I Problems with Einstein's 1920 "Relativity"

[PeroK]

Other people here have explained more or less the same experiment without headache.

You'd be far better off with a modern text that is built on 100 years experience teaching SR.

Also, in my view, the train and lightning experiment is fraught with the potential for misconceptions.

You can study simultaneity more simply with a single light source in the middle of a train carriage.

 

[FactChecker]

there's a "trainload" of problems with it. For one, it starts off with the focus and question on whether the light flashes would be simultaneous with each other alone, not whether they would be simultaneous with the simultaneous positions of the observers.

The diagram shows the events A and B occurring at the instant when M and M' coincide.

EDIT: I stand corrected here. I used the word "instant" when that is relative. I am looking it as an observer on the embankment, not on the train. So I see that there can be multiple interpretations. Much of his description must be interpreted as an observer on the embankment.

It then goes on to specifically state that the light flashes occur when M coincides with M'. You can see where this becomes confusing fast.

That is exactly what the diagram shows and it confirms that aspect of the diagram. There is no conflict, ambiguity, or confusion. I won't continue farther since this point is essential in order to understand the rest.

 

[pheurton]

To make sense of the relativity of simultaneity, I had to go back to Einstein's 1905 paper, On the electrodynamics of moving bodies. Here Einstein proposes a "moving rod" thought experiment that explains relative simultaneity far better than the train-lightning thought experiment in the 1920 popular book. But even the 1905 thought experiment is problematic because Einstein insists on local observations. This makes it much trickier since the clocks attached to the rod have to be set so as to tell the time in the "stationary" frame of reference. So let's try to find a happy medium by presenting an updated "moving rod" thought experiment in which observers are granted the power of observing events and clocks in each other's frames.

A train passes an observer standing on a railway embankment as a light pulse travels the length of the train from the rear to the front where it's then reflected back to the rear. For a passenger on the train, either way the light pulse is traveling, it covers exactly the length of the train. But for the embankment observer, when the light pulse is traveling to the front of the train it covers not only the length of the train but the distance traveled by the train as the pulse is in transit. Since the speed of light is the same for both the passenger and the embankment observer, the pulse cannot travel faster for the embankment observer. The problem is resolved when we consider that speed is just distance over time. Since the distance traveled by the pulse is greater for the embankment observer, the time taken by the pulse as it travels to the front of the train must also be greater for the embankment observer. Likewise, when the pulse travels back from the front of the train to the rear, in the embankment frame it travels less distance than it does for the passenger and therefore takes less time for the embankment observer. Einstein solves the problem by allowing time to vary between reference frames.

Now let's say the train has two clocks, one located at the front and the other at the rear. When the light pulse traveling from the rear of the train illuminates the clock at the front, the clock reads later for the embankment observer than for the passenger. When the light pulse traveling back from the front of the train illuminates the clock at the rear, the clock reads earlier for the embankment observer than for the passenger. This is the relativity of simultaneity. Whereas the passenger sees the clocks on the train as being synchronized, the embankment observer sees them as being out of sync.

In his 1920 thought experiment Einstein replaces the clocks with lightning bolts, which strike at the exact moment the passenger is lined up with the embankment observer. The light rays traveling from the lightning bolts reach the embankment observer simultaneously. But, according to Einstein, the passenger is "hastening towards the beam of light" from the lightning bolt at the front of the train "whilst he is riding on ahead of the beam of light" from the lightning bolt at the rear of the train. "Hence the [passenger] will see the beam of light emitted from [the front lightning] earlier than he will see that emitted from [the rear lightning]."

The problem here is that the passenger's perception of the timing of the lightning bolts follows from the fact that the train has moved closer to one bolt and away from the other while the light rays emitted from the bolts are in transit. Thus the distances traveled by the light rays are different, and this difference alone explains why the light rays take different amounts of time to reach the passenger. Note that the difference in distance is not just a matter of differing perspectives. It's not like the passenger says one thing and the embankment observer says something else. Whether you're looking on from the embankment or from within the train, you're going to see that the passenger's distance from each lightning bolt is different once the light rays arrive. Since it's not a frame-dependent effect, we don't need relativity to explain this. Obviously light or anything else takes different times to travel different distances. What happened to the relativity of simultaneity?

