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tech / sci.physics.relativity / A Precise Statement of Time Dilation

SubjectAuthor
* A Precise Statement of Time DilationRicardo Jimenez
+- Re: A Precise Statement of Time DilationOdd Bodkin
+* Re: A Precise Statement of Time Dilationrotchm
|`- Re: A Precise Statement of Time DilationRichard Hachel
+* Re: A Precise Statement of Time DilationThomas 'PointedEars' Lahn
|`* Re: A Precise Statement of Time DilationMaciej Wozniak
| `* Re: A Precise Statement of Time DilationRicardo Jimenez
|  `* Re: A Precise Statement of Time DilationStan Fultoni
|   `* Re: A Precise Statement of Time DilationRicardo Jimenez
|    +- Re: A Precise Statement of Time DilationOdd Bodkin
|    +* Re: A Precise Statement of Time DilationStan Fultoni
|    |+- Re: A Precise Statement of Time DilationOdd Bodkin
|    |`* Re: A Precise Statement of Time DilationRicardo Jimenez
|    | +- Re: A Precise Statement of Time DilationTom Roberts
|    | +* Re: A Precise Statement of Time DilationStan Fultoni
|    | |`* Re: A Precise Statement of Time DilationOdd Bodkin
|    | | +* Re: A Precise Statement of Time Dilationpatdolan
|    | | |`- Re: A Precise Statement of Time DilationRichard Hachel
|    | | `* Re: A Precise Statement of Time DilationStan Fultoni
|    | |  `* Re: A Precise Statement of Time DilationOdd Bodkin
|    | |   `- Re: A Precise Statement of Time DilationStan Fultoni
|    | +- Re: A Precise Statement of Time DilationThomas 'PointedEars' Lahn
|    | +* Re: A Precise Statement of Time DilationOdd Bodkin
|    | |+- Re: A Precise Statement of Time DilationMaciej Wozniak
|    | |`* Re: A Precise Statement of Time DilationRicardo Jimenez
|    | | +* Re: A Precise Statement of Time DilationOdd Bodkin
|    | | |+* Re: A Precise Statement of Time DilationMaciej Wozniak
|    | | ||`* Re: A Precise Statement of Time DilationJ. J. Lodder
|    | | || `* Re: A Precise Statement of Time DilationMaciej Wozniak
|    | | ||  `* Re: A Precise Statement of Time DilationJ. J. Lodder
|    | | ||   `* Re: A Precise Statement of Time DilationMaciej Wozniak
|    | | ||    `* Re: A Precise Statement of Time DilationJ. J. Lodder
|    | | ||     `- Re: A Precise Statement of Time DilationMaciej Wozniak
|    | | |`- Re: A Precise Statement of Time DilationThe Starmaker
|    | | `* Re: A Precise Statement of Time DilationThomas 'PointedEars' Lahn
|    | |  `* Re: A Precise Statement of Time DilationRichard Hachel
|    | |   `* Re: A Precise Statement of Time DilationPaul Alsing
|    | |    `* Re: A Precise Statement of Time DilationRichard Hachel
|    | |     `* Re: A Precise Statement of Time DilationPython
|    | |      `- Re: A Precise Statement of Time DilationMaciej Wozniak
|    | `- Re: A Precise Statement of Time DilationJ. J. Lodder
|    `- Re: A Precise Statement of Time DilationRichD
+- Re: A Precise Statement of Time DilationDono.
`* Re: A Precise Statement of Time DilationJ. J. Lodder
 `- Re: A Precise Statement of Time DilationMaciej Wozniak

Pages:12
A Precise Statement of Time Dilation

<rmjr6h9kbbc2baqebpbrnalem9psks3ggb@4ax.com>

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From: ricky...@earthlink.net (Ricardo Jimenez)
Newsgroups: sci.physics.relativity
Subject: A Precise Statement of Time Dilation
Date: Sat, 30 Apr 2022 20:31:27 -0400
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 by: Ricardo Jimenez - Sun, 1 May 2022 00:31 UTC

Assume the standard configuration where (t,x) are the coordinates in
the rest frame. Thus the origin's world line is x=0 in the rest
frame. There is also an inertial moving frame with coordinates
(t',x'). It shares a common origin (event (0,0)) with the rest frame
and it's origin's world line is x=vt, |v| < c, in the rest frame. Then
for any event on the world line x=vt, the respective time coordinates
have the relationship, t=gamma*t'.

