Sunday, December 15, 2013

Simultaneity

This thought requires agreeing that, in an equilateral arrangement of three points, every vertex is able to detect simultaneous events occurring at the other two vertexes, also the following:   If you had a tool--let's say, compass and ruler--and you had been able to "square the circle," would you not have shown that it were possible to do so? If you agree, please proceed.

Imagine two points in space A and B. They are any distance apart but stationary with respect to themselves and point C. Each has an identical length of fiber optic cable the ends of which are as close as possible to an event occurring at C. If those cables had an identical shape (both semi-circles, for instance; although a spiral may be more accommodating  in most situations where, for instance, A is closer to C than B is), would A and B not be able to detect an event occurring at C regardless of how far apart they (A and B) are to each other and to C? Also, more traditionally, would C not be able to detect if an event occurred simultaneously at A and B?

What if one point were in motion relative to the others? The speed of light is constant and the distance that information has to travel is the same for CA as it is for CB (following the equidistant path of the fiber optic cable and assuming symmetry can be maintained (in at least one dimension?).