Contradiction in Relativistic Simultaneity in Taylor-Wheeler Spacetime Physics?

[GregAshmore]

In figure 3-1 (page 63) of Taylor and Wheeler's Spacetime Physics, the observer on the train determines that the lightning strikes are not simultaneous because the flashes do not reach her simultaneously.

I see two problems with this.

1. The narrative in figure 3-1 contradicts the text in section 2.7 (pg 39): "Location and time of each event is recorded by the clock nearest to that event." The time of the lighting strike at the front of the train should be recorded by a clock at the front of the train. Likewise, the time of the strike at the rear of the train should be recorded by a clock at the rear of the train. The procedure used in figure 30-1 will lead to incorrect results, as stated in 2.7: "We do not permit the observer to report on widely separated events that he himself views by eye. The reason: The travel time of light."

2. The claim that the observer on the train will see the front flash first is based on a view from the embankment. There is no assurance that the view from inside the train will match the view from the embankment--indeed the exercise is intended to determine whether this is so. For comparison, consider the scene proposed by Menzel in his derivation of the equation of special relativity. A flash of light occurs at the instant a rocket ship (or train) passes a point on Earth. The sphere of the light has two apparent centers: One center (for the observer on earth) is at the point on Earth where the emission was observed; the other center (for the observer on the rocket) is at the point on the rocket where the emission was observed. Of course, these two centers separate with the velocity of the rocket ship. By this reasoning, the two light flashes on the train will reach the observer in the center of the train simultaneously.

Comments?

 

[Doc Al]

1. The narrative in figure 3-1 contradicts the text in section 2.7 (pg 39): "Location and time of each event is recorded by the clock nearest to that event." The time of the lighting strike at the front of the train should be recorded by a clock at the front of the train. Likewise, the time of the strike at the rear of the train should be recorded by a clock at the rear of the train. The procedure used in figure 30-1 will lead to incorrect results, as stated in 2.7: "We do not permit the observer to report on widely separated events that he himself views by eye. The reason: The travel time of light."

I don't see any issue here. As long as the observer takes into account the light travel time, his conclusions will match those of co-moving clocks at the location of the events.

2. The claim that the observer on the train will see the front flash first is based on a view from the embankment. There is no assurance that the view from inside the train will match the view from the embankment--indeed the exercise is intended to determine whether this is so. For comparison, consider the scene proposed by Menzel in his derivation of the equation of special relativity. A flash of light occurs at the instant a rocket ship (or train) passes a point on Earth. The sphere of the light has two apparent centers: One center (for the observer on earth) is at the point on Earth where the emission was observed; the other center (for the observer on the rocket) is at the point on the rocket where the emission was observed. Of course, these two centers separate with the velocity of the rocket ship. By this reasoning, the two light flashes on the train will reach the observer in the center of the train simultaneously.

There's a big difference between:
(1) Light from two sources arrives at the same location at the same time (or at different times)
(2) Light from a single source arrives at two spatially separate locations at the same time

(1) is something that all observers in all frames would agree upon, while (2) depends on who's doing the observing. Whether spatially separated events happen at the same time is frame dependent.

If I can deduce, using accepted facts about light speed, from one frame (the embankment frame) that the light from each flash will arrive at the middle of the train at different times, then all frames will agree on that fact.

 

[pervect]

In figure 3-1 (page 63) of Taylor and Wheeler's Spacetime Physics, the observer on the train determines that the lightning strikes are not simultaneous because the flashes do not reach her simultaneously.

I see two problems with this.

1. The narrative in figure 3-1 contradicts the text in section 2.7 (pg 39): "Location and time of each event is recorded by the clock nearest to that event." The time of the lighting strike at the front of the train should be recorded by a clock at the front of the train. Likewise, the time of the strike at the rear of the train should be recorded by a clock at the rear of the train. The procedure used in figure 30-1 will lead to incorrect results, as stated in 2.7: "We do not permit the observer to report on widely separated events that he himself views by eye. The reason: The travel time of light."

I think you've missed the fact that in Taylor & Wheeler's description, each frame has a large number of clocks in it. All of the clocks in a frame are synchronized by the Einstein convention for the frame.

So, there is some clock in the frame of the train that's close to the event in question, and that clocks reading is what you use for the time of the event in the train frame. There is another clock, in the frame of the station that's close to the event, and that's what you use for the station frame time.

 

[GregAshmore]

I think you've missed the fact that in Taylor & Wheeler's description, each frame has a large number of clocks in it. All of the clocks in a frame are synchronized by the Einstein convention for the frame.

So, there is some clock in the frame of the train that's close to the event in question, and that clocks reading is what you use for the time of the event in the train frame. There is another clock, in the frame of the station that's close to the event, and that's what you use for the station frame time.

No, there are no clocks in the example. Two bolts of lightning hit the train, at front and rar, simultaneously, as measured on the embankment, each leaving a mark on the track. The observer on the train judges the front flash to have hit first because "the flash arrived from the front of the train first." Later, the train observer says to the observer on the bank, "The front mark was made before the back mark--since the flash reached me at the middle of the train before the flash from the back reached me."

The example is labeled, "Einstein's Train Paradox". I remember it from his popular [dumbed down] "Relativity".

