Understanding the theory of special relativity

[Paul.B.Andersen]

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?

[Maciej Wozniak]

Post by Paul.B.Andersen

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.

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.

Fortunately, we have GPS now, so we can be
absolutely sire this insane gedanken/fabricated
bullshit has nothing in common with real clocks,
real observers or real anything.

[Richard Hachel]

Post by Paul.B.Andersen

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.

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.

[Richard Hachel]

Post by Paul.B.Andersen
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.

But there is an error in the way you transpose time into observable time
in the terrestrial frame of reference. How old will Terrence be in this
case?

The first thing is to cut the journey into four, since the four segments
will give Tr=2.25 years.

For the first segment we will have To=Tr/sqrt(1+(1/4)Vr²/c²) if you have
followed what Dr. Hachel says.

Here we can remain Newtonian and set Vr=a.Tr without any problem.

Let To=Tr/sqrt(1+(1/4)a².Tr²/c²)

And, To=3.3867 years

The phenomenon is reproduced four times:
To(final)=13.5468 years

Terrence will be a little over 13 and a half years old and Stella 9 years
old.

Your mistake is to make a wrong integration thinking that it is right, and
this distorts your To/Tr ratio


R.H.

[Richard Hachel]

Terrence will be a little over 13 and a half years old and Stella 9 years old.
Your mistake is to make a wrong integration thinking that it is right, and this
distorts your To/Tr ratio

Note that the same thing is happening here as what I said above.

CONSTANTLY, the chronotropy of the other watch turns less quickly.

Second after second, and whatever the speed reached or the direction used,
each, second after second observes that the chronotropy of the other watch
is less (time passes less quickly elsewhere according to the instantaneous
speed, and constantly, the equation is: To=Tr/sqrt(1-Voi²/c²) where Voi
is the instantaneous observable speed.

R.H.

[Paul.B.Andersen]

Post by Richard Hachel

Post by Paul.B.Andersen
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.

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)

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.

Post by Richard Hachel
But there is an error in the way you transpose time into observable time
in the terrestrial frame of reference. How old will Terrence be in this
case?
The first thing is to cut the journey into four, since the four segments
will give Tr=2.25 years.
For the first segment we will have To=Tr/sqrt(1+(1/4)Vr²/c²) if you have
followed what Dr. Hachel says.
Here we can remain Newtonian and set Vr=a.Tr without any problem.
Let To=Tr/sqrt(1+(1/4)a².Tr²/c²)
And, To=3.3867 years
To(final)=13.5468 years
Terrence will be a little over 13 and a half years old and Stella 9
years old.

You say tau_S = 9 year and tau_T = 13.5 year
I say tau_S = 9 year and tau_T = 23.7 year

Post by Richard Hachel
Your mistake is to make a wrong integration thinking that it is right,
and this distorts your To/Tr ratio

The actual numbers are not important in this case.

What is important is that when Stella is back, Terrence and Stella
are co-located and stationary to each other.

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.

Do you agree? (yes or no, please. There is no third alternative)

[Richard Hachel]

Post by Paul.B.Andersen
You say tau_S = 9 year and tau_T = 13.5 year
I say tau_S = 9 year and tau_T = 23.7 year

Yes, that's absolutely what we're saying.

Post by Paul.B.Andersen
What is important is that when Stella is back, Terrence and Stella
are co-located and stationary to each other.

Absolutely.

Post by Paul.B.Andersen
Terrence can see that his watch shows tau_T
and Stella's watch shows tau_S.

Yes.

Post by Paul.B.Andersen
Stella can see that her watch shows tau_S
and Terrence's clock shows tau_T.

Absolutly.

Post by Paul.B.Andersen
Do you agree? (yes or no, please. There is no third alternative)

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.

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.

You should not use the blue curve which is NOT improper time, but I don't
know what. You should use the red segment which undergoes a progressive
rotation, but whose norm is To, and not the blue line of the diagram.

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.

R.H.

[Paul.B.Andersen]

Post by Richard Hachel

Post by Paul.B.Andersen
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, 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.

Post by Richard Hachel
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.

Post by Richard Hachel
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.

Post by Richard Hachel
"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.

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

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.

[Richard Hachel]

Post by Paul.B.Andersen
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, Paul, je te supplie de ne pas plaisanter.

