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Understanding the theory of special relativity

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  Understanding the theory of special relativity Richard Hachel <r.hachel@liscati.fr.invalid> - 2025-01-17 01:37 +0000
    Re: Understanding the theory of special relativity "Paul.B.Andersen" <relativity@paulba.no> - 2025-01-17 13:32 +0100
      Re: Understanding the theory of special relativity Maciej Wozniak <mlwozniak@wp.pl> - 2025-01-17 14:33 +0100
      Re: Understanding the theory of special relativity Richard Hachel <r.hachel@liscati.fr.invalid> - 2025-01-18 08:47 +0000
      Re: Understanding the theory of special relativity Richard Hachel <r.hachel@liscati.fr.invalid> - 2025-01-18 09:04 +0000
        Re: Understanding the theory of special relativity Richard Hachel <r.hachel@liscati.fr.invalid> - 2025-01-18 09:10 +0000
        Re: Understanding the theory of special relativity "Paul.B.Andersen" <relativity@paulba.no> - 2025-01-18 20:28 +0100
          Re: Understanding the theory of special relativity Richard Hachel <r.hachel@liscati.fr.invalid> - 2025-01-18 19:56 +0000
            Re: Understanding the theory of special relativity "Paul.B.Andersen" <relativity@paulba.no> - 2025-01-19 14:44 +0100
              Re: Understanding the theory of special relativity Richard Hachel <r.hachel@liscati.fr.invalid> - 2025-01-19 14:57 +0000
                Re: Understanding the theory of special relativity "Paul.B.Andersen" <relativity@paulba.no> - 2025-01-20 20:26 +0100
                  Re: Understanding the theory of special relativity Richard Hachel <r.hachel@liscati.fr.invalid> - 2025-01-21 10:30 +0000
                    Re: Understanding the theory of special relativity Maciej Wozniak <mlwozniak@wp.pl> - 2025-01-21 14:27 +0100
                      Re: Understanding the theory of special relativity Richard Hachel <r.hachel@liscati.fr.invalid> - 2025-01-21 13:46 +0000
                        Re: Understanding the theory of special relativity Maciej Wozniak <mlwozniak@wp.pl> - 2025-01-21 16:00 +0100
                    Re: Understanding the theory of special relativity "Paul.B.Andersen" <relativity@paulba.no> - 2025-01-21 15:35 +0100
                      Re: Understanding the theory of special relativity Richard Hachel <r.hachel@liscati.fr.invalid> - 2025-01-21 16:31 +0000
                      Re: Understanding the theory of special relativity Richard Hachel <r.hachel@liscati.fr.invalid> - 2025-01-21 16:51 +0000
                        Re: Understanding the theory of special relativity "Paul.B.Andersen" <relativity@paulba.no> - 2025-01-22 22:13 +0100
                          Re: Understanding the theory of special relativity Maciej Wozniak <mlwozniak@wp.pl> - 2025-01-23 07:41 +0100
                          Re: Understanding the theory of special relativity Richard Hachel <r.hachel@liscati.fr.invalid> - 2025-01-23 07:50 +0000
                          Re: Understanding the theory of special relativity Richard Hachel <r.hachel@liscati.fr.invalid> - 2025-01-23 08:02 +0000
                            Re: Understanding the theory of special relativity "Paul.B.Andersen" <relativity@paulba.no> - 2025-01-23 21:34 +0100
                              Re: Understanding the theory of special relativity Maciej Wozniak <mlwozniak@wp.pl> - 2025-01-23 23:10 +0100
                          Re: Understanding the theory of special relativity Richard Hachel <r.hachel@liscati.fr.invalid> - 2025-01-23 08:22 +0000
                            Re: Understanding the theory of special relativity "Paul.B.Andersen" <relativity@paulba.no> - 2025-01-23 21:54 +0100
                              Re: Understanding the theory of special relativity Maciej Wozniak <mlwozniak@wp.pl> - 2025-01-23 23:12 +0100
                              Re: Understanding the theory of special relativity Richard Hachel <r.hachel@liscati.fr.invalid> - 2025-01-23 22:59 +0000
                                Re: Understanding the theory of special relativity "Paul.B.Andersen" <relativity@paulba.no> - 2025-01-24 12:19 +0100
                                  Re: Understanding the theory of special relativity Richard Hachel <r.hachel@liscati.fr.invalid> - 2025-01-24 11:46 +0000
                                  Re: Understanding the theory of special relativity Thomas Heger <ttt_heg@web.de> - 2025-01-25 07:39 +0100
                          Re: Understanding the theory of special relativity Richard Hachel <r.hachel@liscati.fr.invalid> - 2025-01-23 09:45 +0000
                  Re: Understanding the theory of special relativity Richard Hachel <r.hachel@liscati.fr.invalid> - 2025-01-21 10:56 +0000
              Re: Understanding the theory of special relativity The Starmaker <starmaker@ix.netcom.com> - 2025-01-19 12:14 -0800
          Re: Understanding the theory of special relativity Maciej Wozniak <mlwozniak@wp.pl> - 2025-01-18 23:08 +0100

