Off to do the math. I presume OP is Original Premise. Since that's overly complex, let's get back to the Simplified Premise with just 4 clocks.
One thing I'm not clear on. I think I need a time zero that is zero in multiple frames of reference, at least when calculated from clock Z's frame of...
As the intersections described earlier happen in higher dimensionality space, there are several things that can happen: 1) The line remains a straight line, the flat filled circle remains a flat filled circle. 2) The line becomes a curved line, with more curves possible as dimensionality...
Consider a flatland 2D space with a filled circle and its intersection with a different flatland 2D space. Since we live in a 3D volume rather than a 2D plane, we can visualize such an interaction. Statically, the intersection forms a line when viewed from either of the different flatlands. This...
I'm sure that you're right and that the math will all work out in the end. Perhaps the simplest way of looking at it, from the stay at home clock, is the best.
Still, I'd like to look at it from the point of view of some of the multiple clocks and just do the math for an example or two, but...
Doesn't your answer assume, then, that there is an absolute measurement of speed? Only in relation to the stay at home clock are speed measurements the same.
Clocks that go out in similar directions would move slower in relation to each other. Clocks that go out in differing directions would...
What would a 3D ball look like if it were partially in 4D space when none of the 4th dimension is visible to the 3D observer?
The equivalent question in flatland is: What would a 2D filled circle look like in flatland if it was partially in 3D?
I think that there the answer would be a...
Consider a large number of clocks each within some apparatus programmed to accelerate away from, remain moving for a time, accelerate toward, remain moving for a time and then return to a point of origin. A similar clock simply remains at that point of origin. The accelerated clocks will reach...
As I understand it, clocks run relatively slower the closer they are to the center of a "gravity well" and also each other clock for a pair of observers moving relatively to each other appears to be running slower, relative to each frame of reference.
So, start with a pair of highly accurate...