On peut plaisanter avec le Gourou Sénégalais qui va proposer à votre
épouse un orgasme à 10 000 dollars pièce, on peut plaisanter avec le
gourou québécois Raël qui vous attend avec ses soucoupes volantes et
ses Elohims, on peut plaisanter avec des milliers de singes...

Pas avec moi, Paul.

Pas avec moi.

Cela se saurait.

Il n'y a évidemment qu'une seule réalité contact par contact.

Cela n'empêche pas ce que j'ai dit : "Toujours, toujours, toujours,
qu'on se trouve dans n'importe quel référentiel, la notion de
chronotropie adverse est réciproquement plus faible."

Il est impossible qu'il en soit autrement.

L'équation reste invariablement la même : To=Tr/sqrt(1-v²/c²)

En chaque instant, chaque seconde.

Toujours, toujours, toujours, l'horloge opposée tourne moins vite.

Dans tous les référentiels.

Galiléens, fanatiques, hectiques, accélérés, tournants.

TOUJOURS.

Cela veut dire que pendant que Stella vieillit de 18 ans, toujours
toujours, toujours, elle aura considéré, seconde après seconde, que
l'horloge de Terrence avait une chronotropie interne qui tournait moins
vite.

On respire, on souffle.

Pourtant, Hachel a raison, Stella n'a que 18 ans. Terrence 30.

Dans les milieux accélérés, Terrence a 12.91 ans, Bella a 4.776 ans.

Et pourtant le mécanisme interne de la montre de Terrence, pour Bella,
a constamment tourné moins vite.

Tu comprends Paul?

Post by Paul.B.Andersen
Non, je suis largué.

C'est TON problème, et le fait que tu ne fasses AUCUN effort.

R.H.

[Paul.B.Andersen]

Post by Paul.B.Andersen

Post by Richard Hachel

Post by Paul.B.Andersen
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, 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.

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, 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.

So according to Hachel:

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 13.5 years.
and Stella's watch shows nine years.

Stella can see that her watch shows 9 years.
and Terrence's clock shows 13.5 years.

In every moment, every second.
Always, always, always, the opposite clock ticks slower.
In all repositories.
ALWAYS.
This means that while Stella ages 18 years, always, always,
she will have considered, second after second, that Terrence's
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

[Richard Hachel]

Post by Paul.B.Andersen
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 13.5 years.
and Stella's watch shows nine years.

Yes.

Post by Paul.B.Andersen
Stella can see that her watch shows 9 years.
and Terrence's clock shows 13.5 years.

Absolutely, the opposite would be contradictory.

R.H.

[Maciej Wozniak]

Post by Richard Hachel

Post by Paul.B.Andersen
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 13.5 years.
and Stella's watch shows  nine years.

Yes.

Post by Paul.B.Andersen
Stella can see that her watch shows 9 years.
and Terrence's clock shows 13.5 years.

Absolutely, the opposite would be contradictory.

Fortunately, we have GPS now, so we can be
absolutely sure this absurd bullshit is just
some absurd bullshit having nothing in common
with real clocks, real observers or real
anything.

[Richard Hachel]

Post by Maciej Wozniak
Fortunately, we have GPS now, so we can be
absolutely sure this absurd bullshit is just
some absurd bullshit having nothing in common
with real clocks, real observers or real
anything.

What must be understood is that if the theory of relativity did not exist,
that is, if, at the base, the universe was isochronous even in a simple
stationary frame of reference (there is no movement), there could be no
GPS, because all the information would arrive at the same time, and we
could not know how far away an object is from another.
It is precisely the isochrony of things that means that even if light is,
for the receiver, an instantaneous transaction, that is to say it
propagates infinitely quickly, there is nevertheless a time lag that means
that we can measure the distance.
Distance IS the anisochrony of GPS.
It is absurd to say that GPS invalidates relativity, when it is relativity
that allows GPS to exist.

Without anisochrony, no GPS. Only instantaneous transfers of information
in a hyperplane of absolute simultaneity, and a total impossibility of
calculating any delay of information due to distance.

R.H.

[Maciej Wozniak]

Post by Richard Hachel

Post by Maciej Wozniak
Fortunately, we have GPS now, so we can be
absolutely sure this absurd bullshit is just
some absurd bullshit having nothing in common
with real clocks, real observers or real
anything.

