- #1
Fantasist
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I addressed already recently in this thread the issue of defining the synchronicity of clocks moving relatively to each other (considering that the synchronization by Einstein's method implies clocks at rest), but it occurred to me now that even for clocks at rest relatively to each other there is a problem with the practical definition as far as its frame dependence is concerned. On the basis of his two-way light signal propagation thought experiment, Einstein concludes at the end of paragraph 2 in http://www.fourmilab.ch/etexts/einstein/specrel/www/
So we see that we cannot attach any absolute signification to the concept of simultaneity, but that two events which, viewed from a system of co-ordinates, are simultaneous, can no longer be looked upon as simultaneous events when envisaged from a system which is in motion relatively to that system.
Let us look a little bit closer at the thought experiment on which this conclusion is based. For this purpose, let us slightly modify it for clarity and assume each of the two clocks (stationary with regard to each other) sends out a light signal at the same time (according to each of the clocks). Halfway between the two clocks is a detector that registers both signals. We can now define that the two clocks in question are synchronized with each other if the detector registers them simultaneously (according to its own time). Let's further assume that in this case both signals are completely absorbed by the detector. On the other hand, if the signals do not arrive simultaneously (within a defined window) they are not absorbed but carry on to the other clock (where they can be subsequently detected).
Now with this practical definition of simultaneity, how can this possibly be frame dependent? The two signals are either absorbed or not absorbed. All observers would have to agree about this physical fact. So evidently, this setup could not experimentally define the relativity of simultaneity. The question is how do we have to change/generalize the setup so that it is consistent with Einstein's conclusion?
So we see that we cannot attach any absolute signification to the concept of simultaneity, but that two events which, viewed from a system of co-ordinates, are simultaneous, can no longer be looked upon as simultaneous events when envisaged from a system which is in motion relatively to that system.
Let us look a little bit closer at the thought experiment on which this conclusion is based. For this purpose, let us slightly modify it for clarity and assume each of the two clocks (stationary with regard to each other) sends out a light signal at the same time (according to each of the clocks). Halfway between the two clocks is a detector that registers both signals. We can now define that the two clocks in question are synchronized with each other if the detector registers them simultaneously (according to its own time). Let's further assume that in this case both signals are completely absorbed by the detector. On the other hand, if the signals do not arrive simultaneously (within a defined window) they are not absorbed but carry on to the other clock (where they can be subsequently detected).
Now with this practical definition of simultaneity, how can this possibly be frame dependent? The two signals are either absorbed or not absorbed. All observers would have to agree about this physical fact. So evidently, this setup could not experimentally define the relativity of simultaneity. The question is how do we have to change/generalize the setup so that it is consistent with Einstein's conclusion?