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From: Richard Hachel <r.hachel@tiscali.fr>

Le 30/05/2025 à 14:13, "Paul.B.Andersen" a écrit :
> Den 30.05.2025 01:47, skrev LaurenceClarkCrossen:
> 
>> Paul, that one clock runs a different rate under certain conditions does
>> not warrant the inference that time itself runs at a different rate
> 
> Please define "time itself". How can you measure that the rate of
> "time itself" is different from the rate of your clock?
> 
> See:
> https://paulba.no/pdf/Clock_rate.pdf
> 
> Can you point out an error in 1.1 "What is proper time"?

What is proper time?
It's time measured "loco dolenti," that is, where it hurts, and elsewhere 
in the frame of reference, or worse, elsewhere in another frame of 
reference.
When someone has pain in a joint, such as the shoulder, you don't inject 
the knee. You inject, in loco dolenti.

The same is true for measuring time.

To measure the reality of things, you must measure proper time, that is, 
where it's happening, and with watches tuned to the time of the place 
where it's happening.

If we are elsewhere, in the same frame of reference, of course, time 
passes at the same speed (otherwise it would be absurd, and we would have 
to say that time passes faster in A than in B, without any logic or 
motivation). But the instants don't match. Each watch is ahead of the 
other. This is the concept of anisochrony.

If, moreover, we are not in the same frame of reference, the watches each 
run faster than the watch observed from afar. This is the concept of 
internal chronotropy dilation.

Internal chronotropies and external anisochronies cause the measured times 
to vary depending on the position and relative speed of the observers.

Faced with such a mess, there's nothing better than measuring proper time, 
or real time, the only one that everyone agrees on, at least locally.

Then, we can give an apparent time, which is the proper time of the other 
observer:
Tapp = Tr.(1 + cosµ.Vo/c) / sqrt(1 - Vo² / c²)

It's as simple as that.

The same goes for lengths, distances, and electromagnetic frequencies. All 
ratios, entirely all of them, are under the ratio or counter-ratio (1 + 
cosµ.Vo/c)/sqrt(1 - Vo²/c²).

R.H.