Discussion:
Proper time differences
Stefan Ram
2024-07-08 14:45:12 UTC
From various sources I gather,

dt = "gamma" d"tau".

Where t is the coordinate time in the rest frame, "gamma"
is the Lorentz gamma factor and "tau" is the proper time.

Now, if "gamma" is constant, I think we can replace the "d"
by "D" (triangle which is flat at its bottom), i.e., we can
use finite difference instead of infinitesimal ones:

Dt = "gamma" D"tau".

I believe 0<="gamma"<=1, so, for an example, we can assume
"gamma" to be 0.5:

Dt = 0.5 D"tau",

which means just,

D"tau" = 2 Dt.

So, that would mean: For a moving thing the proper time
difference D"tau" (I assume: between two fixed events) is
/larger/ than the coordinate time difference.

But since falling muons live longer, the proper time distance
should be /smaller/, not larger!

What's wrong here? TIA!
Richard Hachel
2024-07-08 15:33:58 UTC
Post by Stefan Ram
From various sources I gather,
dt = "gamma" d"tau".
Where t is the coordinate time in the rest frame, "gamma"
is the Lorentz gamma factor and "tau" is the proper time.
Now, if "gamma" is constant, I think we can replace the "d"
by "D" (triangle which is flat at its bottom), i.e., we can
Dt = "gamma" D"tau".
I believe 0<="gamma"<=1, so, for an example, we can assume
Dt = 0.5 D"tau",
which means just,
D"tau" = 2 Dt.
So, that would mean: For a moving thing the proper time
difference D"tau" (I assume: between two fixed events) is
/larger/ than the coordinate time difference.
But since falling muons live longer, the proper time distance
should be /smaller/, not larger!
What's wrong here? TIA!
Es gibt ein chinesisches Sprichwort, das besagt: „Es ist besser, fünf
Minuten lang dumm zu erscheinen, als sein ganzes Leben lang dumm zu
bleiben.“
Das bedeutet: Wenn Sie etwas nicht wissen, zögern Sie nicht,
nachzufragen.
In diesem Forum gibt es den besten Theoretiker der speziellen
Relativitätstheorie aller Zeiten, ganz zu schweigen von seinen
Erklärungs- und Popularisierungsmöglichkeiten, und wenn wir eine Frage
in Ihrem Stil stellen, liegt es an ihm, die Sie stellen müssen.

R.H.
Richard Hachel
2024-07-08 15:43:15 UTC
Post by Stefan Ram
From various sources I gather,
dt = "gamma" d"tau".
Where t is the coordinate time in the rest frame, "gamma"
is the Lorentz gamma factor and "tau" is the proper time.
Now, if "gamma" is constant, I think we can replace the "d"
by "D" (triangle which is flat at its bottom), i.e., we can
Dt = "gamma" D"tau".
I believe 0<="gamma"<=1, so, for an example, we can assume
Dt = 0.5 D"tau",
which means just,
D"tau" = 2 Dt.
So, that would mean: For a moving thing the proper time
difference D"tau" (I assume: between two fixed events) is
/larger/ than the coordinate time difference.
But since falling muons live longer, the proper time distance
should be /smaller/, not larger!
What's wrong here? TIA!
You made a mistake in the wording.
The correct equation is To=Tr.gamma
but gamma is 1/sqrt(1-v²/c²).
And not sqrt(1-v²/c²).

Offer you gamma=0.5

It's impossible.

R.H.
Mikko
2024-07-08 17:38:09 UTC
Post by Stefan Ram
From various sources I gather,
dt = "gamma" d"tau".
The defining equation of proper duration is