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#660726

Le 22/01/2025 à 22:11, "Paul.B.Andersen" a écrit :
> Den 21.01.2025 17:51, skrev Richard Hachel:

> But you are very confused, and understand nothing.

  :))
 
> You are referring to the phenomenon that when two _inertial_ clocks
> are in relative motion, then, in the _inertial_ rest frame of each
> clock, the other clock will be measured to run slow.

 That' what I said 
> 
> This phenomenon is called "mutual time dilation".

 Absolutely.

 But the term is slightly improper, because it can make you think that we 
are talking about the times noted on watches.

Paul, Paul, I see that you still haven't understood, and you are still 
repeating the same inaccuracies, the same bad judgments about what I say.

The term "mutual dilation of chronotropies" is more accurate, but 
apparently, the scientific community should be afraid of it, because, 
except in the medical field, it is very difficult to pronounce. LOL.
> 
> =========================================================
> There is reciprocity because _both_ clocks are inertial.
> ==========================================================

 Sure. 

> 
> But the rate of each clock isn't affected in any way by the speed of
> of the other clock, each of the clocks is _always_ running at its
> normal pace, one second per second.

Absolutely. And? 
 
> There is no "internal mechanism" in the clocks which
> is affected by the speed of the other clock.
> 
> This should be blatantly obvious for anybody who can think.
> There are millions of clocks in the world, and each clock
> can't be affected in millions of different ways at the same time.

 That's not what I said. It's an absurd thought that belongs to no one.
> 
> See:
> https://paulba.no/pdf/Mutual_time_dilation.pdf
> 
> Read it!

 Je l'ai lu depuis longtemps. 

R.H. 

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#660727

Le 22/01/2025 à 22:11, "Paul.B.Andersen" a écrit :
> =========================================
> There is no reciprocity in this scenario.
> =========================================

There is reciprocity ; and accelerations, weight, gravity have nothing to 
do with the theory of relativity. I know that by saying this, I have all 
the guns in the world pointed at me, but it is reality. There is 
reciprocity. Why?
Because the theory of relativity, and more precisely the Lorentz factor, 
which is one of the cornerstones of understanding, only relies on one 
thing: relative speed.
This is called the dilation of chronotropies and accelerations have 
nothing to do with it, only the RELATIVE SPEED at each precise moment.
Now dilation of chronotropies does not mean dilation of the times written 
on watches. We must not forget that when I move at high speed, I not only 
move at a certain speed, whatever the direction of my movement, but that I 
also move in space, and that I modify my distance from the observer who 
apprehends me and vice versa. A sort of Doppler effect (anisochrony) will 
be created that must also be taken into account on watches. There are 
therefore two phenomena: anisochrony, and the dilation of chronotropies. 
The internal mechanism of watches (second degree) and the external 
mechanism of watches.
You are not making any effort Paul, it is a pity, because you are still 
one of the best specialists on the problem.

R.H. 

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#660736

Den 23.01.2025 09:02, skrev Richard Hachel:
> Le 22/01/2025 à 22:11, "Paul.B.Andersen" a écrit :
>> =========================================
>> There is no reciprocity in this scenario.
>> =========================================

The subject line is:"Understanding the theory of special relativity"

What SR predicts is not a matter of opinion, it is a matter of fact.

This is the fact:

https://paulba.no/pdf/TwinsByMetric.pdf
See: 2.3 "B travels with constant acceleration"
and: 2.4 "Concrete example"

> 
> There is reciprocity ; and accelerations, weight, gravity have nothing 
> to do with the theory of relativity.

Gravitation has nothing to do with The Special Theory of Relativity.
But in this scenario twin B is accelerating during the whole journey,
and an accelerated object has weight.

> There is 
> reciprocity.  Why?
> Because the theory of relativity, and more precisely the Lorentz factor, 
> which is one of the cornerstones of understanding, only relies on one 
> thing: relative speed.