In the "happy medium" thought experiment, we saw that the light ray traveling from the front of the train gives an early reading of the time, while the light ray traveling from the back of the train gives a late reading. This would seem to explain the effect except for one thing: it applies only in the frame of the embankment observer. The lightning bolt thought experiment, on the other hand, is supposed to demonstrate simultaneous lightning bolts for the embankment observer and successive lightning bolts for the passenger.

At this point I can only conclude that the train-lightning thought experiment fails to express the relativity of simultaneity. It doesn't express the fact that the speed of light is absolute, meaning that light travels at the same speed in all frames of reference. Instead it expresses the much more mundane fact that the speed of light is finite. It takes light rays time to travel from the lightning bolts to the passenger, and during this interval the passenger moves closer to one bolt and away from the other. So what?

I'm beginning to think the reason the 1920 thought experiment is so hard to understand is that it's just wrong. It doesn't express what Einstein wanted it to express.

If I've made a mistake, I would very much appreciate being corrected. Thanks to everyone patient enough to read this!

 

[PeterDonis]

I'm beginning to think the reason the 1920 thought experiment is so hard to understand is that it's just wrong. It doesn't express what Einstein wanted it to express.

No, it does, but what Einstein wanted it to express in the 1920 book is somewhat different from what he wanted the original thought experiment to express in the 1905 paper. (I'll comment separately on your "happy medium" thought experiment, which has its own issues.)

In the 1905 paper, Einstein was concerned with deriving the Lorentz transformations. That meant he had to construct arguments that would validate the Lorentz transformations as the correct ones to use when transforming between inertial frames.

In the 1920 book, at the point where he introduces the lightning bolts thought experiment, he is not yet concerned with deriving the Lorentz transformations in their entirety. He is simply constructing an argument to show that, given the obvious definition of "simultaneity" that he gives, a pair of events that are simultaneous in one frame will not be simultaneous in another frame moving relative to the first. In the specific example he gives, the lightning bolt events are, by construction, simultaneous in the embankment frame; and his argument about the passenger in the train moving towards the light signal from one bolt and away from the other is simply to show that the lightning bolts cannot be simultaneous, by his previous definition of simultaneity, in the train frame. At this point he is not assuming or trying to show that the correct transformation between frames is the Lorentz transformation; that comes later. All he is trying to show is that relativity of simultaneity is a simple consequence of his definition of simultaneity plus the constancy of the speed of light.

 

[PeterDonis]

What happened to the relativity of simultaneity?

Go back to how Einstein defines simultaneity earlier in the 1920 book: he says that two events are simultaneous if light signals from both events arrive at an observer equidistant between them at the same instant. By construction in his lightning bolt thought experiment, this is true for the embankment observer. But it is then obviously not true for the train passenger, since the passenger is equidistant from the front and rear of the train but the light signals from the two bolts do not arrive at the passenger at the same instant.

 

[pheurton]

And the passenger is no longer equidistant between the lightning bolts because the train has moved toward one bolt and away from the other during the time it takes the light signals to reach the center of the train. The difference in the distance of the passenger from each bolt is evident to both the passenger and the embankment observer. Since the difference is independent of reference frame, what does it have to do with the relativity of simultaneity?

 

[Ibix]

The difference in the distance of the passenger from each bolt is evident to both the passenger and the embankment observer.

Is it? Both say the bolts hit the front and back of the train, so both say they are equidistant from the flash sources.

 

[Nugatory]

because the train has moved...

Try thinking of this exact same setup (same flashes reach the ground observer at the same time) in terms of the ground moving and the train at rest.

It also may help to imagine that the lightning strikes leave scorch marks on the train and on the tracks. Both the train observer and the platform observer determine the distance that the light traveled by, after the fact, measuring the distance between where they were standing and the scorch marks that are at rest relative to them. Both find that they are equidistant from the points where the lightning flashes struck.