Does this statement have any non trivial generalizations? Is there an
easy proof that doesn't appeal to adding a third dimension to make a
light clock argument? TIA.

Re: A Precise Statement of Time Dilation

<t4klur$sok$1@gioia.aioe.org>

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From: bodkin...@gmail.com (Odd Bodkin)
Newsgroups: sci.physics.relativity
Subject: Re: A Precise Statement of Time Dilation
Date: Sun, 1 May 2022 00:58:03 -0000 (UTC)
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 by: Odd Bodkin - Sun, 1 May 2022 00:58 UTC

Ricardo Jimenez <rickyjim@earthlink.net> wrote:
> Assume the standard configuration where (t,x) are the coordinates in
> the rest frame. Thus the origin's world line is x=0 in the rest
> frame. There is also an inertial moving frame with coordinates
> (t',x'). It shares a common origin (event (0,0)) with the rest frame
> and it's origin's world line is x=vt, |v| < c, in the rest frame. Then
> for any event on the world line x=vt, the respective time coordinates
> have the relationship, t=gamma*t'.
>
> Does this statement have any non trivial generalizations? Is there an
> easy proof that doesn't appeal to adding a third dimension to make a
> light clock argument? TIA.
>

See Mills, Space, Time and Quanta. He does a good job from the direction
you’re going.

--
Odd Bodkin -- maker of fine toys, tools, tables

Re: A Precise Statement of Time Dilation

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Subject: Re: A Precise Statement of Time Dilation
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 by: rotchm - Sun, 1 May 2022 03:25 UTC

On Saturday, April 30, 2022 at 8:31:34 PM UTC-4, Ricardo Jimenez wrote:
> Assume the standard configuration where (t,x) are the coordinates in
> the rest frame. Thus the origin's world line is x=0 in the rest
> frame. There is also an inertial moving frame with coordinates
> (t',x'). It shares a common origin (event (0,0)) with the rest frame
> and it's origin's world line is x=vt, |v| < c, in the rest frame. Then
> for any event on the world line x=vt, the respective time coordinates
> have the relationship, t=gamma*t'.
>
> Does this statement have any non trivial generalizations?

Using normalized units [c=1], reference frames S' and S, and caps for vectors, and X = A + Vt [if A <> 0 then their origins did not initially coincided; a general case. V is the velocity vector of S' wrt S]. Since you request that the event occur at X' = 0 thus dX' = 0. From the "invariant" we have:

dt'² - dX'² = dt² - dX²
dt'² - 0 = dt² - d(A + Vt) ² [careful with the notations]..
dt'² = dt² - v² dt² [since dA = 0 and V² = V dot V = v²]
dt'² = (1-v²) dt²
dt' = √(1-v²) dt and your result follows.

Note that this was independent of the orientation of the S' frame (the "tetrad"); only the direction V of its origin was used. This is not "non trivial"; its trivial.

> Is there an easy proof that doesn't appeal to adding a third dimension
> to make a light clock argument? TIA.

Just call the direction in which the origin of S' is moving as the "x" direction.
That is, the x axis need not be "drawn to the right". Now you just apply your above reasoning.
No need of 3D/vectors.

Re: A Precise Statement of Time Dilation

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Subject: Re: A Precise Statement of Time Dilation
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 by: Thomas 'Pointed - Sun, 1 May 2022 04:14 UTC

Ricardo Jimenez wrote:

> Assume the standard configuration where (t,x) are the coordinates in
> the rest frame. Thus the origin's world line is x=0 in the rest
> frame. There is also an inertial moving frame with coordinates
> (t',x'). It shares a common origin (event (0,0)) with the rest frame
> and it's origin's world line is x=vt, |v| < c, in the rest frame. Then
> for any event on the world line x=vt, the respective time coordinates
> have the relationship, t=gamma*t'.

