# Observer Frame of Reference

## Main Question or Discussion Point

Practicing Lorentz transformations but still not absolutely clear about conditions for observer's frame of reference. For example:
Suppose that just as one of Einstein's long and surreally fast trains is passing a station platform, lightning strikes the platform at two points making scorch marks just short of each end of the train and on the platform. The strikes are judged simultaneous by an an observer on the platform who is equidistant from both strikes. The train then reverses slowly back to the platform. Can it be stopped so that the scorch marks are precisely aligned in spite of their being made while the train was moving at high speed relative to the platform and subject to length contraction?

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Bill_K
The scorch marks on the train will be a distance L apart, while the ones on the station will be a distance L/γ apart. The observer on the ground will attribute the difference to Lorentz contraction of the train. The observer on the train will say that the lightning strikes were not simultaneous - the one that hit the rear of the train happened later, and that's why it seems to be closer.

The scorch marks on the train will be a distance L apart, while the ones on the station will be a distance L/γ apart. The observer on the ground will attribute the difference to Lorentz contraction of the train. The observer on the train will say that the lightning strikes were not simultaneous - the one that hit the rear of the train happened later, and that's why it seems to be closer.
For the observer on the train the platform does not 'seem' to be closer. In his 3D world the platform is shorter, [STRIKE]therefore the lighning is closer.[/STRIKE]
[I have to correct myself. Actually the lightning is not closer to the observer in the train, because the lightnig happens at the end of his train with length L. The platform is indeed shorter, but the lighting is not closer to the observer in the train.]

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The scorch marks on the train will be a distance L apart, while the ones on the station will be a distance L/γ apart. The observer on the ground will attribute the difference to Lorentz contraction of the train. The observer on the train will say that the lightning strikes were not simultaneous - the one that hit the rear of the train happened later, and that's why it seems to be closer.
For the observer on the train the platform does not 'seem' to be closer. In his 3D world the platform is shorter, [STRIKE]therefore the lighning is closer.[/STRIKE]
[I have to correct myself. Actually the lightning is not closer to the observer in the train, because the lightnig happens at the end of his train with length L. The platform is indeed shorter, but the lighting is not closer to the observer in the train.]

The observer on the train will not see the lightning closer than the observer on the platform does. On the contrary, the observer on the train will see the lightning further than the observer on the platform does!
A Loedel diagram shows you how it works (formulas only can not visualize all this).

Red = train, green = platform. Red distance D (distance from observer on train to lighting) is longer than green distance D (distance from observer on platform).
For the observer on the train the platform is shorter (red P). The fact that for the observer on the train the lightning happens later is not the reason why the platform is shorter. The platform is shorter because the observer on the train can only measure the platform by other simultaneous events (E1 & E3) than the observer on the platform does (E1 & E2).

V.