• Proper time differences

    From Stefan Ram@21:1/5 to All on Mon Jul 8 14:45:12 2024
    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!

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  • From Richard Hachel@21:1/5 to All on Mon Jul 8 15:33:58 2024
    Le 08/07/2024 à 16:45, ram@zedat.fu-berlin.de (Stefan Ram) a écrit :
    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!

    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.

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  • From Richard Hachel@21:1/5 to All on Mon Jul 8 15:43:15 2024
    Le 08/07/2024 à 16:45, ram@zedat.fu-berlin.de (Stefan Ram) a écrit :
    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!

    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.

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  • From Mikko@21:1/5 to Stefan Ram on Mon Jul 8 20:38:09 2024
    On 2024-07-08 14:45:12 +0000, Stefan Ram said:

    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.

    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".

    That's right. That happens when the moving object is not accelerated.

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

    No, gamma is 1 / sqrt(1 - v²) which is 1 when v = 0 and greater otherwise.

    --
    Mikko

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  • From Stefan Ram@21:1/5 to Mikko on Mon Jul 8 17:49:44 2024
    Mikko <mikko.levanto@iki.fi> wrote or quoted:
    I believe 0<="gamma"<=1, so, for an example, we can assume
    "gamma" to be 0.5:
    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!)

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  • From Richard Hachel@21:1/5 to All on Mon Jul 8 19:28:05 2024
    Le 08/07/2024 à 19:38, Mikko a écrit :
    On 2024-07-08 14:45:12 +0000, Stefan Ram said:

    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.

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  • From Sylvia Else@21:1/5 to Stefan Ram on Tue Jul 9 13:21:01 2024
    On 08-July-24 10:45 pm, Stefan Ram wrote:
    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!

    "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 contradictions will go away.

    Sylvia.

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  • From Maciej Wozniak@21:1/5 to All on Tue Jul 9 07:59:25 2024
    W dniu 09.07.2024 o 07:21, Sylvia Else pisze:
    On 08-July-24 10:45 pm, Stefan Ram wrote:
       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!

    "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.

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  • From Richard Hachel@21:1/5 to All on Tue Jul 9 12:47:55 2024
    Le 09/07/2024 à 07:59, Maciej Wozniak a écrit :

    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.

    Your response is excessive.
    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.

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  • From Richard Hachel@21:1/5 to All on Tue Jul 9 13:23:03 2024
    Le 09/07/2024 à 07:21, Sylvia Else a écrit :

    "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 contradictions will go away.

    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 Langevin paradox.

    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?vlbEhM2KsIvNjpx1LgxljHsrF_k@jntp/Data.Media:1>

    R.H.

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  • From Maciej Wozniak@21:1/5 to All on Tue Jul 9 15:28:45 2024
    W dniu 09.07.2024 o 14:47, Richard Hachel pisze:
    Le 09/07/2024 à 07:59, Maciej Wozniak a écrit :

    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.

    Your response is excessive.
    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.

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