No.

> Does this statement have any non trivial generalizations? Is there an
> easy proof that doesn't appeal to adding a third dimension to make a
> light clock argument? TIA.

For the umpteenth time now: There can be no proof because it is a THEORY,
NOT a theorem. So there can be, and is, "only" A LOT of observational
evidence to support it.

As for *your* better _understanding_: Draw the spacetime diagram, or look at
the MANY that I have posted here before. You do not have to accept that
spacetime is a correct model of reality; only that the Lorentz
transformation is a correct coordinate transformation of spatial and
temporal coordinates given the observed constancy of the speed of light.
Then the skewed axes of the diagram for the "moving" frame will naturally
lead to "time dilation", i.e. the fact that less proper time elapses in the
"moving" frame (with the skewed temporal and spatial axes). [It also leads
to the relativity of simultaneity and length contraction.]

And this only requires one spatial dimension; so even the pointless, because
clueless, requirement that you made is satisfied by this.

Also:

“The universe is under no obligation to make sense to *you*.”

–Neil deGrasse Tyson, astrophysicist and science communicator

PointedEars
--
Two neutrinos go through a bar ...

(from: WolframAlpha)

Re: A Precise Statement of Time Dilation

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Subject: Re: A Precise Statement of Time Dilation
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 by: Maciej Wozniak - Sun, 1 May 2022 04:49 UTC

On Sunday, 1 May 2022 at 06:14:34 UTC+2, Thomas 'PointedEars' Lahn wrote:
> Ricardo Jimenez wrote:
>
> > Assume the standard configuration where (t,x) are the coordinates in
> > the rest frame. Thus the origin's world line is x=0 in the rest
> > frame. There is also an inertial moving frame with coordinates
> > (t',x'). It shares a common origin (event (0,0)) with the rest frame
> > and it's origin's world line is x=vt, |v| < c, in the rest frame. Then
> > for any event on the world line x=vt, the respective time coordinates
> > have the relationship, t=gamma*t'.
> No.
> > Does this statement have any non trivial generalizations? Is there an
> > easy proof that doesn't appeal to adding a third dimension to make a
> > light clock argument? TIA.
> For the umpteenth time now: There can be no proof because it is a THEORY,
> NOT a theorem. So there can be, and is, "only" A LOT of observational
> evidence to support it.

In the meantime in the real world, however, forbidden by it
"improper" and "non-standard" TAI and GPS keep measuring
t'=t, just like all serious clocks always did.

Re: A Precise Statement of Time Dilation

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From: ricky...@earthlink.net (Ricardo Jimenez)
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Subject: Re: A Precise Statement of Time Dilation
Date: Sun, 01 May 2022 12:15:36 -0400
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 by: Ricardo Jimenez - Sun, 1 May 2022 16:15 UTC

On Sat, 30 Apr 2022 21:49:01 -0700 (PDT), Maciej Wozniak
<maluwozniak@gmail.com> wrote:

>On Sunday, 1 May 2022 at 06:14:34 UTC+2, Thomas 'PointedEars' Lahn wrote:
>> Ricardo Jimenez wrote:
>>
>> > Assume the standard configuration where (t,x) are the coordinates in
>> > the rest frame. Thus the origin's world line is x=0 in the rest
>> > frame. There is also an inertial moving frame with coordinates
>> > (t',x'). It shares a common origin (event (0,0)) with the rest frame
>> > and it's origin's world line is x=vt, |v| < c, in the rest frame. Then
>> > for any event on the world line x=vt, the respective time coordinates
>> > have the relationship, t=gamma*t'.
>> No.
>> > Does this statement have any non trivial generalizations? Is there an
>> > easy proof that doesn't appeal to adding a third dimension to make a
>> > light clock argument? TIA.
>> For the umpteenth time now: There can be no proof because it is a THEORY,
>> NOT a theorem. So there can be, and is, "only" A LOT of observational
>> evidence to support it.
>
>In the meantime in the real world, however, forbidden by it
>"improper" and "non-standard" TAI and GPS keep measuring
>t'=t, just like all serious clocks always did.