The Lorenz factor depends only on their relative speed.
But their speed in an inertial frame also depends on their
_proper_ accelerations.

See equation (14)

So for the scenario to be reciprocal both their relative speed
and their proper accelerations must be reciprocal.

Their relative speed is reciprocal, but their accelerations are not.

This is the reason why their proper times are different.

Twin A ages 23.664 year
Twin B ages  9.912 year

No reciprocity.
Fact.
Nothing more to discuss.


-- 
Paul

https://paulba.no/

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#660744

W dniu 23.01.2025 o 21:34, Paul.B.Andersen pisze:
> Den 23.01.2025 09:02, skrev Richard Hachel:
>> Le 22/01/2025 à 22:11, "Paul.B.Andersen" a écrit :
>>> =========================================
>>> There is no reciprocity in this scenario.
>>> =========================================
> 
> The subject line is:"Understanding the theory of special relativity"
> 
> What SR predicts is not a matter of opinion, it is a matter of fact.
> 
> This is the fact:
> 
> https://paulba.no/pdf/TwinsByMetric.pdf
> See: 2.3 "B travels with constant acceleration"
> and: 2.4 "Concrete example"
> 
>>
>> There is reciprocity ; and accelerations, weight, gravity have nothing 
>> to do with the theory of relativity.
> 
> Gravitation has nothing to do with The Special Theory of Relativity.
> But in this scenario twin B is accelerating during the whole journey,
> and an accelerated object has weight.
> 
>> There is reciprocity.  Why?
>> Because the theory of relativity, and more precisely the Lorentz 
>> factor, which is one of the cornerstones of understanding, only relies 
>> on one thing: relative speed.
> 
> The Lorenz factor depends only on their relative speed.
> But their speed in an inertial frame also depends on their
> _proper_ accelerations.
> 
> See equation (14)
> 
> So for the scenario to be reciprocal both their relative speed
> and their proper accelerations must be reciprocal.
> 
> Their relative speed is reciprocal, but their accelerations are not.
> 
> This is the reason why their proper times are different.
> 
> Twin A ages 23.664 year
> Twin B ages  9.912 year
> 
> No reciprocity.
> Fact.

No fact, just a scenario/delusion  of a brainwashed
idiot.

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#660728

Le 22/01/2025 à 22:11, "Paul.B.Andersen" a écrit :
> Den 21.01.2025 17:51, skrev Richard Hachel:
> =========================================
> There is no reciprocity in this scenario.
> =========================================
> 
> After the journey Stella's clock shows 10 (9) years while
> Terrence clock shows 23.9 (13.5) years.
> PERIOD.
> 
> How can you call this reciprocal?
> 
>> 
>> Paul, Paul, you do not understand anything at all of what I am saying, 
>> and instead of trying to understand, you take the theory as a joke.
> 
> A very bad joke. Not funny at all. I don't laugh.
> 
> Case closed.

There is a flaw in your way of understanding the ratio of observable time 
(terrestrial) and proper time (rockets in general).
As much in Galilean environments, where you only involve the reciprocal 
internal mechanism of watches, as in accelerated frames of reference, 
where you confuse the progression of observable times (red line) with the 
rotating path on a drawing (blue line) of the end of the segment To.
This results in a lower Tr/To ratio and an incorrect and too low predicted 
Tr (tau). All physicists do this, but it is wrong.
The correct equation is however very simple, and there is not even any 
need to go through an integration (I do not use one, as I do not use the 
invariance of the space-time interval or the Minkowski block, which bring 
more misunderstandings than practical solutions).

The correct equation is To(observable time reference Earth) with 
To=Tr.sqrt(1+(1/4)Vr²/c²) where Vr is the real speed of the object at a 
given time.

We can then write:
To=Tr².sqrt(1+(1/4)a².Tr²/c²)

I'll let you do the math, you'll see that my To is slightly lower than 
yours, and conversely if you have To and you look for Tr, you will have a 
higher rate than expected by your calculation.

Je rappelle que ce qui est réciproque, toujours, seconde après seconde, 
c'est la chronotropie interne des montres. Toujours, l'autre montre bat 
plus lentement en son mécanisme interne, et toujours, toujours, toujours 
: To=Tr/sqrt(1-Vo²/c²) où Vo est la vitesse relative instantanée à 
chaque instant. 