You will be comfortable using this procedure for the platform observer. The conceptual hurdle for most people is realizing that this comfort comes from the fact that nothing is moving in the platform frame - and therefore if we choose to consider the platform to be moving and the train at rest, it’s also a valid procedure for the train observer.

 

[PeterDonis]

And the passenger is no longer equidistant between the lightning bolts because the train has moved toward one bolt and away from the other during the time it takes the light signals to reach the center of the train.

You are measuring distances relative to the embankment frame. But the passenger measures distances relative to the train frame. Remember that Einstein has already adopted the principle of relativity, which says that no frame has any special preferred or absolute status. So measuring distances relative to the train is just as valid as measuring distances relative to the embankment.

 

[FactChecker]

And the passenger is no longer equidistant between the lightning bolts because the train has moved toward one bolt and away from the other during the time it takes the light signals to reach the center of the train.

The observer on the ground agrees with what you say. But the whole point is that the observer on the train is allowed to consider himself stationary. In that case, he would not agree with you and he would not agree that the lightning bolts were simultaneous. That makes the concept of simultaneity relative.

 

[pheurton]

Okay. The passenger is at rest as the embankment moves by. The scorch marks left by the lightning bolts on the embankment are also in motion relative to the passenger. The mark from the bolt ahead moves closer to the passenger, while the mark from the bolt behind moves away. So by the time the light signals emitted from the bolts reach the passenger at the center of the train, the source of the signal from the bolt ahead is closer to the passenger than the source of the signal from behind. This explains why the passenger thinks the lightning ahead preceded the lightning behind. It's just a function of the finite speed of light and the fact that the embankment has moved relative to the train during the time it takes the light signals to reach the passenger. This is completely different from the relativity of simultaneity as a function of the absolute speed of light.

 

[FactChecker]

Okay. The passenger is at rest as the embankment moves by. The scorch marks left by the lightning bolts on the embankment are also in motion relative to the passenger. The mark from the bolt ahead moves closer to the passenger, while the mark from the bolt behind moves away.

This is irrelevant. Why should the passenger care what happened to the scorch marks after the lightning strikes? That doesn't make sense from his point of view. You seem to be grasping for illogical reasons to deny Einstein's theory rather than trying to understand it.

 

[Pencilvester]

This explains why the passenger thinks the lightning ahead preceded the lightning behind. It's just a function of the finite speed of light and the fact that the embankment has moved relative to the train during the time it takes the light signals to reach the passenger.

Can you give one reason why the passenger must treat the rest frame of the embankment as if it takes precedence over his own frame of reference? You keep filtering everything through the embankment frame, so can you give a reason for that?

 

[Nugatory]

The mark from the bolt ahead moves closer to the passenger, while the mark from the bolt behind moves away. So by the time the light signals emitted from the bolts reach the passenger at the center of the train, the source of the signal from the bolt ahead is closer to the passenger than the source of the signal from behind.

You are treating the scorch mark on the tracks as the “real” source of the signal, the one that matters. But why should it be any more relevant than the scorch mark on the train? As I said above, this is the big conceptual hurdle that you must pass.

Before you respond, read the next paragraph and then take a few minutes to consider the situation if you consider the train to be at rest instead of the platform.

Here’s another possibility to imagine. Suppose that the train is windowless so the train observer has no way of looking out and seeing the ground go by. Indeed, let us further suppose that immediately after the lightning strikes have made their scorch marks on the train the platform, rails, and platform observer are all quietly vaporized so that we have a train floating in empty space. Of course the train observer doesn’t know this - he has no windows, so he wasn’t aware that the platform and rails ever existed. The two light signals reach him at different times; he measures the distance to the two scorch marks on the train and finds them the same; what possible basis is there for the claim that the strikes “really” happened at the same time?