With only the added assumption that in both coordinate systems, there
is a light cone at each event (t0,x0), (c*t - c*t0)^2 = (x - x0)^2
with the same equation holding with S' coordinates, I think there
should be a rigorous mathematical derivation of what I stated using
simple linear algebra. Neither physics nor reality should be invoked
in the derivation. Of course, if anybody can demonstrate that such a
derivation is impossible, I would very much like to understand that
argument.

Re: A Precise Statement of Time Dilation

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Subject: Re: A Precise Statement of Time Dilation
From: fultonis...@gmail.com (Stan Fultoni)
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 by: Stan Fultoni - Sun, 1 May 2022 16:31 UTC

On Sunday, May 1, 2022 at 9:15:42 AM UTC-7, Ricardo Jimenez wrote:
> For any event on the world line x=vt, the respective time coordinates
> have the relationship, t=gamma*t'. Does this statement have any
> non trivial generalizations?

The fully general statement, not restricted to just the x,t coordinates
along a single world, but applicable to the x,t coordinates for all events,
is the Lorentz transformation, i.e., t'=(t-vx)g, x'=(x-vt)g where g=1/sqrt(1-v^2).

> Is there an easy proof...

Well, given the principle of relativity and the inertia of energy (or, equivalently,
the invariance of light speed in vacuum, or any other equivalent principle), yes,
the Lorentz transformation can be derived easily, as shown in any good book
on relativity.

> that doesn't appeal to adding a third dimension...

The usual derivation can be carried out in just one space and one time dimension,
since it's clear the perpendicular space dimensions map trivially.

> to make a light clock argument?

A third dimension isn't needed to describe a light clock, since we can consider
such a clock oriented along the x axis (parallel to the direction of motion, rather
than perpendicular). We just need to account for length contraction.

> With only the added assumption that in both coordinate systems, there
> is a light cone at each event (t0,x0), (c*t - c*t0)^2 = (x - x0)^2
> with the same equation holding with S' coordinates, I think there
> should be a rigorous mathematical derivation of what I stated using
> simple linear algebra.

Sure, that's just the light speed principle, and you can combine that with
Galileo's principle of relativity to easily derive the full Lorentz transformation,
from which your highly specialized and restricted formula follows trivially.

Re: A Precise Statement of Time Dilation

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Subject: Re: A Precise Statement of Time Dilation
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 by: Ricardo Jimenez - Sun, 1 May 2022 20:38 UTC

On Sun, 1 May 2022 09:31:00 -0700 (PDT), Stan Fultoni
<fultonistan@gmail.com> wrote:

>> With only the added assumption that in both coordinate systems, there
>> is a light cone at each event (t0,x0), (c*t - c*t0)^2 = (x - x0)^2
>> with the same equation holding with S' coordinates, I think there
>> should be a rigorous mathematical derivation of what I stated using
>> simple linear algebra.
>
>Sure, that's just the light speed principle, and you can combine that with
>Galileo's principle of relativity to easily derive the full Lorentz transformation,
>from which your highly specialized and restricted formula follows trivially.

I should have added the assumption that in S' coordinates, the formula
for the S world line is x'=-vt'. I have never seen a rigorous Lorentz
transform derivation that didn't assume time dilation has already been
established, the linearity of the transform and or/some other extras.
I think you should state what you mean by "Galileo's principle of
relativity" as precisely as I have tried to be.

Re: A Precise Statement of Time Dilation

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Subject: Re: A Precise Statement of Time Dilation
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 by: Odd Bodkin - Sun, 1 May 2022 21:11 UTC

