Re: Sync two clocks

On 2024-08-25 06:55:16 +0000, Thomas Heger said:

Am Samstag000024, 24.08.2024 um 10:02 schrieb Mikko:
...
 

How is it possible to fail to understand this?
 If we have two stationary clocks in an inertial frame,
 and clock A shows tA = t1 when it emits light,
 and clock B shows tB = t1 + td when the light hits it,
 and clock A shows tA'= t1 + 2⋅td when it is hit by the reflected light,
 then tA, tB, tA', t1 and td are all proper times which are frame
independent (invariants) and "the same for all".
  tB − tA = t'A − tB = td
 The transit time td is a frame independent invariant and
the same in both directions, which means that the clocks according
to Einstein's _definition_ are synchronous in the inertial frame.

 You introduced t_d or 'transit time' (aka 'delay'), while Einstein didn't use any of these terms.

 Einstein used tB - tA and similar expressions. Nothing else needs be
said about delays. The equation tB − tA = t'A − tB and the text that
describes the situation and defines what tA, t'A and tB mean define
clearly and unambiguously what simultaneity and synchronity mean.

 But this has nothing to do with synchronicity, but with a process to turn remote clocks to the same time value.

 That is the same thing. Two clocks are sychronous if and only if the
show the same at the same time.

 Well, I would agree on that.
 But what do you mean with 'at the same time'?

Basically it means that the time coordinates of the events have the
same value.
As Einstein noted, these words don't mean anything until a defintion
is given. Then he gave his definition. That is a reasonable definition
but you may choose a different one if you need a differenct concept.

As I see it, we need to adress the so called 'hyperplane of the present' with 'at the same time'.
 This is the set of events, which would require an infinetely fast signal, to recognize them at the same time.
 Since no such signal exists, the hyperplane of the present is mainly invisible.
 What we actually see, like in the nicht sky and call 'universe', is visible, hence does not belong to the hyperplane of the present.

But it does belong to another useful hypersurface: a light cone.

Therefore, synchronization with light signals isn't a very good idea, because it is light what we see and light would not allow infinite fast communication.

It is, though of course not necessary. For Einstein's article light is
a good choice becoase his tpoic was electrodynamics and his theory had
simple postulates about the behaviour of light. The partiular way to
use light was the one that gives the synchoriniztion the desired
properties, in particular that if clock A is synchronous with clock B
then clock B is synchronous with clock A.
Although Einstein worked in a different order, it is often clearer to
postulate that isometric coordinate systems are related by Poincaré
(or just Lorentz) transformations and infer the rest from that. Then
one may define simultaneity as "at the same time" and prove form that
that Einstein's method gives that concept of simultaneity.
--
Mikko