 

[pheurton]

I'm certainly not claiming the strikes really happened at the same time, though that's what the embankment observer thinks. The question is why the passenger thinks they happened at different times. Is it because of the relativity of simultaneity or the finite speed of light? In contrast to the moving rod thought experiment from the 1905 paper, I think Einstein set this one up such that the relativity of simultaneity fails to explain the discrepancy of opinion between observers in different frames.

 

[FactChecker]

I'm certainly not claiming the strikes really happened at the same time, though that's what the embankment observer thinks. The question is why the passenger thinks they happened at different times.

The real reason is experimental. Suppose the train used the best physical methods to synchronize its clocks from front to rear. Experiments show that those clocks will measure the speed of light as being identical going forward or back. The only way that is possible is if those clocks are not set the same way that clocks on the ground are set. So if the ground people at the two lightning-strike locations think that the strikes are simultaneous, the passengers on the front and back of the train will look at their clocks when the lightning strikes occur and say that the strikes are not simultaneous.

 

[pheurton]

Clocks that are synchronized in one frame are not synchronized in another frame. So clocks that are synchronized in a speeding train are not synchronized in the ground frame. This is the relativity of simultaneity. The question is whether this is the cause of the outcome of the train-lightning thought experiment. Also, just as an aside, clocks can't measure the speed of light. To measure the speed of anything, you need a measurement of distance as well as time.

 

[Dale]

And the passenger is no longer equidistant between the lightning bolts

This is incorrect. The passenger remains in the middle of the train car and the lightning bolts struck on the ends of the train car. He is, at all times, equidistant from where the bolts struck in his frame.

the train has moved toward one bolt and away from the other

In the train’s frame the train has not moved, by definition. The embankment has moved.

The question is why the passenger thinks they happened at different times

The passenger thinks they happened at different times because he is equidistant between the strikes and he received the light at different times.

 

[FactChecker]

Clocks that are synchronized in one frame are not synchronized in another frame. So clocks that are synchronized in a speeding train are not synchronized in the ground frame. This is the relativity of simultaneity. The question is whether this is the cause of the outcome of the train-lightning thought experiment.

Don't you think that is sufficient? If people on the ground at both strike locations say that the times were identical by the ground clocks, then passengers on the train at both strike locations must say that the strikes happened at different times by the train clocks.

Also, just as an aside, clocks can't measure the speed of light. To measure the speed of anything, you need a measurement of distance as well as time.

Of course. I didn't think it was necessary to fill in the details.

 

[Nugatory]

Is it because of the relativity of simultaneity or the finite speed of light?

Some people buy chickens to lay eggs. Other people buy eggs to hatch chickens. The same biology is at work either way

In contrast to the moving rod thought experiment from the 1905 paper, I think Einstein set this one up such that the relativity of simultaneity fails to explain the discrepancy of opinion between observers in different frames.

What is the difference between “relativity of simultaneity” and “discrepancy of opinion [about simultaneity] between observers”?

 

[pheurton]

Dale said:
The passenger remains in the middle of the train car and the lightning bolts struck on the ends of the train car. He is, at all times, equidistant from where the bolts struck in his frame.

He is at all times equidistant from the front and rear of the train. Since the lightning strikes the front and rear of the train, that means over the next few moments he approaches the site where the lightning struck the front of the train and recedes from the site where the lightning struck the rear of the train.

Dale said:
In the train’s frame the train has not moved, by definition. The embankment has moved.

Sure. The site where the front and rear of the train were struck by lightning is also registered by burn marks on the embankment. After the lightning, those marks move relative to the passenger.

Dale said:
The passenger thinks they happened at different times because he is equidistant between the strikes and he received the light at different times.

Only at the moment of the lightning strikes is the passenger equidistant between them. Due to the relative motion of train and embankment, in the following moments the passenger approaches the site of one lightning strike and recedes from the site of the other strike. So, since the passenger is no longer equidistant between the strikes, why would he infer that the strikes were successive just because he receives the light from the strikes at different times?

 

[pheurton]

What is the difference between “relativity of simultaneity” and “discrepancy of opinion [about simultaneity] between observers”?