Ricardo Jimenez <rickyjim@earthlink.net> wrote:
> On Sun, 1 May 2022 09:31:00 -0700 (PDT), Stan Fultoni
> <fultonistan@gmail.com> wrote:
>
>>> With only the added assumption that in both coordinate systems, there
>>> is a light cone at each event (t0,x0), (c*t - c*t0)^2 = (x - x0)^2
>>> with the same equation holding with S' coordinates, I think there
>>> should be a rigorous mathematical derivation of what I stated using
>>> simple linear algebra.
>>
>> Sure, that's just the light speed principle, and you can combine that with
>> Galileo's principle of relativity to easily derive the full Lorentz transformation,
>> from which your highly specialized and restricted formula follows trivially.
>
> I should have added the assumption that in S' coordinates, the formula
> for the S world line is x'=-vt'. I have never seen a rigorous Lorentz
> transform derivation that didn't assume time dilation has already been
> established, the linearity of the transform and or/some other extras.
> I think you should state what you mean by "Galileo's principle of
> relativity" as precisely as I have tried to be.
>

There are lots of ways to go about this, but the point is that you have to
start with some non-Newtonian fact (experimental observation) that is taken
to be true, and then the principle of relativity provides the rest. Whether
that experimental fact is the null results of Michelson Morley or the
observed invariance of c or the disproportion between force and coordinate
acceleration doesn’t really matter. Robert Mills used the principle of
relativity and the MMX as a starting point in the reference I cited, but
there are other choices.

--
Odd Bodkin — Maker of fine toys, tools, tables

Re: A Precise Statement of Time Dilation

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Subject: Re: A Precise Statement of Time Dilation
From: fultonis...@gmail.com (Stan Fultoni)
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 by: Stan Fultoni - Sun, 1 May 2022 21:46 UTC

On Sunday, May 1, 2022 at 1:39:12 PM UTC-7, Ricardo Jimenez wrote:
> >> With only the added assumption that in both coordinate systems, there
> >> is a light cone at each event (t0,x0), (c*t - c*t0)^2 = (x - x0)^2
> >> with the same equation holding with S' coordinates, I think there
> >> should be a rigorous mathematical derivation of what I stated using
> >> simple linear algebra.
> >
> >Sure, that's just the light speed principle, and you can combine that with
> >Galileo's principle of relativity to easily derive the full Lorentz transformation,
> >from which your highly specialized and restricted formula follows trivially.
>
> I should have added the assumption that in S' coordinates, the formula
> for the S world line is x'=-vt'.

That's just reciprocity, which follows from the relativity principle and isotropy.

> I have never seen a rigorous Lorentz transform derivation that didn't
> assume time dilation has already been established...

Huh? No derivation of the Lorentz transformation (not "transform") assumes
time dilation per se. To the contrary, time dilation is a derived consequence of
the Lorentz transformation. The only assumptions in the derivation are (1) Galileo's
principle of relativity, (2) some principle that entails the inertia of energy, (3) isotropy,
(4) memorylessness, and a few other premises that you wouldn't dream of challenging
(even if you thought of them).

> the linearity of the transform...

That is already entailed by the relativity principle, because it implies that the
transformation (not "transform") must map contiguous straight lines to contiguous
straight lines. This condition can only be met by linear transformations.

> I think you should state what you mean by "Galileo's principle of relativity" ...

I mean the same thing that every scientist means. This isn't some obscure or
controversial concept. The principle of relativity asserts that all the equations of
physics take their simple homogeneous and isotropic form in terms of any (local)
system of inertia-based coordinates. This is an extremely restrictive principle,
such that there is only a single degree of freedom in the transformations that
must relate inertia-based coordinate systems.

oddbodkin wrote:
>Robert Mills used the principle of relativity and the MMX as a starting point

The combination of those two things is not sufficient to serve as a starting point,
because the Michelson experiment, by itself, doesn't constrain the single degree
of freedom. Remember, Einstein cited failure of the ether drift experiments not in
support of his light speed principle, but merely in support of the relativity principle.
He did not make the mistake of confusing them. Hopefully Mills doesn't really
make the mistake that you attribute to him.

Re: A Precise Statement of Time Dilation

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 by: Dono. - Sun, 1 May 2022 21:47 UTC

On Saturday, April 30, 2022 at 5:31:34 PM UTC-7, Ricardo Jimenez wrote:
> Assume the standard configuration where (t,x) are the coordinates in
> the rest frame. Thus the origin's world line is x=0 in the rest
> frame. There is also an inertial moving frame with coordinates
> (t',x'). It shares a common origin (event (0,0)) with the rest frame
> and it's origin's world line is x=vt, |v| < c, in the rest frame. Then
> for any event on the world line x=vt, the respective time coordinates
> have the relationship, t=gamma*t'.
>
> Does this statement have any non trivial generalizations? Is there an
> easy proof that doesn't appeal to adding a third dimension to make a
> light clock argument? TIA.

