Re: 1. On the notion of simultaneity in special relativity

On 2024-08-29 11:32:26 +0000, Richard Hachel said:

Le 29/08/2024 à 10:40, Mikko a écrit :

 We also can do otherwise. It is best to define simultaneity so that it
can be used for the construction of the time coordinate of a coordinate
system. If we can find a signal that has the same speed in all directions
we can use that. For example, sound in a metal bar that is stationary
with respect to the coordinate system being constructed.
 Mikko

 If I could send a sound along a metal bar from here to the moon (a bar 3.10^8m long for example). The sound itself would not be constant according to the longitudinal direction of travel.
It would be faster in the return direction. And vice versa for a lunar observer.

There is no basis to say that the speed of sound is different in different
directions or for different pbserves. The speed is the distance divided by
the duration. But the duration does not exists unless the notion "at the
same time" is defined, and if the duration doesn't exist then neither does
the speed.
EInstein's synchronization is for clocks that are at rest relative to
each other. Moon and therefore a clock on Moon is not at rest relative
to a Earth and a clock on Earth. Therefore the defintion of "at the
same time" must be chosen differently if Moon needs be covered.
--
Mikko