MAIS il faut prendre en compte les problémes :
1) d'anisochronie (traverser de l'espace, c'est traverser AUSSI du temps, 
car la simultanéité est relative an fonction de l'endroit de l'espace 
où l'on se trouve)
2) d'effet-zoom spatial énorme (l'espace est un mollusque de 
référence). Je le répète, même si ça rend fou tout le monde : 
lorsque Terrence voit Stella virer, et revenir sur lui, rien ne se passe. 
Il la voit, évidemment, à 12 ly. Le contraire serait absurde. 
Mais Stella voit Terrence à 36ly!!!
C'est là la dernière et la plus formidable clé de l'explication du 
voyageur de Langevin. Explication que je donne depuis des années, et qui 
fait rire tout le monde, parce que personne ne comprend cette géométrie 
magnifique de l'espace et du temps. 

R.H. 

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#660738

Den 23.01.2025 09:22, skrev Richard Hachel:
> 
> There is a flaw in your way of understanding the ratio of observable 
> time (terrestrial) and proper time (rockets in general).

In physics, proper time is what clocks show.
The only way to observe time is to read it off a clock.
So "observed time" and "proper time" are the same.


https://paulba.no/pdf/Clock_rate.pdf

See: 1.1 "What is proper time?"



-- 
Paul

https://paulba.no/

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#660745

W dniu 23.01.2025 o 21:54, Paul.B.Andersen pisze:
> Den 23.01.2025 09:22, skrev Richard Hachel:
>>
>> There is a flaw in your way of understanding the ratio of observable 
>> time (terrestrial) and proper time (rockets in general).
> 
> In physics, proper time is what clocks show.

Bullshit, anyone can check GPS, your delusional
idiocies have nothing in common with "what clocks
show".
It is just "what a relativistic idiot imagines clocks
show".


> The only way to observe time is to read it off a clock.

Or - imagine a clock with the readings  you
like.

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#660752

Le 23/01/2025 à 21:51, "Paul.B.Andersen" a écrit :
> Den 23.01.2025 09:22, skrev Richard Hachel:
>> 
>> There is a flaw in your way of understanding the ratio of observable 
>> time (terrestrial) and proper time (rockets in general).
> 
> In physics, proper time is what clocks show.
> The only way to observe time is to read it off a clock.
> So "observed time" and "proper time" are the same.
> 
> 
> https://paulba.no/pdf/Clock_rate.pdf
> 
> See: 1.1 "What is proper time?"

It's more complicated than that, breathe, blow...

Observable time is an abstract entity that, in fact, no one really 
measures.

It is based on the chronotropy of watches, that is to say the speed at 
which their internal mechanism evolves in relation to another watch.

This mechanism is always symmetrical, and always, we have 
To=Tr/sqrt(1-v²/c²) for two reciprocal watches.

Each has an internal mechanism that turns reciprocally faster than the 
other. This effect is very strange and disorienting (especially for 
Maciej), but it is a fundamental paradox.

Then, there is the apparent time Tapp.

Apparent time is the examiner's own time.

If we want to know the proper time of the examiner in relation to the 
proper time of the examinee, we must write:

Tapp=Tr.(1+cosµv/c)/sqrt(1-v²/c²)

or Tr(for me)=Tr(yours).(1+cosµv/c)/sqrt(1-v²/c²)

R.H. 

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#660766

Den 23.01.2025 23:59, skrev Richard Hachel:
> Le 23/01/2025 à 21:51, "Paul.B.Andersen" a écrit :
>> Den 23.01.2025 09:22, skrev Richard Hachel:
>>>
>>> There is a flaw in your way of understanding the ratio of observable 
>>> time (terrestrial) and proper time (rockets in general).
>>
>> In physics, proper time is what clocks show.
>> The only way to observe time is to read it off a clock.
>> So "observed time" and "proper time" are the same.
>>
>>
>> https://paulba.no/pdf/Clock_rate.pdf
>>
>> See: 1.1 "What is proper time?"

> 
> It's more complicated than that, breathe, blow...

Are you inflating your rubber duck?

> 
> Observable time is an abstract entity that, in fact, no one really 
> measures.

So "observable time" is not observable,
and isn't the time observed on a clock.

Stands to reason, doesn't it? :-D

> 
> It is based on the chronotropy of watches, that is to say the speed at 
> which their internal mechanism evolves in relation to another watch.

So "the internal mechanism" make the abstract entity "observable time",
that, in fact, no one really can observe, show something in relation
to another watch.

How can "the internal mechanism" know which watch is
the "another watch"?
How can "the internal mechanism" know the reading of
the "another watch"?
How can "the internal mechanism" know the speed of
the "another watch"?

------------------

It isn't really funny.

So why am I amused?