dτ² = dt² - dx²

which is equivalent to your equatio.
Post by Stefan Ram
Where t is the coordinate time in the rest frame, "gamma"
is the Lorentz gamma factor and "tau" is the proper time.
Now, if "gamma" is constant, I think we can replace the "d"
by "D" (triangle which is flat at its bottom), i.e., we can
Dt = "gamma" D"tau".
That's right. That happens when the moving object is not accelerated.
Post by Stefan Ram
I believe 0<="gamma"<=1, so, for an example, we can assume
No, gamma is 1 / sqrt(1 - v²) which is 1 when v = 0 and greater otherwise.
--
Mikko
Stefan Ram
2024-07-08 17:49:44 UTC
Post by Mikko
Post by Stefan Ram
I believe 0<="gamma"<=1, so, for an example, we can assume
No, gamma is 1 / sqrt(1 - v²) which is 1 when v = 0 and greater otherwise.
Thank you! This seems to solve my problem. (I wanted to quickly learn
the possible values of "gamma" and looked at a curve on an image
search result page, from which I took the wrong 0 <= "gamma" <= 1!)
Richard Hachel
2024-07-08 19:28:05 UTC
Post by Mikko
Post by Stefan Ram
From various sources I gather,
dt = "gamma" d"tau".
The defining equation of proper duration is
dτ² = dt² - dx²
I think it is better to write:
To²=Tr²+Et²
This is a beautiful Pythagirism that not only can we teach in high school
classes, but which will prove magnificent when we move on to the study of
uniformly accelerated frames of reference.

For accelerated repositories it's the same:
To²=Tr²+Et²
To²=Tr²+(1/2a.Tr²)²/c²
To²=Tr²(1+1/4Vr²/c²) where Vr is the speed at a given time at a given
location.
To=Tr.sqrt(1+(1/4)Vr²/c²)
On the other hand, I do not recommend putting this equation on your exam
papers.
You would systematically have zero. The correctors do not joke with the SR
taught by Doctor Hachel.

R.H.
Sylvia Else
2024-07-09 05:21:01 UTC
Post by Stefan Ram
From various sources I gather,
dt = "gamma" d"tau".
Where t is the coordinate time in the rest frame, "gamma"
is the Lorentz gamma factor and "tau" is the proper time.
Now, if "gamma" is constant, I think we can replace the "d"
by "D" (triangle which is flat at its bottom), i.e., we can
Dt = "gamma" D"tau".
I believe 0<="gamma"<=1, so, for an example, we can assume
Dt = 0.5 D"tau",
which means just,
D"tau" = 2 Dt.
So, that would mean: For a moving thing the proper time
difference D"tau" (I assume: between two fixed events) is
/larger/ than the coordinate time difference.
But since falling muons live longer, the proper time distance
should be /smaller/, not larger!
What's wrong here? TIA!
"Time dilation" is a special case of the Lorentz transform, and due to
continued lack of clarity on this point in popular science media, people
tie themselves in knots by trying to use time dilation in situations
that do not match the special case.

Apply the complete Lorentz transform to your problem, and any apparent

Sylvia.
Maciej Wozniak
2024-07-09 05:59:25 UTC
Post by Sylvia Else
From various sources I gather,
dt = "gamma" d"tau".
Where t is the coordinate time in the rest frame, "gamma"
is the Lorentz gamma factor and "tau" is the proper time.
Now, if "gamma" is constant, I think we can replace the "d"
by "D" (triangle which is flat at its bottom), i.e., we can
Dt = "gamma" D"tau".
I believe 0<="gamma"<=1, so, for an example, we can assume
Dt = 0.5 D"tau",
which means just,
D"tau" = 2 Dt.
So, that would mean: For a moving thing the proper time
difference D"tau" (I assume: between two fixed events) is
/larger/ than the coordinate time difference.
But since falling muons live longer, the proper time distance
should be /smaller/, not larger!
What's wrong here? TIA!
"Time dilation" is a special case of the Lorentz transform,
Nope, Lorentz transform was invented for
an ether theory, which was free of The
Holiest Postulate.
Time dilation is just nonsensical, denying
itself concept of an insane, mumbling crazie.
Richard Hachel
2024-07-09 12:47:55 UTC
Post by Maciej Wozniak
Nope, Lorentz transform was invented for
an ether theory, which was free of The
Holiest Postulate.
Time dilation is just nonsensical, denying
itself concept of an insane, mumbling crazie.
You should know the proverb: "If you don't tighten your guitar string, it
makes a deep and unpleasant sound; but if you tighten it too much, it
breaks."
I have already said many times that there are irregularities,
misunderstandings, and real paradoxes in this theory. It must therefore be
rectified. But throwing the baby out with the bath water is not right.
By doing this, you harm the idea more than you carry science and truth
further.