 

[GregAshmore]

I don't see any issue here. As long as the observer takes into account the light travel time, his conclusions will match those of co-moving clocks at the location of the events.

The observer does take into account the speed of light; that's what leads to the claim that the strikes occurred at different times.

My problem is with the claim that the flash from the front of the train reaches the observer on the train before the flash from the rear of the train.

It is given that: The observer on the train is in the middle of the train, equidistant from front and rear. As the train passes an observer on the bank, two bolts of lightning strike simultaneously, one at the front, one at the rear. Thus, at the time of the strikes, both observers are equidistant from the flashes.

The two flashes reach the observer on the embankment simultaneously, as expected.

The claim is that the front flash reaches the observer on the train first, due to the velocity of the train. This cannot be true. The velocity of the train relative to the embankment has no effect on the laws of physics within the train. The train is moving at constant speed. The observer on the train has zero velocity relative to the train. He is in the middle of the train. Therefore, the flashes must arrive at the observer simultaneously.

I expect that the observer on the train will see the flashes reach the observer on the embankment at a different time than they reach him, and vise versa. (I'll try to calculate this using the invariant spacetime interval.) That is, for each observer the flashes arrive simultaneously, but the two arrival events are separated in time, as measured by each observer.

 

[bcrowell]

Great to see that you're digging into Spacetime Physics, which I think is an excellent introduction to SR.

The claim is that the front flash reaches the observer on the train first, due to the velocity of the train. This cannot be true. The velocity of the train relative to the embankment has no effect on the laws of physics within the train. The train is moving at constant speed. The observer on the train has zero velocity relative to the train. He is in the middle of the train. Therefore, the flashes must arrive at the observer simultaneously.

As a preliminary to this argument, you seem to be assuming that the flashes are simultaneous. Just because they're simultaneous in the frame D of an observer at rest with respect to the dirt, that doesn't mean they're simultaneous in the frame T of an observer moving with the train.

So let's consider the two possibilities:
A: The lightning flashes are simultaneous in both D and T.
B: The lightning flashes are simultaneous in D, but not in T.

A is what you seem to have assumed. In this case, we get a logical contradiction. The collision of the light rays from the two flashes is an event E. E can't occur both at the location P of the dirt half-way between the two embankments as determined in frame D and at the location Q of the passenger at the midpoint of the train as determined in frame T. P and Q don't coincide at the time when E occurs.

 

[Doc Al]

It is given that: The observer on the train is in the middle of the train, equidistant from front and rear.

OK.

As the train passes an observer on the bank, two bolts of lightning strike simultaneously, one at the front, one at the rear.

The lightning strikes are simultaneous according to embankment observers, not necessarily according to the train observers. (In fact, the point of the thought experiment is to show that the lightning flashes could not have been simultaneous according to the train observers.)

Thus, at the time of the strikes, both observers are equidistant from the flashes.

Again, only according to the embankment observers.

The two flashes reach the observer on the embankment simultaneously, as expected.

OK.

The claim is that the front flash reaches the observer on the train first, due to the velocity of the train. This cannot be true. The velocity of the train relative to the embankment has no effect on the laws of physics within the train. The train is moving at constant speed. The observer on the train has zero velocity relative to the train. He is in the middle of the train. Therefore, the flashes must arrive at the observer simultaneously.

You are looking at things from the train observer's viewpoint, but you are tacitly assuming that the lightning strikes were simultaneous. But they are only simultaneous from the embankment observer's view. But you're correct that the laws of physics are the same in both frames.

I expect that the observer on the train will see the flashes reach the observer on the embankment at a different time than they reach him, and vise versa. (I'll try to calculate this using the invariant spacetime interval.) That is, for each observer the flashes arrive simultaneously, but the two arrival events are separated in time, as measured by each observer.

That last statement seems self-contradictory.

Everyone must agree whether or not the light from the two flashes arrives at the train observer at the same time. To see this, imagine that the train observer is replaced by a device that detects the arrival of the light beams. That device is arranged--via some electronic circuitry--so that if the light arrives simultaneously (within whatever margin of accuracy desired) a giant fireball is created. If the light arrives at different times, no fireball. Would you not agree that either the fireball was created or not? Everyone must agree on that!

 

[GregAshmore]

As a preliminary to this argument, you seem to be assuming that the flashes are simultaneous. Just because they're simultaneous in the frame D of an observer at rest with respect to the dirt, that doesn't mean they're simultaneous in the frame T of an observer moving with the train.

The statement of the problem is that "lightning strikes the front and back ends of a rapidly moving train." No simultaneity is assumed at the outset. So in my discussion of the problem I have not been as careful as I should be of the details. Whether this changes anything about my conclusion regarding the observer on the train remains to be seen.

The two flashes reach the observer on the ground simultaneously. Therefore, the flashes are simultaneous in the D (dirt) frame.

The text goes on, "A second observer rides in the middle of the train. From the viewpoint of the observer on the ground, the train observer moves toward the flash coming from the front of the train and moves away from the flash coming from the rear. Therefore the train observer receives the flash from the front of the train first."