:-D

<snip more nonsense>

-- 
Paul

https://paulba.no/

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#660768

Le 24/01/2025 à 12:17, "Paul.B.Andersen" a écrit :
> Are you inflating your rubber duck?
> 
>> 
>> Observable time is an abstract entity that, in fact, no one really 
>> measures.
> 
> So "observable time" is not observable,
> and isn't the time observed on a clock.
> 
> Stands to reason, doesn't it? :-D
> 
>> 
>> It is based on the chronotropy of watches, that is to say the speed at 
>> which their internal mechanism evolves in relation to another watch.
> 
> So "the internal mechanism" make the abstract entity "observable time",
> that, in fact, no one really can observe, show something in relation
> to another watch.
> 
> How can "the internal mechanism" know which watch is
> the "another watch"?
> How can "the internal mechanism" know the reading of

There are three notions of time in Dr. Hachel's work.

Proper time (Tr, tau), which is the simplest notion to understand, and 
which I don't even have to explain.

Observable time, which is an abstract notion, but which we all use for 
convenience, and which rather defines the chronotropy of each frame of 
reference in relation to another.

Apparent time, which, in fact, is the proper time during which an observer 
observes an event that happens elsewhere.

These are very simple notions, once we understand the principle.

Let's take an event that occurs in Stella's rocket, and which lasts one 
hour. We will note that the proper time (tau), for Stella, is 1 hour. We 
will also call it real time (Tr).

Tr = tau = 1 h

Now, this real time, this proper time, is also the observable time in 
Stella's frame of reference. That is to say that for all the stationary 
observers present in its frame of reference will measure To=1h.

But it is no longer the time measured in another frame of reference, since 
we said that the observable time, that is to say the chronotropy was 
relative. In another frame of reference animated by a uniform rectilinear 
movement of speed Vo=0.8c, the proper time of the event in R becomes an 
observable time in R' which is 1h20. This is called the dilation of the 
chronotropy (Lorentz factor).

But that is not all, it is ALSO necessary as Dr. Hachel says (who is 
obviously completely crazy) to take into account the position of the 
observer, who will note an apparent time measured with his own proper 
time.

Let's admit that the rocket is hurtling towards the earth, and that we 
want to know how long the event lasts for the terrestrial observer.

Tapp=Tr(1+cosµ.v/c)/sqrt(1-v²/c²)=20mn.

That is to say that for Stella, it lasted 1 hour of proper time, but for 
Terrence, it lasted 20' of proper time.

I have been explaining it for years, and unfortunately it seems that no 
one makes the effort to understand a reasoning that is both true, 
experimentally proven, and conceptually very beautiful. So we mock, and we 
spit.

It is obviously stupid.

Let's add a poignant reflection: if already, this, which is only simple 
Galilean relativistic logic is difficult for you to understand, how do I 
explain relativity in uniformly accelerated media and in rotating 
relativistic media?

I just have to watch others explain this with pure mathematical 
theoretical madness, and start crying at the abstract and ridiculous 
notions they teach.

R.H. 

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#660793

Am Freitag000024, 24.01.2025 um 12:19 schrieb Paul.B.Andersen:
> Den 23.01.2025 23:59, skrev Richard Hachel:
>> Le 23/01/2025 à 21:51, "Paul.B.Andersen" a écrit :
>>> Den 23.01.2025 09:22, skrev Richard Hachel:
>>>>
>>>> There is a flaw in your way of understanding the ratio of observable 
>>>> time (terrestrial) and proper time (rockets in general).
>>>
>>> In physics, proper time is what clocks show.
>>> The only way to observe time is to read it off a clock.

This is total nonsense, since a clock is a man-made device, while time 
is not.

A clock is a tiny machine and counts ticks of some sort internally and 
shows the results in a user-friendly way.

But this is not equal to the phenomenon 'time', because that is 
something observable in nature.

For instance we can easily observe the passing of time in the passing of 
days and years.

And the Earth and the Sun are definitely not man-made.


>>> So "observed time" and "proper time" are the same.
>>>
>>>
>>> https://paulba.no/pdf/Clock_rate.pdf
>>>
>>> See: 1.1 "What is proper time?"
> 
>>
>> It's more complicated than that, breathe, blow...
> 
> Are you inflating your rubber duck?
> 
>>
>> Observable time is an abstract entity that, in fact, no one really 
>> measures.
> 
> So "observable time" is not observable,
> and isn't the time observed on a clock.

Clocks do not show time, but the result of a process, which counts ticks.