1. Start with t'=\gamma(t-vx/c^2)
2. Make x=vt
What did you get?

Generalization for arbitrary direction of motion between frames.

Look here: https://en.wikipedia.org/wiki/Lorentz_transformation#Vector_transformations

Re: A Precise Statement of Time Dilation

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Subject: Re: A Precise Statement of Time Dilation
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 by: Odd Bodkin - Sun, 1 May 2022 22:02 UTC

Stan Fultoni <fultonistan@gmail.com> wrote:
> On Sunday, May 1, 2022 at 1:39:12 PM UTC-7, Ricardo Jimenez wrote:
>>>> With only the added assumption that in both coordinate systems, there
>>>> is a light cone at each event (t0,x0), (c*t - c*t0)^2 = (x - x0)^2
>>>> with the same equation holding with S' coordinates, I think there
>>>> should be a rigorous mathematical derivation of what I stated using
>>>> simple linear algebra.
>>>
>>> Sure, that's just the light speed principle, and you can combine that with
>>> Galileo's principle of relativity to easily derive the full Lorentz transformation,
>>> from which your highly specialized and restricted formula follows trivially.
>>
>> I should have added the assumption that in S' coordinates, the formula
>> for the S world line is x'=-vt'.
>
> That's just reciprocity, which follows from the relativity principle and isotropy.
>
>> I have never seen a rigorous Lorentz transform derivation that didn't
>> assume time dilation has already been established...
>
> Huh? No derivation of the Lorentz transformation (not "transform") assumes
> time dilation per se. To the contrary, time dilation is a derived consequence of
> the Lorentz transformation. The only assumptions in the derivation are (1) Galileo's
> principle of relativity, (2) some principle that entails the inertia of
> energy, (3) isotropy,
> (4) memorylessness, and a few other premises that you wouldn't dream of challenging
> (even if you thought of them).
>
>> the linearity of the transform...
>
> That is already entailed by the relativity principle, because it implies that the
> transformation (not "transform") must map contiguous straight lines to contiguous
> straight lines. This condition can only be met by linear transformations.
>
>> I think you should state what you mean by "Galileo's principle of relativity" ...
>
> I mean the same thing that every scientist means. This isn't some obscure or
> controversial concept. The principle of relativity asserts that all the equations of
> physics take their simple homogeneous and isotropic form in terms of any (local)
> system of inertia-based coordinates. This is an extremely restrictive principle,
> such that there is only a single degree of freedom in the transformations that
> must relate inertia-based coordinate systems.
>
> oddbodkin wrote:
>> Robert Mills used the principle of relativity and the MMX as a starting point
>
> The combination of those two things is not sufficient to serve as a starting point,
> because the Michelson experiment, by itself, doesn't constrain the single degree
> of freedom. Remember, Einstein cited failure of the ether drift experiments not in
> support of his light speed principle, but merely in support of the relativity principle.
> He did not make the mistake of confusing them. Hopefully Mills doesn't really
> make the mistake that you attribute to him.
>

You can check for yourself. The principle of relativity is assumed. The
result of the MMX is taken as true. A hypothesis of time dilation (or
alternatively length contraction) is shown to be consistent with those
results, which consistency is all that is expected of a hypothesis. Then
the Lorentz transformations follow.

This is the Mills of Yang-Mills fame, btw.

--
Odd Bodkin — Maker of fine toys, tools, tables

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From: r.hac...@tiscali.fr (Richard Hachel)
 by: Richard Hachel - Sun, 1 May 2022 22:10 UTC

Le 01/05/2022 à 05:25, rotchm a écrit :

> its trivial.

Oui, c'est très facile, mais bourré de petits pièges.

