because it is difficult to find any reason why the involved parties should care about whether the signature was simultaneous or not. He made a better choice in the duel example of the Fabric of the Cosmos, where the question is whether the duel is fair. We discussed this in other threads and I think you agreed, but I always appreciate your comments.

 

[JesseM]

Let me check first if I understand well what is meant when the SCT method is invoked:

- To synchronize two distant clocks what you do is (i) synchronizing them when they are together and (ii) then moving one of them away, either slowly or quickly.
- No matter the speed of the transportation, the result is always, according to experiments, the same as if the clocks had been always apart from each other and had been synchronized through light signals, through the Einstein convention. In their rest frame, the clocks are deemed to be synched and in all others they are deemed to be out-of-sync by the factor predicted by SR. Likewise, clocks synchronized this way measure the speed of light to be c.
- What is meant by “slow” is that even if the transportation were extremely slow, with the speed of the clock approaching zero, there would still exist some minimal time dilation which –extended over the almost infinite time required for the operation- would account for the above mentioned result.

Is this correct?

It's true that if you move them apart symmetrically in your rest frame, they will stay synchronized in your frame regardless of the speed you move them apart, but the idea of "slow transport" is that even if you don't move them symmetrically--even if you just leave one clock at rest where it was and move the other away slowly, for example--in the limit as the ratio between the speed of the clock and c approaches zero, the clocks will still be synchronized at the end of the transport, regardless of how great the distance you moved them apart (and of course for a given slow speed, the greater the distance the greater the time at least one clock was being moved). I gave a simple derivation for the case of moving one clock while leaving the other clock at rest in [post=2937771]this post[/post].

Ok, your comment is that “how simultaneity is measured” is indifferent in the sense that it must always give the same result, whether you use a round trip of light (like in Einstein convention) or SCT method or any other. Agreed. Yet to specify that the result is what it is because of the need to carry out some physical procedure, whatever it is, to synchronize clocks is not redundant. Maybe the detailed development is not necessary, but to mention this principle would not be “pedantic”. On the contrary, it is a must to make the illustration useful instead of misleading.

Greene’s illustration is not good because it does not make the meaning of SR shine up and easier to understand, instead it obscures such meaning: he gives the impression that the two frames can be right in giving two dissenting solutions to the practical problem at hand, which is absurd.

I don't know what you mean by "can be right" here. Both answers are right in the context of frame-dependent facts in each frame, but if you're talking about some sort of "objective" frame-dependent rightness, then in relativity there are no frame-independent facts about simultaneity one way or another.

In the Elegant Universe’ example, ground and train frame should of course dissent as to whether the signatures were simultaneous, but they should both admit that this disagreement is, for practical purposes, irrelevant. Alternatively, Greene could have made a much better (and still amusing) illustration of SR by pointing out, that in spite of their discrepancy on an instrumental concept (simultaneity), both frames should agree on the solution to the ultimate practical problem.

What is the problem here? The example chosen by Greene is not very fortunate, because it is difficult to find any reason why the involved parties should care about whether the signature was simultaneous or not. He made a better choice in the duel example of the Fabric of the Cosmos, where the question is whether the duel is fair. We discussed this in other threads and I think you agreed, but I always appreciate your comments.

As I recall I was uncomfortable with the idea of invoking the subjective human notion of "fairness" in a physics problem, though I suppose if you add that both parties have agreed in advance to define "fairness" in a certain physically well-defined way, then it does become just a "practical problem" to decide whether a given physical setup is "fair" according to that definition.

 

[ghwellsjr]

In fact, earlier, he specifically states that the one-way speed of light has been measured to be a constant, as opposed to being defined as a constant in Special Relativity.

And that's true, it has. You can test it by using the slow transport method of clock synchronization, see my comment [post=2936648]here[/post]--if the laws of physics weren't Lorentz-symmetric this could lead to an observation of an asymmetry in the one-way speed even if the two-way speed were constant.

Although it is true that the slow transport method of clock synchronization will yield the same result as any other legitimate method of clock synchronization in the rest frame of an observer, it also yields the same result for a second observer that is moving in that same frame and in which the first observer, according to SR, concludes that the two one-way times for light to travel a round trip for the second observer are not equal and so it can't distinguish between the two situations.

In other words, a light-clock that is being transported is performing a round-trip speed of light timing in which the one-way timings cannot be determined and moving it from one location to the other is no different than have a much larger light-clock that we are trying to decide on the two one-way timings.

 

[JesseM]

Although it is true that the slow transport method of clock synchronization will yield the same result as any other legitimate method of clock synchronization in the rest frame of an observer, it also yields the same result for a second observer that is moving in that same frame and in which the first observer, according to SR, concludes that the two one-way times for light to travel a round trip for the second observer are not equal and so it can't distinguish between the two situations.

In other words, a light-clock that is being transported is performing a round-trip speed of light timing in which the one-way timings cannot be determined and moving it from one location to the other is no different than have a much larger light-clock that we are trying to decide on the two one-way timings.