According to standard interpretation, the discrepancy of opinion between observers results from the relativity of simultaneity, which follows from relative motion in the context of the absolute speed of light. I think a better explanation is that the discrepancy results from the fact that one of the observers, the passenger, moves towards the site of one of the lightning strikes and away from the site of the other lightning strike during the time taken by the light signals emitted from the lightning events to reach the center of the train. In this case the discrepancy of opinion is caused by the finite speed of light.

 

[Pencilvester]

Since the lightning strikes the front and rear of the train, that means over the next few moments he approaches the site where the lightning struck the front of the train and recedes from the site where the lightning struck the rear of the train.

How on Earth can you say that when in the previous sentence you say:

He is at all times equidistant from the front and rear of the train.

Do you not see the blatant contradiction?

 

[Dale]

He is at all times equidistant from the front and rear of the train. Since the lightning strikes the front and rear of the train, that means

He is at all times equidistant from the front and rear of the train. Since the lightning strikes the front and rear of train, that means he is at all times equidistant from where the lightning strikes.

He is at all times equidistant from points A and B. The lightning strikes at points A and B. Therefore he is at all times equidistant from the points where the lightning strikes.

I don’t know how this could possibly be more clear.

over the next few moments he approaches the site where the lightning struck the front of the train and recedes from the site where the lightning struck the rear of the train

No. He is at rest in the train frame so he cannot approach anything nor recede from anything.

Only at the moment of the lightning strikes is the passenger equidistant between them. Due to the relative motion of train and embankment, in the following moments the passenger approaches the site of one lightning strike and recedes from the site of the other strike

At all times the passenger is equidistant between the front and rear of the train, which is where the lightning struck. The passenger and the train are motionless in that frame, but in the following moments the embankment moves. The motion of the embankment does nothing to change the location where the lightning struck.

 

[FactChecker]

Only at the moment of the lightning strikes is the passenger equidistant between them. Due to the relative motion of train and embankment, in the following moments the passenger approaches the site of one lightning strike and recedes from the site of the other strike.

I think it is conceptually easier to think of clocks on the train that are synchronized ahead of time using a perfect physical method and the same on the ground. At the instant the lightning strikes, observers right at the strike locations record the time there. In that scenario, nothing after the strikes matters. Experiments show that the two sets of clocks (on train versus on ground) can not agree because they both indicate that the speed of light is c in their own reference frame. Therefore, if the ground people say the strikes are simultaneous, the passengers on the train can not say that the strikes are simultaneous.

 

[PeterDonis]

He is at all times equidistant from the front and rear of the train. Since the lightning strikes the front and rear of the train, that means over the next few moments he approaches the site where the lightning struck the front of the train and recedes from the site where the lightning struck the rear of the train.

As @Pencilvester has pointed out, these statements are contradictory.

The site where the front and rear of the train were struck by lightning is also registered by burn marks on the embankment.

There are burn marks on the embankment and burn marks on the train. The burn marks on the embankment move relative to the train passenger. The burn marks on the train do not. And the principle of relativity says that the train passenger is perfectly justified in treating the burn marks on the train, which are not moving relative to him, as marking where in space the lightning strikes happened.

This has already been pointed out to you, but you don't appear to have grasped the implications:

Only at the moment of the lightning strikes is the passenger equidistant between them.

Only at the moment of the lightning strikes is the passenger equidistant between the locations on the embankment where the burn marks are made. But the passenger is always equidistant between the locations on the train where the burn marks are made.

Again, this has already been pointed out to you, but you don't appear to have grasped the implications.

According to standard interpretation, the discrepancy of opinion between observers results from the relativity of simultaneity, which follows from relative motion in the context of the absolute speed of light.

You are conflating two different things, only one of which is a "discrepancy of opinion".