R.H.
Maciej Wozniak
2024-07-09 13:28:45 UTC
Post by Richard Hachel
Post by Maciej Wozniak
Nope, Lorentz transform was invented for
an ether theory, which was free of The
Holiest Postulate.
Time dilation is just nonsensical, denying
itself concept of an insane, mumbling crazie.
You should know the proverb: "If you don't tighten your guitar string,
it makes a deep and unpleasant sound; but if you tighten it too much, it
breaks."
I have already said many times that there are irregularities,
misunderstandings, and real paradoxes in this theory. It must therefore
be rectified. But throwing the baby out with the bath water is not right.
It's not a baby, it's some inconsistent
mumble of an insane crazie.

Richard Hachel
2024-07-09 13:23:03 UTC
Post by Sylvia Else
"Time dilation" is a special case of the Lorentz transform, and due to
continued lack of clarity on this point in popular science media, people
tie themselves in knots by trying to use time dilation in situations
that do not match the special case.
Apply the complete Lorentz transform to your problem, and any apparent
Sylvia.
It is notorious today that physicists (no physicist in the world) do not
understand the theory of relativity which is a very simple concept when we
see it (I spent 40 years sometimes thinking about it whole nights).
Many idiots insult Doctor Hachel, because he doesn't think exactly like
them, and thus believe he is doing a good job.
The charming Sylvia says that today there is no more paradox and falsity
in the theory, she is wrong. She doesn't realize that it's just a very
imperfect mathematical work, as if we were approaching the truth and the
solution, but without fully finding it.
Certainly the Poincaré-Lorentz transformations are correct, and
certainly, they induce a relativity of times, and on this she is
absolutely right, and we prove it both mathematically (theoretical
internal perfection) and physically (experimental perfection).
But apart from the brilliant transformations of the French mathematician,
the understanding of the problem becomes, for men, completely vague, and
they no longer understand correctly what they are saying or saying is
false.
We then enter into the behavior of the human male: denial.
The greatest of the relativist theorists today is me, and if so many
idiots stopped being monkeys and listened to me a little we wouldn't be in
so much darkness, and with so many cranks who want to impose concepts even
more stupid than those of Minkowski.
The main errors are:
1. Physicists confuse time measurement and the internal chronotropy of
watches. This is also what explains why they were never able to resolve,
even remotely, the Langevin paradox, and that I am the only one who can
really do it and explain it clearly.
Let's take the example of Stella and Terrence, she comes back aged 18, he
is 30 years old. This is certain, we cannot contradict. But this is a
criterion of the MEASUREMENT OF TIME and not of chronotropy. They do not
have the same measure of time, far from it, but always, always, always,
they have had the same reciprocity of chronotropy, that is to say that not
a single second, for any of them , throughout the outward and return
journey the chronotropy of the other continued to be weaker. For each, the
internal mechanism of the other watch ALWAYS turned slower, second after
second. The paradox seems obvious and likely to drive one crazy after 120
years of theoretical physics. We forget one thing: Poincaré's equations
have a numerator and a denominator. The numerator is at the top and
represents the effects of external anisochrony, the numerator is at the
bottom, and represents the effects of internal chronotropy. If we only
take the denominator (Lorentz factor) we enter into absurdity. If we take
both terms, everything is nothing more than logic and fantastic
mathematical beauty. But that's not all to have the full resolution of the
paradox, and physicists forget a second thing.
2. Physicists, very strangely, absolutely do not understand (but
absolutely not) the brilliant sentence of Richard Hachel (that's me):
"There is no absolute frame of reference, and all the laws of physics are
invariant (in particular the observable speed of light) by change of frame
of reference; and the effects of physics are symmetrical and reciprocal by
permutation of observer.
This seems very simple, even obvious, but physicists do not fully
understand the meaning of the second part of the sentence. They do not
understand the reciprocity of the effects of elasticity of lengths and
distances by permutation of observer.

In summary, there are two major misunderstandings if only to explain the

The rest is, I repeat again, only a human religious and philosophical
problem: "We do not want this man to reign over us."

For Sylvia, as she is kind, which is rare on usenet, and as she likes the
gifts and the transformations of Poincaré-Lorentz, which she knows by
heart, I dedicate to her the transformations of Hachel which are valid
this time for rotating relativistic environments. She can learn them by
heart if she wants, and even teach them to anyone she wants (if she is not
afraid of being assassinated like President Kennedy). It's free.

<http://news2.nemoweb.net/jntp?***@jntp/Data.Media:1>

R.H.