These ticks are assume to come in a constant frequency, hence we base or 
measurements of time upon this axiom.

But in fact we don't know, whether or not this is the case and that time 
flows always at the same speed.

Possibly this ain't true and time jumps occasionally (or often).

But we cannot measured such 'jumps', if all measuring devices would 
perform the same jumps, too.

So: steady and universal flow of time is an axiom.

But we have actually reason to believe, that this axiom is false.

Most likely time is local only and other places have local time, too, 
but other tick rates (and possibly other time directions).


> Stands to reason, doesn't it? :-D
> 
>>
>> It is based on the chronotropy of watches, that is to say the speed at 
>> which their internal mechanism evolves in relation to another watch.
> 
> So "the internal mechanism" make the abstract entity "observable time",
> that, in fact, no one really can observe, show something in relation
> to another watch.

'observable' is not the same as 'measurement'.

Observable are day and night, while clocks provide a measurement.

> How can "the internal mechanism" know which watch is
> the "another watch"?

Machines don't know anything.

It's the people ('observers') who know something (occasionally).

Such observer are usually somewhere and call the remote clocks 'the 
other clock'.

> How can "the internal mechanism" know the reading of
> the "another watch"?

If you would allow unconscious 'knowledge', then it would be possible to 
transmit a timing signal from one machine to the other.
That signal is used then by internal 'intelligence' of one of the 
clocks, which sets the hand according to the internal program in synch 
with the other clock.

> How can "the internal mechanism" know the speed of
> the "another watch"?

That could be measured by a series of timing signals.

...

TH

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#660729

Le 22/01/2025 à 22:11, "Paul.B.Andersen" a écrit :
> Den 21.01.2025 17:51, skrev Richard Hachel:
> =========================================
> There is no reciprocity in this scenario.
> =========================================
> 
> After the journey Stella's clock shows 10 (9) years while
> Terrence clock shows 23.9 (13.5) years.
> PERIOD.
> 
> How can you call this reciprocal?
> 
>> 
>> Paul, Paul, you do not understand anything at all of what I am saying, 
>> and instead of trying to understand, you take the theory as a joke.
> 
> A very bad joke. Not funny at all. I don't laugh.
> 
> Case closed.

There is a flaw in your way of understanding the ratio of observable time 
(terrestrial) and proper time (rockets in general).
As much in Galilean environments, where you only involve the reciprocal 
internal mechanism of watches, as in accelerated frames of reference, 
where you confuse the progression of observable times (red line) with the 
rotating path on a drawing (blue line) of the end of the segment To.
This results in a lower Tr/To ratio and an incorrect and too low predicted 
Tr (tau). All physicists do this, but it is wrong.
The correct equation is however very simple, and there is not even any 
need to go through an integration (I do not use one, as I do not use the 
invariance of the space-time interval or the Minkowski block, which bring 
more misunderstandings than practical solutions).

The correct equation is To(observable time reference Earth) with 
To=Tr.sqrt(1+(1/4)Vr²/c²) where Vr is the real speed of the object at a 
given time.

We can then write:
To=Tr.sqrt(1+(1/4)a².Tr²/c²)

I'll let you do the math, you'll see that my To is slightly lower than 
yours, and conversely if you have To and you look for Tr, you will have a 
higher rate than expected by your calculation.

Je rappelle que ce qui est réciproque, toujours, seconde après seconde, 
c'est la chronotropie interne des montres. Toujours, l'autre montre bat 
plus lentement en son mécanisme interne, et toujours, toujours, toujours 
: To=Tr/sqrt(1-Vo²/c²) où Vo est la vitesse relative instantanée à 
chaque instant. 

MAIS il faut prendre en compte les problémes :
1) d'anisochronie (traverser de l'espace, c'est traverser AUSSI du temps, 
car la simultanéité est relative an fonction de l'endroit de l'espace 
où l'on se trouve)
2) d'effet-zoom spatial énorme (l'espace est un mollusque de 
référence). Je le répète, même si ça rend fou tout le monde : 
lorsque Terrence voit Stella virer, et revenir sur lui, rien ne se passe. 
Il la voit, évidemment, à 12 ly. Le contraire serait absurde. 
Mais Stella voit Terrence à 36ly!!!
C'est là la dernière et la plus formidable clé de l'explication du 
voyageur de Langevin. Explication que je donne depuis des années, et qui 
fait rire tout le monde, parce que personne ne comprend cette géométrie 
magnifique de l'espace et du temps. 

R.H. 