You're talking about what's true in SR where the laws of physics are Lorentz-symmetric. When I say that the one-way speed of light can be tested, what I mean is that there are SR-violating, non-Lorentz-symmetric theories where the two-way speed of light would still be constant, but clocks synchronized by the slow transport method would find a non-isotropic speed in different directions. Using actual clocks synchronized by the slow transport method, we can test whether SR's predictions or the predictions of one of these alternate theories are correct, and that's what I mean by measuring the one-way speed of light.

 

[Saw]

It's true that if you move them apart symmetrically in your rest frame, they will stay synchronized in your frame regardless of the speed you move them apart, but the idea of "slow transport" is that even if you don't move them symmetrically--even if you just leave one clock at rest where it was and move the other away slowly, for example--in the limit as the ratio between the speed of the clock and c approaches zero, the clocks will still be synchronized at the end of the transport, regardless of how great the distance you moved them apart (and of course for a given slow speed, the greater the distance the greater the time at least one clock was being moved). I gave a simple derivation for the case of moving one clock while leaving the other clock at rest in [post=2937771]this post[/post].

Ah, it seems I was misunderstanding SCT.

I have always referred to the situation where one clock A remains still and only the other B is transported away.

What I now understand about this is the following:

- B becomes unsynchronized, i.e. it acquires an “error”.
- To the extent that the speed of transport approaches zero (“slow transport”), the error is minimized.
- SR predicts the amount of the error or quasi-non-error in the case of slow transport (that is your derivation).
- Other alternative theories don’t make that prediction and so can be experimentally falsified by demonstrating that things happen as predicted by SR.

Is that correct?

I don't know what you mean by "can be right" here. Both answers are right in the context of frame-dependent facts in each frame, but if you're talking about some sort of "objective" frame-dependent rightness, then in relativity there are no frame-independent facts about simultaneity one way or another.

When I used the expression “can be right”, it was in this sentence: “he gives the impression that the two frames can be right in giving two dissenting solutions to the practical problem at hand, which is absurd.”

I did not say that there is a judgment on simultaneity that is more right than others. I perfectly assume that simultaneity is a relative, frame-dependent concept. I only said that the practical solution to a practical problem cannot be frame-dependent.

As I recall I was uncomfortable with the idea of invoking the subjective human notion of "fairness" in a physics problem, though I suppose if you add that both parties have agreed in advance to define "fairness" in a certain physically well-defined way, then it does become just a "practical problem" to decide whether a given physical setup is "fair" according to that definition.

Well, I could try again to convince you that “fairness” is as much a “legal” as a “physical” concept, but I am not sure you are interested in that and in any case it might be off-thread, unless the OP gets interested in the subject.

Although it is true that the slow transport method of clock synchronization will yield the same result as any other legitimate method of clock synchronization in the rest frame of an observer, it also yields the same result for a second observer that is moving in that same frame and in which the first observer, according to SR, concludes that the two one-way times for light to travel a round trip for the second observer are not equal and so it can't distinguish between the two situations.

In other words, a light-clock that is being transported is performing a round-trip speed of light timing in which the one-way timings cannot be determined and moving it from one location to the other is no different than have a much larger light-clock that we are trying to decide on the two one-way timings.

I do not follow you here. I am still trying to understand SCT but certainly I do not think that it is a proof that the one-way speed of light is the same in all directions *as measured by an absolute clock*, since obviously a clock that gives the same result (or almost) as one synched with the Einstein convention is not an “absolute clock”. Is that more or less coincident with what you point at?

 

[ghwellsjr]

- Other alternative theories don’t make that prediction and so can be experimentally falsified by demonstrating that things happen as predicted by SR.

LET is an alternative theory that does make the same predictions as SR but in which the one-way speed of light is c only in the presummed absolute ether rest frame, all observers moving with respect to the ether experience time dilation and length contraction which cause them to get the same results in all experiments that they would have gotten if they were at rest with respect to the ether. If SR cannot be experimentally falsifed, then LET cannot be experimentally falsified either.

 

[Saw]

LET is an alternative theory that does make the same predictions as SR but in which the one-way speed of light is c only in the presummed absolute ether rest frame, all observers moving with respect to the ether experience time dilation and length contraction which cause them to get the same results in all experiments that they would have gotten if they were at rest with respect to the ether. If SR cannot be experimentally falsifed, then LET cannot be experimentally falsified either.

Yes, I think JesseM referrred to alternative theories other than LET.

 

[JesseM]

LET is an alternative theory that does make the same predictions as SR but in which the one-way speed of light is c only in the presummed absolute ether rest frame, all observers moving with respect to the ether experience time dilation and length contraction which cause them to get the same results in all experiments that they would have gotten if they were at rest with respect to the ether. If SR cannot be experimentally falsifed, then LET cannot be experimentally falsified either.

There are different variants of what people mean by "Lorentz Ether Theory", but I would say that the version of LET that's truly indistinguishable from SR should not really be called an alternate "theory" at all, rather it is a different "interpretation" of SR akin to the different interpretations of QM. Distinct scientific theories should at least in principle make different predictions of some kind!