This statement contradicts the principle of relativity. According to that principle, what happens on the train is in no way influenced by the motion of the train. If it should happen that the observer on the train sees the front flash first, it will have nothing to do with the motion of the train.

Now I move on from my disagreement with the text to consider whether the flashes are simultaneous on the train.

According to the statement of the problem, lightning struck the ends of the train, and the observer on the train is in the middle of the train. When will the flashes reach the observer? To solve this problem we need not consider the motion of the train relevant to the embankment. But we do need to know when the flashes hit in the frame of the train. That information is not provided in the statement of the problem. Nor is any information given which can be used to determine the times of the flashes in the T (train) frame.

I have to get off this public terminal. I'll think about this more and get back.

[half hour later. I see no way to solve the problem with the information given]

 

[GregAshmore]

You are looking at things from the train observer's viewpoint, but you are tacitly assuming that the lightning strikes were simultaneous.

True. On closer reading, I see that the problem does not declare simultaneity in either frame. Simultaneity for the observer on the embankment is determined by measurement.

But they are only simultaneous from the embankment observer's view.

This is not established in the problem. See my response to bcrowell.

That last statement seems self-contradictory.
Everyone must agree whether or not the light from the two flashes arrives at the train observer at the same time. To see this, imagine that the train observer is replaced by a device that detects the arrival of the light beams. That device is arranged--via some electronic circuitry--so that if the light arrives simultaneously (within whatever margin of accuracy desired) a giant fireball is created. If the light arrives at different times, no fireball. Would you not agree that either the fireball was created or not? Everyone must agree on that!

Agreed.

The larger problem of whether the flashes reach the observer in the middle of the train simultaneously remains unresolved. If it is true that the motion of the train relative to the embankment cannot affect the outcome on the train, then the problem as stated does not provide any information by which we can determine when the flashes will reach the center of the train.

 

[Doc Al]

The statement of the problem is that "lightning strikes the front and back ends of a rapidly moving train." No simultaneity is assumed at the outset. So in my discussion of the problem I have not been as careful as I should be of the details. Whether this changes anything about my conclusion regarding the observer on the train remains to be seen.

The two flashes reach the observer on the ground simultaneously. Therefore, the flashes are simultaneous in the D (dirt) frame.

Exactly. So now we know that the flashes were simultaneous in the ground frame.

The text goes on, "A second observer rides in the middle of the train. From the viewpoint of the observer on the ground, the train observer moves toward the flash coming from the front of the train and moves away from the flash coming from the rear. Therefore the train observer receives the flash from the front of the train first."

Note that this is a perfectly valid conclusion which follows from the principle of the invariance of the speed of light. If you dispute it, you'll need to explain why. Further, as I attempted to illustrate in my last post, that the train observer receives the light flashes at different times is a fact that everyone must agree upon. Just because we deduced this fact based on measurements made in the ground frame doesn't make it any less correct.

This statement contradicts the principle of relativity. According to that principle, what happens on the train is in no way influenced by the motion of the train. If it should happen that the observer on the train sees the front flash first, it will have nothing to do with the motion of the train.

The principle of relativity says no such thing. What it does say is that the laws of physics are the same in all inertial frames, that an experiment done totally on the train will produce the same results as it would if it were done on the ground, and that either frame is perfectly entitled to its own measurements as if it were at rest. But if someone on the ground is observing a train move past, the fact that the train is moving has plenty to do with what is observed.

Now I move on from my disagreement with the text to consider whether the flashes are simultaneous on the train.

According to the statement of the problem, lightning struck the ends of the train, and the observer on the train is in the middle of the train. When will the flashes reach the observer? To solve this problem we need not consider the motion of the train relevant to the embankment. But we do need to know when the flashes hit in the frame of the train. That information is not provided in the statement of the problem. Nor is any information given which can be used to determine the times of the flashes in the T (train) frame.

You are given all the information needed to conclude that the lightning strikes were not simultaneous in the train frame. You even quoted it above. But for some reason, you are discounting it. Now that contradicts the principle of relativity.

 

[GregAshmore]

Note that this is a perfectly valid conclusion which follows from the principle of the invariance of the speed of light.

I don't see it. Certainly, the observer on the train will reach the front flash first as judged from the embankment. But in relativity we are not permitted to assume that a position and time as judged from the embankment will match the position and time as judged from the train.

If one accepts the point of the argument--that times and positions in one frame are not what they appear to be in another frame--then the argument itself is invalid, as it makes a statement about the time of an event in the train frame based on reasoning set in the embankment frame.

The experimental method used in this example is "not permitted", according to Taylor. The proper way to answer the question of simultaneity, as stated by Taylor (and by Einstein) is to record the time of each event on a clock which is at rest at the location of the event. Then, the readings on the two clocks may be compared at leisure.

Further, as I attempted to illustrate in my last post, that the train observer receives the light flashes at different times is a fact that everyone must agree upon. Just because we deduced this fact based on measurements made in the ground frame doesn't make it any less correct.

Meaning no disrespect, the result of a thought experiment cannot be considered a fact. It is an educated conjecture, and no more. I will accept the claim of relative simultaneity (as stated in this thought experiment) when I see the records on the four clocks. (Two clocks on the ground, two on the train.)

