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Referring to Einstein's train hit by lightning bolts thought experiment.

What if, in the middle of the train, together with the moving observer there is a stopwatch, with 2 displays.

One display stops counting when the clock is hit by the beam coming from the left, and the other stops with the beam coming from the right.

At the end of the experiment, would the displays report the same time or different times?

It seems to me that in both cases, one of the observers should see the displays increasing at different speeds. If so, how could it be explained, since the clock is the same and the displays have the same momentum?

drawing

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    $\begingroup$ It depends when the bolts strike. Also: trains move forward/backward, not left/right--so it's very unclear what your are asking. $\endgroup$ – JEB Mar 11 '18 at 15:16
  • $\begingroup$ @JEB, be fair! In a drawing that illustrates the experiment, the "forward" direction of the train normally will be toward either the left or the right edge of the page. $\endgroup$ – Solomon Slow Mar 11 '18 at 15:28
  • $\begingroup$ It would greatly help to include a diagram. Right now it seems slightly unclear what you are asking. $\endgroup$ – QuIcKmAtHs Mar 11 '18 at 15:29
  • $\begingroup$ @QuIcKmAtHs, added a 'diagram' $\endgroup$ – freddyfx Mar 11 '18 at 16:22
  • $\begingroup$ @jameslarge I was fair, I didn't understand the question, and now that I do: I think it is a great one-I was stumped for a while. Of course, the resolution as always is the relativity of simultaneity. $\endgroup$ – JEB Mar 11 '18 at 16:58
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Based on the left drawing: Clocks on train, Bolts simultaneous on train: the train observer of course sees the 2 bolts at the same time and the clocks tick to the same number. The train station observer see the right flash first (it travels further to reach the center of the left moving train).

So your question is working backwards: how does the platform observer see the 2 clocks agree (which he has to: if they both display 0.02 he sees a big red 0.02 on each--there is no Lorentz transform that makes a clock display change)--when he thinks they should start at different times? This is good question and the resolution to the paradox is as follows:

The 1st problem is how do the clocks start? Note that they start simultaneously with the bolts in the train's reference frame: the bolt and the timer start have a space like separation, so it's an experiment that can't be done.

Nevertheless, it's a thought experiment: suppose the clocks just happen to be started correctly on the train. What happens is the platform observer says the clocks start at the wrong times. He see the following (time ordered):

1) Right lightning bolt

2) Both clocks start from 0.00

3) Left lightning bolt

4) Bolts hit middle, both clocks stop, reading 0.02.

So for the platform observer, neither clock measured the transit time of the lightning flash it was observing.

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  • $\begingroup$ Whatever the initial value is, both displays are synchronized. For the train observer, they stop at the same value. For the platform observer, there is an interval between the first display being stopped and the second. How is it possible for the second display to stop without being hit by the second lightning bolt? According to the platform's observer laws of physics, the second display should keep running, and stop only when the complicated machinery of 'stop value' is activated by the second lighnting. $\endgroup$ – freddyfx Mar 14 '18 at 16:14
  • $\begingroup$ For the platform observer, the start times of the clocks are not related to the lightning bolt strikes. Nothing is synchronized for him. Intervals with space-like separation cannot be time ordered in all reference frames. $\endgroup$ – JEB Mar 14 '18 at 22:57
  • $\begingroup$ Also: If by "complicated machinery" you mean something that can get signals instantaneously across a distance, that is, from outside its lightcone, then yes: you will violate the laws of physics. $\endgroup$ – JEB Mar 14 '18 at 23:12
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Are you asking about this gedankenexperiment?

If so, then the whole point of it is to prove that observers in different reference frames will not be able to agree on the time-order of the lightning strikes. Your fancy clock-with-two-displays is just a schematic representation of an "observer."

At the end of the experiment, would the displays report the same time or different times?

The answer depends on the clock's frame of reference. A clock on the train will give one answer. A clock on the ground will give a different answer.

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  • $\begingroup$ @SrikarAnandYellapragada, The clocks are schematic representations of observers. If you were on the train, and you observed the lightning bolts to flash in a particular order, would you subsequently change your mind about what you had seen if the train subsequently stopped? $\endgroup$ – Solomon Slow Mar 11 '18 at 15:48
  • $\begingroup$ Thanks for answering. I understand that my question was not clear, I added a drawing. There is only one watch on the top of the train. How could the two observers versions conciliate? $\endgroup$ – freddyfx Mar 11 '18 at 16:26
  • $\begingroup$ @FedericoInfanti, The "watch" that you have described is the observer. It observes the two flashes, and it records the timestamps of each flash on its two displays. The two humans that you have drawn are not observers. They only look at what the device recorded after the experiment is over. There is only one device in your picture, and it records what it records, and there is no reason to think that the two humans would see the record any differently. $\endgroup$ – Solomon Slow Mar 11 '18 at 16:54
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The left case is not equivalent to the right one. If the bolts are simultaneous on the train frame, they CANNOT be simultaneous on the station frame. So you compare two different experiments. Hence it is normal that results are different !

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