Re: Understanding the theory of special relativity

Le 17/01/2025 à 13:30, "Paul.B.Andersen" a écrit :

Den 17.01.2025 02:37, skrev Richard Hachel:

Langevin's paradox.
 What is true is that, continuously, second after second, in Terrence's frame of reference, the internal mechanism of Stella's watch will beat less quickly. It is said that this one has a lesser internal chronotropy compared to Terrence's watch.

 Consider the following scenario:
 Terrence is inertial somewhere in space.
 Stella is in a rocket and is co-located with Terrence when
she starts her rocket engine and accelerates at 1 c/year
away from Terrence for 2.25 year on her clock.
Then she turns her rocket around and accelerates at 1 c/year
towards Terrence for 4.5 years.
Then she turns her rocket around and accelerates (brakes) at 1 c/year
away from Terrence for 2.25 years.
 When Stella is back at Terrence both stop their watches.
They are now co-located and stationary to each other.
Their clocks are side by side and can easily be compared.
Terrence clock shows 23.7 years.
Stella's watch shows 9 years.
 

 But what is also true is that the laws of physics are the same in all frames of reference, and that the effects of physics are reciprocal by permutation of observer. For Stella, and this is where humanity makes an extraordinary block on the theory, it is the opposite that is true. For her, it is the internal mechanism of Terrence's watch that beats constantly less quickly, during  his journey.

 Are you saying saying that Terrence watch shows  23.7 years,
but Stella will see that Terrence's clock shows 9 years?
 Are you saying saying that Stella's watch shows 9 years,
but Terrence will see that Stella's clock shows 23.7 years?
 How can Stella and Terrence see two different readings
on the watches which are right in front of them?
 Or what are you saying?

No, that's not what I'm saying.
What I'm saying is that depending on the relative speed, the CHRONOTROPY of watches is reciprocally lower elsewhere.
RECIPROCALLY.
This is very difficult to understand for a Newtonian, but for anyone who has read Henri Poincaré, it SHOULD be understandable.
This means that:
1. In the story of the traveler of Langevin, and at all times of all existences, EACH will notice that the chronotropy of the other watch is constantly lower.
A bit like a bad watchmaker who will make a clock whose internal mechanism turns less quickly than a normal hormole.
This phenomenon of relativity of chronotropy is due to the relative speed. It is reciprocal. The equation is absolutely invariable and concerns the entire universe.
To=tau/sqrt(1-Vo²/c²)
There is no other equation to predict or to look for.
This equation is constantly being refined, and constantly the other person's watch will run slower for us, second after second.
Conversely.
2. It is strictly the same thing in rotating, accelerated, hysterical frames of reference or whatever you want.
Always, always, always, there will be an instantaneous speed, and at this instantaneous speed, the equation will have to be applied.
On the other hand, there is an error in your solution to the problem posed.
But it is not surprising, you follow the teachings of relative physicists by arguing that they are stronger than me, and I can do nothing about that.
R.H.