I Problems with Einstein's 1920 "Relativity"

[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.