 

[bcrowell]

I don't see it. Certainly, the observer on the train will reach the front flash first as judged from the embankment. But in relativity we are not permitted to assume that a position and time as judged from the embankment will match the position and time as judged from the train.

If one accepts the point of the argument--that times and positions in one frame are not what they appear to be in another frame--then the argument itself is invalid, as it makes a statement about the time of an event in the train frame based on reasoning set in the embankment frame.

I think the crucial thing you're missing here is that although coordinates of events are frame-dependent, the fact that two events coincide or don't coincide is not frame-dependent. We have two events here, A and B. A=observer reaches the front flash, B=observer reaches the back flash. The fact that A and B coincide is frame-independent. They coincide in the dirt's frame by symmetry. Therefore they coincide in the train's frame as well.

 

[matheinste]

the result of a thought experiment cannot be considered a fact. It is an educated conjecture, and no more. I will accept the claim of relative simultaneity (as stated in this thought experiment) when I see the records on the four clocks. (Two clocks on the ground, two on the train.)

This thought experiment, as others of its kind, demonstrates a principle. We are not bound to use the same experimental set up in practice to demonstate this principle. Any relevant experiment can be used.

Matheinste.

 

[bcrowell]

Meaning no disrespect, the result of a thought experiment cannot be considered a fact. It is an educated conjecture, and no more. I will accept the claim of relative simultaneity (as stated in this thought experiment) when I see the records on the four clocks. (Two clocks on the ground, two on the train.)

A real experiment that may address some of your doubts about the non-absolute nature of time in relativity: http://en.wikipedia.org/wiki/Hafele-Keating_experiment

 

[GregAshmore]

I think the crucial thing you're missing here is that although coordinates of events are frame-dependent, the fact that two events coincide or don't coincide is not frame-dependent. We have two events here, A and B. A=observer reaches the front flash, B=observer reaches the back flash. The fact that A and B coincide is frame-independent. They coincide in the dirt's frame by symmetry. Therefore they coincide in the train's frame as well.

But the claim is that A and B coincide in the dirt frame, but do not coincide in the train frame.
That's what I am disputing--or, rather, I contend that there is not enough evidence given in the example to support the claim.

 

[GregAshmore]

A real experiment that may address some of your doubts about the non-absolute nature of time in relativity: http://en.wikipedia.org/wiki/Hafele-Keating_experiment

I'll check out the article. For the record, I do not dispute that time is in some sense relative. It seems to me that the evidence of particle lifetimes is pretty solid. However, I'm not yet convinced that we fully understand the nature of relativity. On that score, the statement that "we are unable to define reality" tends to reduce my confidence in our analysis.

I took a quick look. Actually, I have a problem with this sort of test. It seems to me that the equation of General Relativity by itself should give the correct answer. This because GR includes (generalizes) SR. An appeal to SR apart from GR to correct the results of GR seems to imply a failure in the equation of GR. Or, perhaps the failure is in our ability to solve the equation of GR for this case?

Another issue: Why is it the moving clock which runs slower, and not the clock on the ground? If the answer is that the moving clock is not in an inertial frame, then it must be admitted that one of the bodies is truly accelerating and the other is not. In that case, we are in the same position with regard to acceleration as Newton--there is something about the nature of spacetime which is absolute with regard to acceleration.

 

[bcrowell]

I took a quick look. Actually, I have a problem with this sort of test. It seems to me that the equation of General Relativity by itself should give the correct answer.

Yes, and it did give the correct answer for this experiment.

 

[ghwellsjr]

In figure 3-1 (page 63) of Taylor and Wheeler's Spacetime Physics, the observer on the train determines that the lightning strikes are not simultaneous because the flashes do not reach her simultaneously.

I see two problems with this.

1. The narrative in figure 3-1 contradicts the text in section 2.7 (pg 39): "Location and time of each event is recorded by the clock nearest to that event." The time of the lighting strike at the front of the train should be recorded by a clock at the front of the train. Likewise, the time of the strike at the rear of the train should be recorded by a clock at the rear of the train. The procedure used in figure 30-1 will lead to incorrect results, as stated in 2.7: "We do not permit the observer to report on widely separated events that he himself views by eye. The reason: The travel time of light."

2. The claim that the observer on the train will see the front flash first is based on a view from the embankment. There is no assurance that the view from inside the train will match the view from the embankment--indeed the exercise is intended to determine whether this is so. For comparison, consider the scene proposed by Menzel in his derivation of the equation of special relativity. A flash of light occurs at the instant a rocket ship (or train) passes a point on Earth. The sphere of the light has two apparent centers: One center (for the observer on earth) is at the point on Earth where the emission was observed; the other center (for the observer on the rocket) is at the point on the rocket where the emission was observed. Of course, these two centers separate with the velocity of the rocket ship. By this reasoning, the two light flashes on the train will reach the observer in the center of the train simultaneously.

Comments?

I believe the reason you are having so much problem with this is because you are thinking of the "scene proposed by Menzel" where a single flash of light, set off at the location of when two observers, one stationary and the other moving, produces an expanding sphere of light in which the stationary and the moving observers both observe themselves to be at the center, even though they continue to get farther apart. This is very true but they only tell you half of the story. What they don't tell you is how you observe yourself to be in the center of an expanding sphere of light.