The fact that the embankment observer has both light signals arrive at him at the same instant, while the train observer has the light signals arrive at him at different instants--the front signal first, then the back--is not a "discrepancy of opinion". It is a direct observable, and both observers will agree on it--that is, both observers will agree that the embankment observer has both signals arrive at him at the same instant, while the train observer has the front signal arrive at him first, then the back signal. There is no matter of "opinion" here; these are directly observed facts. The embankment observer could even watch the train observer and see that the two light signals arrive at the train observer at different instants.

The "discrepancy of opinion" is over how the embankment and train observers assign a "time" to events that do not happen where they are located, such as the lightning strikes. And Einstein's argument is that the obvious way to do this, which is to simply subtract the light travel time (given that the distance to the event is known) from the time of arrival at the observer, results in relativity of simultaneity when combined with the postulate of the constancy of the speed of light and the directly observed facts I described in the previous paragraph.

I think a better explanation is that the discrepancy results from the fact that one of the observers, the passenger, moves towards the site of one of the lightning strikes and away from the site of the other lightning strike during the time taken by the light signals emitted from the lightning events to reach the center of the train. In this case the discrepancy of opinion is caused by the finite speed of light.

First, the finite speed of light is necessary anyway. Try analyzing the experiment with an infinite speed of light in the embankment frame; you will see that it is impossible to have the two light signals arrive at the same instant at the embankment observer, but different instants at the train observer. This is because the scenario, by construction, has the two observers passing each other at the same time, in the embankment frame, as the lightning strikes.

Second, once again, you are treating "motion" as absolute, but that contradicts the principle of relativity. The train observer is perfectly justified in treating the locations of the lightning strikes as marked by the burn marks on the train, which do not move relative to him. And that means he cannot explain the fact that the light signals from the strikes arrive at him at different instants, by the finite speed of light alone. He also has to assign different times to the strikes themselves.

 

[pheurton]

What you're saying is that the locations of the lightning strikes stay with the train even as it continues traveling. So if my car is hit with hail when I'm on the highway, even after I get home and see the dents in the roof of my car, I'm still at the location where the car was damaged because wherever the car goes, the site of the damage goes with it.

It's just hard to believe you would maintain this position outside the context of Einstein's train-lightning thought experiment. My sense is that you're telling yourself a story to justify your belief that the thought experiment captures the relativity of simultaneity. I think his 1905 thought experiment, which is totally different from this one, does in fact illustrate the relativity of simultaneity. But this one just illustrates the banal fact that if you don't take into account the finite speed of light, your estimate of the timing of an event will be off.

 

[PeterDonis]

if my car is hit with hail when I'm on the highway, even after I get home and see the dents in the roof of my car, I'm still at the location where the car was damaged because wherever the car goes, the site of the damage goes with it.

You're at the location where the car was damaged relative to the car. You are not at the location where the car was damaged relative to the road. Location is relative.

It's just hard to believe you would maintain this position outside the context of Einstein's train-lightning thought experiment.

Only if you fail to grasp the implications of the principle of relativity. Which you apparently have. You will not make any progress in understanding relativity if you do not grasp that.

My sense is that you're telling yourself a story to justify your belief that the thought experiment captures the relativity of simultaneity. I think his 1905 thought experiment, which is totally different from this one, does in fact illustrate the relativity of simultaneity. But this one just illustrates the banal fact that if you don't take into account the finite speed of light, your estimate of the timing of an event will be off.

We have repeatedly tried to explain to you how relativity works and how the lightning bolt thought experiment illustrates it. But we can't make you let go of your preconceptions. You have to do that yourself.

Thread closed.

 

[Nugatory]

What you're saying is that the locations of the lightning strikes stay with the train even as it continues traveling

You are still stuck at the big conceptual hurdle: when you say “the train is traveling” you are actually saying “I have made the completely arbitrary choice to consider the platform to be at rest and the train moving, and not the other way around”. That choice is why it feels natural to think that the location of the lightning strikes “stays with” the platform but not the train.

Suppose that you were in Mars, moving at several kilometers per second relative to the earth, and watching this whole thing through a telescope. Why would you expect the locations of the lightning strikes to “stay with” the platform instead of the train? They’re both moving (at different speeds) relative to you.