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Consider the classic example to show that simultaneity does not hold:

Have a photon gun firing two counter-propogating photons from the center of a moving train. The observer inside the train sees both photons hit the ends of the train simultaneously, whereas an outside observer sees the photon hit the rear-end of the train first.

Now if you modify the experiment by adding two photosensitive devices on the end of the train, and have an explosion that occurs when both photosensitive devices are triggered simultaneously.

From the reference frame inside the train, since the photons hit both ends simultaneously, the explosion will occur and the train will blow up.

However, from the reference frame outside, since the events are not simultaneous, nothing happens.

Clearly you cannot have two possible outcomes to the same event, but how do you resolve this apparent paradox?

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    $\begingroup$ The explosion occurs when the devices are hit simultaneously from what frame of reference? That is the key question. $\endgroup$ – Javier Aug 15 '15 at 3:01
  • $\begingroup$ @Javier Ah I think I get it. When you install the device you will be working in the reference frame of the train so that it triggers when the devices are hit simultaneously from the reference frame of the moving train. However, what is simultaneous inside the train is not necessarily simultaneous to an outside observer. Hence to the outside observer the device will trigger when the events are not simultaneous, as governed by the lorentz transformations. So the device will indeed explode in both cases. $\endgroup$ – 1110101001 Aug 15 '15 at 3:07
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    $\begingroup$ @1110101001 Feel free to answer your own question :) $\endgroup$ – user10851 Aug 15 '15 at 3:25
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//Answering my own question with a modified version of my comment

The key is that the devices are defined to only explode when hit simultaneously from the reference frame of the moving train. However, what is simultaneous inside the train is not necessarily simultaneous to an outside observer. Hence to an outside observer the device will appear to be defined as triggering when the events are not simultaneous (as governed by the lorentz transformations). So the device will indeed trigger in both reference frames due to their respective definitions in those frames.

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