Here's the rest of the story: You cannot see light as it travels away from you unless you reflect it off of something and some of that light comes back to you. You cannot even tell where the light is. So what you do is put up a bunch of mirrors some equal distance from you in all directions so that when the sphere of light hits them they will start their trip back to you and when they arrive at your location, you can see that all of the returned light reflections arrive simultaneously. Now the other observer is doing the same thing except he has a different set of mirrors. Both of you are in the center of your set of mirrors but the traveling one's mirrors are moving with him. Now if you think very carefully about how this experiment could work, you will discover that it is necessary for the moving observer to have his mirrors not really equal distant from him, they are closer to him along the direction of motion. This is the Lorentz contraction. And for him, the light does not arrive at all the mirrors simultaneously but in such a manner as to cause the reflections to arrive simultaneously from all the mirrors at his location. Also, the two sets of reflections, one for the stationary observer and one for the traveling observer do not collapse on their respective observers at the same time. The stationary observer sees the reflections first and then some time later the traveling observer sees his reflections. Once you understand how this works, you will see that in this "scene proposed by Menzel" the light is making a round trip, starting from the co-location of the two observers and ending up after being reflected off of two separate sets of mirrors, on the two observers at different times and at different locations.

In the train situation, there are two flashes of light coming from a single pair of sources that are stationary with one observer. It would be like if the Menzel scene had only one set of mirrors for the stationary observer. It wouldn't work the same. That is why the Menzel scene is not the same as the train scene.

I know this is kind of hard to follow without a visual but it's the direction you're going to have to take to understand what's going on and why the two situations are completely different.

 

[GregAshmore]

I believe the reason you are having so much problem with this is because you are thinking of the "scene proposed by Menzel" where a single flash of light, set off at the location of when two observers, one stationary and the other moving, produces an expanding sphere of light in which the stationary and the moving observers both observe themselves to be at the center, even though they continue to get farther apart. This is very true but they only tell you half of the story. What they don't tell you is how you observe yourself to be in the center of an expanding sphere of light.

Here's the rest of the story: You cannot see light as it travels away from you unless you reflect it off of something and some of that light comes back to you. You cannot even tell where the light is. So what you do is put up a bunch of mirrors some equal distance from you in all directions so that when the sphere of light hits them they will start their trip back to you and when they arrive at your location, you can see that all of the returned light reflections arrive simultaneously. Now the other observer is doing the same thing except he has a different set of mirrors. Both of you are in the center of your set of mirrors but the traveling one's mirrors are moving with him. Now if you think very carefully about how this experiment could work, you will discover that it is necessary for the moving observer to have his mirrors not really equal distant from him, they are closer to him along the direction of motion. This is the Lorentz contraction. And for him, the light does not arrive at all the mirrors simultaneously but in such a manner as to cause the reflections to arrive simultaneously from all the mirrors at his location. Also, the two sets of reflections, one for the stationary observer and one for the traveling observer do not collapse on their respective observers at the same time. The stationary observer sees the reflections first and then some time later the traveling observer sees his reflections. Once you understand how this works, you will see that in this "scene proposed by Menzel" the light is making a round trip, starting from the co-location of the two observers and ending up after being reflected off of two separate sets of mirrors, on the two observers at different times and at different locations.

In the train situation, there are two flashes of light coming from a single pair of sources that are stationary with one observer. It would be like if the Menzel scene had only one set of mirrors for the stationary observer. It wouldn't work the same. That is why the Menzel scene is not the same as the train scene.

I know this is kind of hard to follow without a visual but it's the direction you're going to have to take to understand what's going on and why the two situations are completely different.

Which one is the moving observer?

 

[Doc Al]

But the claim is that A and B coincide in the dirt frame, but do not coincide in the train frame.

No it isn't. Events A and B, as defined by bcrowell in post 12, are the arrivals of the light from each flash at the ground observer. They coincide in all frames, not just the ground frame.

Similarly, events C and D, the arrivals of the light at the train observer do not coincide in any frame.

The conclusion is the that the lightning flashes (not the arrival of the light from those flashes at the two observers) were simultaneous in the ground frame but not in the train frame.

 

[ghwellsjr]

Which one is the moving observer?

Take your pick, assume one is stationary and the other one moving. Or they can both be moving with respect to your frame of reference. It doesn't matter. I'm trying to help you understand why the two examples that you gave in your opening post are totally different situations. Do you want to understand?

 

[nismaratwork]

I don't get it... where's the contradiction here except that someone is reading Spacetime Physics and doesn't quite get the basics of what relativity means? I mean, "which is the moving observer?"... it's RELATIVE! GregAshmore, maybe you should just read the book with an open mind, and write down each question like this you have as it occurs to you. At the end of the book, check your list and if the book didn't answer those question, re-read the relevant sections... and if that's not working, take those question and ask them. This is just... a lot less than the title promised.

 

[ghwellsjr]

I mean, "which is the moving observer?"... it's RELATIVE!

