🚀 go-pugleaf

Edward Green says...
>
>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.

[stuff deleted]

>Obviously the situation is fully symmetric, but then, so is the
>situation of inertial observers passing each other at constant
>velocity: why bother with the rotation, when we could already argue
>that "each clock is running slower with respect to the other, which is
>obviously impossible".

Well, there is a big difference in that, for the case of
two inertial observers, each can consistently believe that
the other clock is "running slower" and no observation will
ever contradict that assumption.

In contrast, with the two orbiting observers, there is an easy
way to show that the other clock isn't "really" running
slower: if each observer sends out a light signal once per
second (as measured by his local clock), then those signals
will be received exactly once per second by the other observer.

>The "non-inertial observer" thing seems cheap to me, and possibly off
>the mark.  Rotating rings force SR to show its cards by allowing
>movement in a closed path, but acceleration is not necessarily crucial:
>it can be made as small as we like for fixed speed of the circumferance
>by choosing a large enough ring.

The important fact about non-inertial observers is not (necessarily)
that the observer feels any acceleration. It's the fact that he cannot
use an inertial *coordinate* system (at least not if he wants to consider
himself at "rest"). For an orbiting observer to consider himself at
rest, he has to use a non-inertial coordinate system, and for such
a coordinate system, one cannot simply calculate the time on a distant
clock by using velocity-dependent time dilation. Time dilation for
non-inertial coordinates depends on position and time, as well as
velocity.

>Both clocks are running slow as
>according to an inertial observer at the hub.  How do they describe
>each others behavior?  They had better be careful to make some
>empirical predictions!  Then they will agree.  Distrust glib language.

Right.

--
Daryl McCullough
Ithaca, NY