🚀 go-pugleaf

Wolfgang G. Gasser wrote:
> Two distant observers with each a (transversal) LIGHT CLOCK orbit at a
> constant distance around their common center (assumed at rest).
> 
> Special relativity postulates that the light beams in both light clocks
> propagate at c relative to both (almost inertially moving) observers.

That is the key point -- these observers are NOT moving inertially. The 
approximation is important (see below), and negates your claims.


> This requires that for each observer the clock rate of the opposite clock
> CAN be lower than the clock rate of his own clock.
> Because of symmetry and unchanging distance, clock rate CANNOT differ.

The error is in your gedanken, not in SR itself.

For approximately inertial motion, the basic equations of SR are only 
APPROXIMATELY valid. You ignored the approximation you, yourself, made.

At a deeper level, however, such orbiting observers cannot be treated as 
inertial observers, because a circle is different topologically from a 
line. In SR's Minkowski spacetime, inertial observers move in straight 
lines, not in circles, and the basic equations of SR are valid for 
inertial observers and coordinates. Yes, for a very large radius a 
circle is approximately a straight line for a small portion of its 
circumference, but if one uses the fact it is a circle in any way, or 
uses a large fraction of the circumference, then these are not inertial 
observers, not even approximately.

In your gedanken, you are using the circular motion when you say 
"because of symmetry and unchanging distance".


The right way to consider this is to ask: for two observers on the 
circumference of a rotating disk, how do they observe the tick rate of 
each others' clocks? Assuming that each clock emits an EM signal at each 
tick, and the other observer receives this signal and compares the rate 
of the received signal to their own clock's tick rate, the answer is 
that both received signals have the same rate as the local clock. This 
answer is independent of radius, rotation rate, and separation of the 
two observers around the circle.


Francois Guillet wrote:
> Special relativity doesn't apply to non inertial reference frames.

This is not true. The basic equations of SR are written in terms of 
inertial coordinates, and these equations are valid only in inertial 
frames. But one can use calculus to determine transforms to non-inertial 
coordinates, and SR remains valid using such coordinates and the 
transformed equations.

SR applies only to Minkowski spacetime, however. That is, neither 
curvature of the manifold nor topology other than R^4 can be handled in SR.


Tom Roberts