What must be understood is that if the theory of relativity did not
exist, that is, if, at the base, the universe was isochronous even in a
simple stationary frame of reference (there is no movement), there could
be no GPS, because all the information would arrive at the same time,
and we could not know how far away an object is from another.

What should be understood is that both
physicists and wannabe physicists feel
incredibly important for no real reason (not
counting their delusion of grandeur, which is
of course a real reason for that, but in a
different meaning).

[Paul.B.Andersen]

Post by Richard Hachel

Post by Paul.B.Andersen
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 13.5 years.
and Stella's watch shows  nine years.

Yes.

Post by Paul.B.Andersen
Stella can see that her watch shows 9 years.
and Terrence's clock shows 13.5 years.

Absolutely, the opposite would be contradictory.

Post by Paul.B.Andersen

In every moment, every second.
Always, always, always, the opposite clock ticks slower.
In all repositories.
ALWAYS.
This means that while Stella ages 18 years, always, always,
she will have considered, second after second, that Terrence's
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

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)
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).

:-D

Post by Richard Hachel
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.

Of course it is easy to understand that when Stella sees that
her watch shows 9 years and she sees that Terrence's watch
shows 13.5 years, then Stella will consider that
the INTERNAL MECHANISM of Terrence's watch beats less quickly,
the opposite would be contradictory.

I have got it now, so can I please get my Nobel?

[Richard Hachel]

Post by Paul.B.Andersen

Post by Richard Hachel

Post by Paul.B.Andersen
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 13.5 years.
and Stella's watch shows  nine years.

Yes.

Post by Paul.B.Andersen
Stella can see that her watch shows 9 years.
and Terrence's clock shows 13.5 years.

Absolutely, the opposite would be contradictory.

Post by Paul.B.Andersen

In every moment, every second.
Always, always, always, the opposite clock ticks slower.
In all repositories.
ALWAYS.
This means that while Stella ages 18 years, always, always,
she will have considered, second after second, that Terrence's
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

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)
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).

:-D

Post by Richard Hachel
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.

Of course it is easy to understand that when Stella sees that
her watch shows 9 years and she sees that Terrence's watch
shows 13.5 years, then Stella will consider that
the INTERNAL MECHANISM of Terrence's watch beats less quickly,
the opposite would be contradictory.
I have got it now, so can I please get my Nobel?

[Richard Hachel]

Post by Paul.B.Andersen

Post by Richard Hachel

Post by Paul.B.Andersen
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 13.5 years.
and Stella's watch shows  nine years.

Yes.

Post by Paul.B.Andersen
Stella can see that her watch shows 9 years.
and Terrence's clock shows 13.5 years.

Absolutely, the opposite would be contradictory.

Post by Paul.B.Andersen

In every moment, every second.
Always, always, always, the opposite clock ticks slower.
In all repositories.
ALWAYS.
This means that while Stella ages 18 years, always, always,
she will have considered, second after second, that Terrence's
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

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)
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).

:-D

Post by Richard Hachel
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.

Of course it is easy to understand that when Stella sees that
her watch shows 9 years and she sees that Terrence's watch
shows 13.5 years, then Stella will consider that
the INTERNAL MECHANISM of Terrence's watch beats less quickly,
the opposite would be contradictory.
I have got it now, so can I please get my Nobel?

The internal mechanism of watches beats reciprocally faster than the other
watch.
The physical relationship is To=tau/sqrt(1-v²/c²).
All physicists in the world know it.
This is called the Lorentz factor.
And this principle manifests itself second after second, and for both
protagonists, and vice versa.

There is nothing difficult to understand here.

It is true that when said like that, hundreds of physicists opposed
Poincaré, saying that it was absurd.

The problem is that anti-relativistic physicists, like relativists, drown
in a theory that they do not understand.

It is beyond them that, for example, if we take the example of the
Langevin traveler, Stella comes back younger than her brother (18 years
old against 30 years old if the journey was made at Vo=0.8c over 24 light
years) while second after second, the INTERNAL mechanism of Terrence's
watch, FOR Stella beat less quickly.

Just as Paul does not understand this apparent absurdity, thousands of
physicists have not understood it either.