It's not relative once you decide on a frame of reference. Everything is absolute in that frame of reference. You decide who gets to be stationary in the FoR and who is moving. They you can pick a different FoR relative to the first one and do it all over again and you will see that every measurement and observation that any observer makes in the first FoR will be the same in the second FoR or any other one.

 

[nismaratwork]

It's not relative once you decide on a frame of reference. Everything is absolute in that frame of reference. You decide who gets to be stationary in the FoR and who is moving. They you can pick a different FoR relative to the first one and do it all over again and you will see that every measurement and observation that any observer makes in the first FoR will be the same in the second FoR or any other one.

Yes, but for the purposes of this argument you get to choose ANY FoR you want to start with, which makes it... completely relative at the outset. Yes, once you've constructed the thought experiment you stick by the rules, but he's having trouble with any formulation of the initial conditions!

 

[JM]

Greg, your questions of fig 3-1 are valid. The statement that 'the front flash arrived first ...' is not supported by the info in the figure. Also, the idea that 'the train observer is moving toward the front flash...' doesn't support the conclusion because the arrival time depends also on the time of the origin of the flashes.
So, consider the following reasoning. The flashes arrive at the mid track at t = L/2c, where L is the space between the flashes. But in this time the train has moved right a distance vt. So according to the train the flashes meet a distance vt to the left of center and the time taken for the front flash to reach this point is L/2c + vt/c. Subtracting this from the time of meeting, L/2c, results in the time of origin of the front flash t = -vL/2c^2, relative to the train. Parallel reasoning leads to the origin of the rear flash at t = + vL/2c^2. Thus the flashes are not simultaneous relative to the train.
The Lorentz transforms can be applied: x = m( X -vT), ct = m( cT -vX/c), where (x,t) and (X, T) are coordinates of the train/track with origin at the mid point, L is train length, and m is usually called 'gamma'. The track coordinates of the front/rear flashes are T= 0, and X= L/2, and -L/2. Substitution leads to the same results as above 'times m'.
So flashes sumultaneous on the track are not simultaneous on the train.
JM

 

[GregAshmore]

Greg, your questions of fig 3-1 are valid. The statement that 'the front flash arrived first ...' is not supported by the info in the figure. Also, the idea that 'the train observer is moving toward the front flash...' doesn't support the conclusion because the arrival time depends also on the time of the origin of the flashes.
So, consider the following reasoning. The flashes arrive at the mid track at t = L/2c, where L is the space between the flashes. But in this time the train has moved right a distance vt. So according to the train the flashes meet a distance vt to the left of center and the time taken for the front flash to reach this point is L/2c + vt/c. Subtracting this from the time of meeting, L/2c, results in the time of origin of the front flash t = -vL/2c^2, relative to the train. Parallel reasoning leads to the origin of the rear flash at t = + vL/2c^2. Thus the flashes are not simultaneous relative to the train.
The Lorentz transforms can be applied: x = m( X -vT), ct = m( cT -vX/c), where (x,t) and (X, T) are coordinates of the train/track with origin at the mid point, L is train length, and m is usually called 'gamma'. The track coordinates of the front/rear flashes are T= 0, and X= L/2, and -L/2. Substitution leads to the same results as above 'times m'.
So flashes sumultaneous on the track are not simultaneous on the train.
JM

Thanks for the alternate approach. I think what bothers me most about the example (after thinking about it some more after the original post) is brought out by your final paragraph, in which you suggest the use of the Lorentz transformations.

In Einstein's book, "Relativity", the example of the Train Paradox (which is included in T-W with credit to Einstein) is two articles before the article which introduces the Lorentz transform. The example is intended to demonstrate that simultaneity is not absolute, but relative, thus giving a logical basis for application of the Lorentz transform.

It is by no means clear to me that the motion of the train relative to the ground is a sufficient basis for the claim that the observer on the ground [edit: train] will see the front flash first--at least not for the reason which Einstein had in mind. It seemed to me when I read the article the first time several years ago that the claim is valid if one assumes a light-bearing ether. In retrospect, I still think the ether is a more natural argument for having the observer on the train see the front flash first. (Note to all: I am not advocating the existence of the ether. I'm only pointing out that, in the context of the example as presented by Einstein, the ether is a more intuitive way of supporting the claim that the observer on the train will see the front flash first.)

If we assume neither an ether nor the constant speed of light in a vacuum [edit: relative to all observers in inertial frames], then I don't think the claim is supported at all by the evidence provided in the example itself.

So, while I was wrong in saying that the example contradicts the principle of relativity, I still think that the example fails to accomplish the purpose for which it was intended.

 

[ghwellsjr]

When you arbitrarily select any inertial reference frame, it is exactly like an absolute ether frame at rest, that is, one of the kind that Lorentz had speculated about with his length contraction and time dilation of moving objects and absolute time for the ether and light traveling at c through the ether. You can analyze the entire scenario in this context to help you understand what is going on.

Then, if you want, you can pick a different reference frame and treat it as an absolute ether rest frame and analyze everything all over again from that perspective.

But, you have to be careful when you do this, just like when selecting any reference frame that you transform correctly to take care of the relativity of simultaneity issues, which is very important in these kinds of problems.

 

[JesseM]

It is by no means clear to me that the motion of the train relative to the ground is a sufficient basis for the claim that the observer on the ground will see the front flash first--at least not for the reason which Einstein had in mind.