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#660637

Le 20/01/2025 à 20:24, "Paul.B.Andersen" a écrit :
>> clock had an internal chronotropy which was running slower.
> 
> Stella can see that her watch shows 9 years.
> and Terrence's clock shows 13.5 years.
> 
> So Stella will have considered, second after second, that Terrence's
> clock had an internal chronotropy which was running slower.
> 
> 
> Always, always, always, Stella will see that Terrence clock
> shows two different times at the same time.
> 
> :-D

Damn, Paul, will you stop your bullshit?

Do you want to make a fool of yourself or what?

I'm not sure that your smileys and sallys are so funny.

I repeat once again (I've already had students who were speechless and 
didn't understand anything, but there...):

There exists, in the theory of relativity, a notion of relative 
chronotropy.

I repeat again for you: "There exists, in the theory of relativity, a 
notion of relative chronotropy".

That is to say that the INTERNAL mechanism of watches, watches makes that 
they do not conceive of time in the same way; each watch, and it is 
reciprocal, notes that the other watch has a slower internal mechanism, 
according to the relative speed, the faster we go between them, the more 
the other watch has a real internal mechanism that seems to beat slowly.

The equation has been known since 1905: To=tau/sqrt(1-v²/c²)

We breathe, we exhale.

This means (5632nd edition by Hachel, the next one is on rotary press) 
that second after second, Stella will consider that the INTERNAL MECHANISM 
of Terrence's watch beats less quickly. This means that for all the 
seconds of Stella's life (9 years in the stars), she will consider that 
the internal chronotropy of Terrence's watch counts 4/3 of a second.

And vice versa.

We breathe, we exhale, and we convince ourselves that Paul has not yet 
understood Hachel's genius (three Nobels, a doctorate, a powerful thought 
nonetheless).

Yet in the end, they compare their watches, she is nine years old, he is 
13.5, and they obviously agree on that, otherwise it is absurd.

However, nothing interesting happened during the U-turn, she ages a few 
hours (let's say 24 hours), and he ages 40 hours, so it's pretty ordinary.

So what's happening?

We breathe, we blow, we let the master (Richard Hachel) speak.

Everything happens for Stella, as if a bad watchmaker had made a 
completely faulty watch for Terrence, and that the INTERNAL mechanism of 
the watch beat 4/3 times faster if v=0.8c for example.

It's easy to understand.

But it's as if the watch that was going to measure the journey had a 
second problem, this one of the first degree. This watch considers that 
there is also a universal anisochrony, a defect of LOCAL, positional 
simultaneity.

It will then be necessary to make a SECOND correction, of the type 
Tapp=To(1+cosµ.v/c).

We then arrive at the equation t'=t.(1+cosµ.v/c)/sqrt(1-v²/c²) which is 
the real time marked on watches.

In short, affirming that internal chronotropy is relative, we have known 
this since 1905, but that is not enough.

We must take into account universal anisochrony.

And there, everything falls into place with a theory of great majesty.

It may make you laugh, but frankly, I do not see where it is so funny.

So in total, he has 13.5 years (in your example) of accelerated traveler 
at a=1ly/year, and she has 9 (time that you chose).

I beg you to make the effort to understand what I have been explaining for 
years, and which you seem to mock.

R.H. 