An attempt to drown the fish, or to sweep dust under the carpet was
attempted by proposing, at the time of the U-turn, a time-gap, which
however does not exist. By imagining a U-turn on a large curve in 24 hours
at 0.8c, Stella will age by 24 hours, and Terrence by 40 hours, without
anything more happening.

I repeat, all this is true and correct, and there is no need to laugh
(unless you don't understand anything at all, and you start laughing
stupidly).

What physicists have forgotten, and there, it takes a stroke of genius and
40 years of thinking to understand, is that another phenomenon exists,
anisochrony, explaining the second part of things (the first is the
Lorentz factor and the internal beat of watches). The third part
disorients the physicist, and leaves him in a state of stupid
incomprehension to cry: spatial elasticity, and the incredible spatial
zoom effect that occurs
when Stella turns, and returns to the earth. while she sees, over there
the earth which returns to Vo=0.8c, that is to say at an apparent speed of
Vapp=4c, for nine years. Which is infinitely logical with the spatial zoom
effect (space is a reference mollusk) which carries the earth, during the
half-turn at a distance of 4ly, up to a distance of 36 ly.

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.

Just as I pointed out to you that your integration of the ratio proper
time/earth time was invalid, because you use the blue curve and not the
red segment whose end follows the blue curve while undergoing a rotation.

You take all this as a joke.

Too bad.

R.H.

[Maciej Wozniak]

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.

Fortunately, we have GPS now, so we can be
absolutely sure this absurd bullshit is just
some absurd bullshit, having nothing in common
with real clocks or real measurements.

[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.

https://paulba.no/pdf/Mutual_time_dilation.pdf
Read it!

Je l'ai lu depuis longtemps.

R.H.

[Richard Hachel]

=========================================
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.

[Paul.B.Andersen]

Post by Richard Hachel

=========================================
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"

Post by Richard Hachel
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.

Post by Richard Hachel
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.

[Maciej Wozniak]

Post by Paul.B.Andersen

Post by Richard Hachel

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

Post by Richard Hachel
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.

Post by Richard Hachel
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.

[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?

Post by Richard Hachel
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.

[Paul.B.Andersen]

Post by 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?"

[Maciej Wozniak]

Post by Paul.B.Andersen

Post by 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".

Post by Paul.B.Andersen
The only way to observe time is to read it off a clock.

Or - imagine a clock with the readings you
like.

[Richard Hachel]

Post by Paul.B.Andersen

Post by 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.

[Paul.B.Andersen]

Post by Richard Hachel

Post by Paul.B.Andersen

Post by 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?

Post by Richard Hachel
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

Post by Richard Hachel
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>

[Richard Hachel]

Post by Paul.B.Andersen
Are you inflating your rubber duck?

Post by Richard Hachel
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

Post by Richard Hachel
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.

[Thomas Heger]

Post by Paul.B.Andersen

Post by Richard Hachel

Post by Paul.B.Andersen

Post by 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.

Post by Paul.B.Andersen

Post by Richard Hachel

Post by Paul.B.Andersen
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?

Post by Richard Hachel
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).

Post by Paul.B.Andersen
Stands to reason, doesn't it? :-D

Post by Richard Hachel
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.

Post by Paul.B.Andersen
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'.

Post by Paul.B.Andersen
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.

Post by Paul.B.Andersen
How can "the internal mechanism" know the speed of
the "another watch"?

That could be measured by a series of timing signals.

...

TH

[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?

Post by Richard Hachel
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.

[Richard Hachel]

Post by Paul.B.Andersen

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.

[The Starmaker]

Post by Paul.B.Andersen

Post by Richard Hachel

Post by Paul.B.Andersen
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, 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.

Post by Richard Hachel
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.
Terrence's watch shows tau_T and Stella's watch shows tau_S,
tau_T > tau_S and both can see both watches.

Post by Richard Hachel
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.
| "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.
"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.

Post by Richard Hachel
"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?
"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...

Post by Paul.B.Andersen
-----------------------------------------
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/

[Maciej Wozniak]

Post by Paul.B.Andersen

Post by Richard Hachel

Post by Paul.B.Andersen
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.

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.

https://paulba.no/pdf/TwinsByMetric.pdf
See: 2.2 B travels with constant speed and instant acceleration
And: 2.4 Concrete example
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.