Hey Jorrie,

This is smooth, but I'm afraid its too smooth for my liking!

You are saying that it all depends on how clocks are synchronized. You are also saying that clocks should be synchronized a-la Einstein. So why do we have to believe Einstein's method? I'm sure there must be other ways to synchronize clock that does not lead to these paradoxes.

Guest, you wrote: "So why do we have to believe Einstein's method? I'm sure there must be other ways to synchronize clock that does not lead to these paradoxes."

Yep, there are other ways, but the only ones that produce consistent results, give synchronization that is indistinguishable from Einstein's method. Two examples are: slow transport of clocks synchronized in one location and the firing of high speed material particles (with a known speed) between clocks.

Regards, Jorrie

OK, let's modify our arrow-in-a-box experiment. Now we have a linear chain of LED+photodiods (couples) with equal distances 'a' between them. The light beam of each couple can be interrupted by a fast moving plate, which is 2.1*a long (when it is still). Now we make a simple electric circuit: if only one couple disrupted -- nothing happens, but if two or more -- siren sounds. In still reference frame of opto-couples a very fast moving plate is short, shorter than 1*a, so no siren sounds. But from the point of view of the moving plate the distance between couples is shorter than 1*a, while the plate is 2.1*a long, so we definitely disrupt two or more light beams. Hence a siren must sound. But how could it be that there are two such different result of the same experiment?

Hi guest. This is an interesting question, with a simple solution (if I understand your scenario correctly), but before attempting an answer, let me verify the scenario with a diagram.

Is this more or less the setup that you intended? The green (static) plate always interrupts 2 or 3 couples, while a fast moving plate, Lorentz contracted to x-dimension shorter than a, can only interrupt 0 or 1 couple. Note that this is a space-space diagram, not a spacetime diagram.

If my interpretation is correct, would you mind if I use this as a "challenge question" in a separate thread to attract more comments (before answering it)?

Jorrie

PS: if this question is answered somewhere in the literature, it may perhaps not be a viable challenge question...(?)

Hi Jorrie,

Excellent illustration (sure this is a space-space diagram). This is exactly my question. Depending on reference frame, the green "plate" is either longer or shorter than the distance between sensors, and we should be able to detect which way it is. Am I right?

Thanks,

my name is Vladimir.

Of course, you may use my question as a "challenge". Do whatever you want with it.

Did this post ever get an answer? It is a very interesting question. Either the siren sounds or it doesn't - it can't sound in one frame of reference and not in another. But either behaviour would seem to be inexplicable for one of the two observers.