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#660565

Paul.B.Andersen wrote:
> 
> Den 18.01.2025 20:56, skrev Richard Hachel:
> > Le 18/01/2025 à 20:25, "Paul.B.Andersen" a écrit :
> >
> >> 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.
> >>
> >> The important point is:
> >>
> >> When Stella is back, Terrence and Stella are co-located and
> >> stationary to each other, and both can see both clocks which are
> >> side by side.
> >>
> >> Terrence can see that his watch shows tau_T
> >> and Stella's watch shows tau_S.
> >>
> >> Stella can see that her watch shows tau_S
> >> and Terrence's clock shows tau_T.
> 
> >
> > I've always said it, you're absolutely right,
> > the two times don't match.
> >
> > Stella looks at her watch, and she sees that her watch marks 9 years.
> >
> > She shows her watch to Terrence, and asks him what he sees, and he
> > answers: "Your watch marks nine years".
> >
> > I don't see where the difficulty is.
> >
> > On the other hand, Terrence asks Stella, and you, what do you see on my
> > watch, and she answers your watch marks 13.5 years.
> >
> > I don't understand how you can see a difficulty there.
> 
> We agree, there are no difficulties.
> 
> >
> > It's the notion of the relativity of time.
> >
> > The only thing that opposes us is the way you calculate the ratio of the
> > two watches, because you make a colossal error by using an incorrect
> > integration taught by the theorists, and which gives you a smaller
> > proper time, or a larger improper time.
> 
> We do not agree about the actual numbers.
> I tell what SR predicts, you tell what Hachel predicts.
> 
> The important point is that we agree that:
> Terrence's watch shows tau_T and Stella's watch shows tau_S,
> tau_T > tau_S and both can see both watches.
> 
> > Finally, you should not confuse chronotropy and the passage of time on
> > watches.
> >
> > The relationship between Tr and To is a relationship of chronotropy.
> >
> > The time that passes on watches is not ONLY that, you have to take into
> > account universal anisochrony, as well as the distances traveled by
> > watches (and not just their relative speed).
> >
> > This is what makes it so that although the mechanisms of watches have
> > always turned according to the same reciprocity, each one sees the other
> > which turns less quickly in its internal mechanism, and this explains,
> > as in the Langevin paradox, that however in the end, the two watches do
> > not correspond, while the reciprocity of the internal beats is perfect.
> >
> > It is anisochrony that will actually induce the shift, not chronotropy.
> >
> > I have told you this 50 times.
> >
> > You do not, but then not at all, make the effort to understand me,
> > stuck in the idea that physicists cannot be wrong.
> >
> > Your bad faith becomes faith.
> >
> 
> I can't see how all these words relate to the scenario at hand.
> 
> Here comes YOUR problem:
> 
> In the post I originally responded to, you, Richard Hachel wrote:
> | "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."
> 
> OK. This is your explanation for why tau_T > tau_S.
> According to Richard hachel:
>   "Stella looks at her watch, and she sees that her watch marks 9 years.
>    She shows her watch to Terrence, and asks him what he sees, and he
>    answers: "Your watch marks nine years".
>    On the other hand, Terrence asks Stella, what do you see
>    on my watch, and she answers your watch marks 13.5 years.
> 
> But you also wrote:
> > "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 it is
> >  the opposite that is true. For her, it is the internal mechanism
> >  of Terrence's watch that beats constantly less quickly, and this
> >  during his journey."
> 
> Doesn't this mean that Stella should see that Terrence watch
> shows less than her watch?
> 
> But you said:
>   "Stella looks at her watch, and she sees that her watch marks 9 years.
>    Terrence asks Stella, what do you see on my watch,
>    and she answers your watch marks 13.5 years."
> 
> How can Stella see that Terrence watch has two different readings at
> the same time?
> 
> Please explain.




Are you sayin Richard hachel is a fraudster? A con artists?? I'm
schocked! Sacre bleu!!!!




and paris is not a city of romance...




> 
> -----------------------------------------
> 
> A word about frames of reference.
> 
> The phrase "to be in different frames" is nonsense.
> 
> We both are in my rest frame.
> I am stationary, and you are probably moving.
> 
> We both are in your rest frame.
> You are stationary, and I am probably moving.
> 
> Saying "we are in different frames" sounds like we are in
> different worlds, with different realities.
> 
> But we are in the same world, the real world with one reality.
> 
> What's true in Terrence's rest frame is true in Stella's rest frame.
> There is but one world and one reality.
> 
> Remember this in your response.
> 
> --
> Paul
> 
> https://paulba.no/

-- 
The Starmaker -- To question the unquestionable, ask the unaskable,
to think the unthinkable, mention the unmentionable, say the unsayable, 
and challenge the unchallengeable.

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#660529

W dniu 18.01.2025 o 20:28, Paul.B.Andersen pisze:
> Den 18.01.2025 10:04, skrev Richard Hachel:
>> Le 17/01/2025 à 13:30, "Paul.B.Andersen" a écrit :
>>>
>>> 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.
>>
>> In the problem you pose:
>> A rocket leaves the earth and accelerates (a=1ly/year).
>> This during a proper time Tr (or tau) = 2.25 years.
>> Which gives a total of Tr=9 years.
> 
> It is the very same as this scenario:
> https://paulba.no/pdf/TwinsByMetric.pdf
> See: 2.2 B travels with constant speed and instant acceleration
> And: 2.4 Concrete example
> 
> This is what SR predicts:
> 
> When Terrence (Twin A) is back, his watch show 23.664 y ≈ 23.7 y
> When Stella is back (Twin B), her watch show 9.912y ≈ 9 y
> (bad round off, but doesn't really matter)

This is what SR predicts, and anyone can check
GPS - it has nothing in commom with real clocks.

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