On Friday, August 25, 2023 at 12:41:27=E2=80=AFAM UTC-5, Luigi Fortunati wrote:
...
> The graduated belt of my animation is directly *bound* to the Earth and
> its rotation.
>
> This makes its measurement (direct and immediate) more reliable than
> the measurement at distance with light.
I'll try one last time to make this point. The time "now" for events outside
the light cone, e.g. events that are spatially separated, are not uniquely
defined for different observers.
I must ask what meaning you attach to a time "now" back on earth? It
is not the time you can see, via light, from earth. In fact there is nothing
you can do to interact with earth "now" in any way. The only way to
know what is happening "now" is to wait for that event to enter your
past light cone, at which time you can see it. At that later time you can
know what happened back when you identified a time as "now".
If you want to define some time as "now" by some mechanism like you
describe, that is OK. But the conventional way to define "now" is to
synchronize clocks as described in most any book on special relativity.
That process allows you to define a "now" that conforms with what
we all normally think of as "now". It gives a different result for different
inertial observers, but it gives a result that each observer can make
sense of as "now". That is, if they do some experiment such as send
a time message via light, the result is consistent with special relativity.
There is another factor that you are not taking into account: The
Lorentz contraction of each side of the belt will be different for
moving observers. This may seem as it should be negligible for
such a slow moving belt, but note that magnetic fields are the result
of just such a difference in Lorentz contraction even though the
electrons in a wire are moving at less than 1 mm/second. In the
case of your belt model, a rapidly moving observer will see that
one side of the belt has shrunk compared to the other, and thus
the earth is rotated relative to what the "stationary" observer
calculates.
Rich L.
[[Mod. note -- That's a very clear (and completely correct) exposition.
Thank you!
-- jt]]