It is if you assume both lightning strikes happened at the same time-coordinate in the ground frame (part of Einstein's statement of the problem), and if you assume the second postulate of relativity, which says that light must have a coordinate speed of c in every inertial frame, which would naturally include the ground frame. The Lorentz transformation is normally derived from the two basic postulates, so there's no problem in starting with this postulate to draw some conclusion about simultaneity will have to work in the transform even before you've derived the full details of the transform.

If we assume neither an ether nor the constant speed of light in a vacuum [edit: relative to all observers in inertial frames], then I don't think the claim is supported at all by the evidence provided in the example itself.

But he does assume the second one.

So, while I was wrong in saying that the example contradicts the principle of relativity, I still think that the example fails to accomplish the purpose for which it was intended.

What do you think that purpose was? I would say the purpose was to show what conclusions we can draw about simultaneity given the two basic postulates, which he had already discussed in sections 5 (first postulate) and and [url=http://www.bartleby.com/173/8.html]8 (second postulate) of the book where he discussed the train/lightning scenario.

 

[yuiop]

It is by no means clear to me that the motion of the train relative to the ground is a sufficient basis for the claim that the observer on the ground will see the front flash first--at least not for the reason which Einstein had in mind.

Not quite sure what you mean by "the observer on the ground will see the front flash first--". Do you mean he will the front flash before he sees the rear flash or do you mean he will the front flash before the observer on the train sees the front flash?

There are two possible cases, where at least one observer sees the flashes simultaneously.

Case 1:

Observer on the train sees front and rear flashes simultaneously.
Observer on the ground sees the rear flash before he sees the front flash.

Case 2:

Observer on the train sees the front flash before he sees the rear flash.
Observer on the ground sees front and rear flashes simultaneously.


In neither case does the ground observer see the front flash before he sees the rear flash.

Here is an animation I made a while ago of the second case that might help:
[URL]http://i910.photobucket.com/albums/ac304/kev2001_photos/Etrain2e.gif[/URL]


In the illustrated case, the observer on the ground does not see the flash from the front of the train, before the observer on the train sees the flash from the front, in either frame, but I am not sure if that is always the case.

 

[GregAshmore]

I made an error in my #26--I said 'ground' where I meant to say 'train'. The post has been edited to correct the problem.

 

[GregAshmore]

What do you think that purpose was? I would say the purpose was to show what conclusions we can draw about simultaneity given the two basic postulates, which he had already discussed in sections 5 and 8 of the book where he discussed the train/lightning scenario.

I've read sections 5 through 9 on multiple occasions, over a period of four years. I read through them again just now. I have once again found it difficult to fully accept the truth of this statement:

That light requires the same time to traverse the path A->M as for the path B->M is in reality neither a supposition nor a hypothesis about the physical nature of light, but a stipulation which I can make of my own free will in order to arrive at a definition of simultaneity.

I therefore do not agree that the assertion in the next paragraph is, as Einstein asserts, "clear". That is, it is not clear to me that this definition can be used to give an exact meaning to two events.

Having suspended judgment as to the validity of the proposition (or stipulation), I come to this statement in section 9:

Are two events which are simultaneous with reference to the railway embankment also simultaneous relative to the train? We shall show directly that the answer must be in the negative.

A few paragraphs later he presents his proof:

If an observer sitting at M' in the train did not possesses this velocity , then he would remain permanently at M...and the light flashes would reach him simultaneously. Now in reality considered with reference to the railway embankment he is hastening toward the light coming from B, whilst he is riding on ahead of the beam coming from A. Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A.

I don't see that the conclusion necessarily follows from the evidence, even if one accepts the stipulation that c is a physical constant for all inertial observers. Thinking about it, I have sometimes been able to convince myself that the conclusion is wrong, given the stipulation of c. When I run across this sort of problem at work--which happens on a regular basis--I build a system, create the conditions, and measure the results. This usually clears things up.

In this case, I would want to do exactly what Taylor-Wheeler suggest. I'd put six clocks in the apparatus, three on the ground and three in the train. I'd create two sparks simultaneously on the ground. Then I'd record the time at which the flashes are seen at each of the six positions.

Of course, that is much easier said than done, given the precision required. So far as I know, we have never constructed a rigid frame, equipped it with clocks, and moved it in one direction at any significant fraction of light speed.

 

[ghwellsjr]

Greg, I sure hope you're not thinking that Einstein's postulate, that the one-way speed of light is c in all inertial frames (one at at time, please) is something that can be proved or even measured. It cannot, just like the idea that the one-way speed of light is c in only one frame, an assumed absolute ether rest frame, cannot be proven or measured. Once you accept the experimental evidence that the measured round-trip speed of light is always c for any inertial observer (independent of any assumed frame) and that it is impossible for any such observer to know if the time for light to travel both halves of that round trip are equal or not, then you will be on your way to understanding what Special Relativity is all about. It is simply about declaring that those two times are equal for any inertial observer and building a frame of reference around that declaration.

 

[JesseM]

I don't see that the conclusion necessarily follows from the evidence, even if one accepts the stipulation that c is a physical constant for all inertial observers.

What part of the logic don't you agree with? Do you agree that if we start from the stipulation that light travels at c in all inertial frames, then if in the ground frame the two lightning strikes happen simultaneously, it follows that a detector midway between the positions of the strikes will get the light from them at the same time, while a detector at some position other than the midpoint will not?

Thinking about it, I have sometimes been able to convince myself that the conclusion is wrong, given the stipulation of c.

How so? Try presenting a numerical example where you give both the position and times of the strikes and the position and time of each detector receiving the light from them, using the coordinates of the ground frame where the strikes happened at the same time-coordinate.

In this case, I would want to do exactly what Taylor-Wheeler suggest. I'd put six clocks in the apparatus, three on the ground and three in the train. I'd create two sparks simultaneously on the ground. Then I'd record the time at which the flashes are seen at each of the six positions.

Of course, that is much easier said than done, given the precision required. So far as I know, we have never constructed a rigid frame, equipped it with clocks, and moved it in one direction at any significant fraction of light speed.

This isn't an experimental question about whether light actually does move at c in all inertial frames, it's a mathematical question of what conclusions would follow if the two postulates of SR were valid. Logically the two postulates do imply the relativity of simultaneity, so any failure of your experiment could only mean that one of the postulates was in fact false. Best to try to master the basic logic before going on to ask about whether the postulates actually hold in reality.

Incidentally, it's also true logically that the two postulates will hold as long as the equations of the fundamental laws of physics as expressed in any one frame all have a mathematical property called "Lorentz-invariance" (meaning they are unchanged under the Lorentz transformation). So in that sense you don't actually need to get different observers (or different ruler/clock systems) moving at relativistic speeds relative to one another to test relativity, you can just determine the laws in a single frame and check whether they are Lorentz-invariant. All the most fundamental laws known so far (the equations of quantum field theory for example) have had this property.

 

[GregAshmore]

Greg, I sure hope you're not thinking that Einstein's postulate, that the one-way speed of light is c in all inertial frames (one at at time, please) is something that can be proved or even measured. It cannot, just like the idea that the one-way speed of light is c in only one frame, an assumed absolute ether rest frame, cannot be proven or measured. Once you accept the experimental evidence that the measured round-trip speed of light is always c for any inertial observer (independent of any assumed frame) and that it is impossible for any such observer to know if the time for light to travel both halves of that round trip are equal or not, then you will be on your way to understanding what Special Relativity is all about. It is simply about declaring that those two times are equal for any inertial observer and building a frame of reference around that declaration.

My reticence is not related to the experimental evidence which we have. Nor do I have a problem (any longer) with the concept of relative time. I have a problem with dogmatic statements concerning aspects of the theory which we have not tested directly, such as "time travel" on a cosmological scale, or even the conceptually simple experiment of moving two equivalent rigid bodies past each other at a significant fraction of light speed to directly test the relativity of simultaneity and (perhaps) length contraction.

I might be less of a stickler on these points if we had a better understanding of light itself. It seems to me that while we have learned much about how light interacts with other particles, we know precious little about what goes on in the interval between the creation of a photon and its destruction on our detectors. In my view, this gap in our knowledge (which I understand to be typical of all particles) leaves open the possibility of unexpected behavior as we expand the range of our practical operations.

What I say may sound silly to people who work in this arena every day. Certainly, I respect the understanding which can only come through hands-on experience. But my reservations are sound in principle, and they are informed by the experience of one who knows his own field pretty well, yet has had the humbling experience of discovering that "we don't know what we don't know."

 

[nismaratwork]

My reticence is not related to the experimental evidence which we have. Nor do I have a problem (any longer) with the concept of relative time. I have a problem with dogmatic statements concerning aspects of the theory which we have not tested directly, such as "time travel" on a cosmological scale, or even the conceptually simple experiment of moving two equivalent rigid bodies past each other at a significant fraction of light speed to directly test the relativity of simultaneity and (perhaps) length contraction.

I might be less of a stickler on these points if we had a better understanding of light itself. It seems to me that while we have learned much about how light interacts with other particles, we know precious little about what goes on in the interval between the creation of a photon and its destruction on our detectors. In my view, this gap in our knowledge (which I understand to be typical of all particles) leaves open the possibility of unexpected behavior as we expand the range of our practical operations.

What I say may sound silly to people who work in this arena every day. Certainly, I respect the understanding which can only come through hands-on experience. But my reservations are sound in principle, and they are informed by the experience of one who knows his own field pretty well, yet has had the humbling experience of discovering that "we don't know what we don't know."

If you hadn't started the thread with the notion that this was some flaw in the theory, maybe what you say would fly. As it is, I think your reservations are absurd unless you're really waiting for proof on a cosmological scale. Just because an observation or experiment is grand or massive doesn't make it less accurate or any less compatible with other observations and/or experimental evidence. SR and GR have had decades of challenges, and the areas where it fails to make useful predictions is nowhere NEAR what you're talking about.

It shouldn't take pages to agree what a postulate is, and how that differs from an experimentally verified value. Take some friendly advice and save the critique for after you master the material a bit, when you'll be far less likely to hare off after shadows, and more likely to identify and ponder real problems.