Posons mes deux équations qui font tire tout le monde (surtout la
première car pour la deuxième
les physiciens ont la même que moi, et ils détestent rire d'eux mêmes)
:

Dans les milieux accélérés, on a :
Tr=sqrt(2x/a)
To=(x/c).sqrt(1+2c²/ax)

Pourtant, si l'on fait une somme mathématiquement correcte (par somme ou
par intégration),
il semblerait qu'on problème se pose pour Tr.

Comme si d'un côté, on avait bien Tr=∫ΔTr mais PAS To=∫ΔTo ce qui
paraît entraîner un immense étonnement de ceux qui lisent.

On oublie peut-être que plus la vitesse d'un référentiel augmente par
rapport au notre, plus son axe des y est dévié en arrière du mouvement
d'un angle β=Vo/c, et que la métrique spatiale devient différente.

On n'est donc plus en milieu newtonien ou leibnizien.

Les transformations usuelles deviennent fausses.

Ce n'est pas gênant pour les vitesses uniformes, car la métrique, une
fois définie, ne varie pas.

Pour les référentiels accélérés, la métrique change en continue, et
l'axe des y est de plus en plus dévié en contresens du mouvement.

Cela veut dire que si on objet va de A à B, puis de B à C, puis de C à
D, en mouvement accéléré,
la métrique, pour cet objet lui-même, restera newtonienne.

Mais pour le référentiel observant, quand A va en B, B recule
légèrement puisqu'il n'est plus à la même vitesse qu'en A, et ainsi de
suite pour C, D, E qui reculent de plus en plus, la distance parcourue
devenant plus courte par effet relativiste (Métrique de Lorentz).

Il va donc y avoir une modification supplémentaire à prendre en compte,
le temps observable (impropre)
paraissant un peu plus court que prévu.

Et à l'inverse, le temps propre étant un peu plus long que prévu.

Il doit automatiquement retomber sur Tr=sqrt(2x/a)

R.H.

Re: A Precise Statement of Time Dilation

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From: ricky...@earthlink.net (Ricardo Jimenez)
Newsgroups: sci.physics.relativity
Subject: Re: A Precise Statement of Time Dilation
Date: Sun, 01 May 2022 18:35:50 -0400
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 by: Ricardo Jimenez - Sun, 1 May 2022 22:35 UTC

On Sun, 1 May 2022 14:46:54 -0700 (PDT), Stan Fultoni
<fultonistan@gmail.com> wrote:

>On Sunday, May 1, 2022 at 1:39:12 PM UTC-7, Ricardo Jimenez wrote:
>> >> With only the added assumption that in both coordinate systems, there
>> >> is a light cone at each event (t0,x0), (c*t - c*t0)^2 = (x - x0)^2
>> >> with the same equation holding with S' coordinates, I think there
>> >> should be a rigorous mathematical derivation of what I stated using
>> >> simple linear algebra.
>> >
>> >Sure, that's just the light speed principle, and you can combine that with
>> >Galileo's principle of relativity to easily derive the full Lorentz transformation,
>> >from which your highly specialized and restricted formula follows trivially.
>>
>> I should have added the assumption that in S' coordinates, the formula
>> for the S world line is x'=-vt'.
>
>That's just reciprocity, which follows from the relativity principle and isotropy.
>
>> I have never seen a rigorous Lorentz transform derivation that didn't
>> assume time dilation has already been established...
>
>Huh? No derivation of the Lorentz transformation (not "transform") assumes
>time dilation per se. To the contrary, time dilation is a derived consequence of
>the Lorentz transformation. The only assumptions in the derivation are (1) Galileo's
>principle of relativity, (2) some principle that entails the inertia of energy, (3) isotropy,
>(4) memorylessness, and a few other premises that you wouldn't dream of challenging
>(even if you thought of them).
>
>> the linearity of the transform...
>
>That is already entailed by the relativity principle, because it implies that the
>transformation (not "transform") must map contiguous straight lines to contiguous
>straight lines. This condition can only be met by linear transformations.
>
>> I think you should state what you mean by "Galileo's principle of relativity" ...
>
>I mean the same thing that every scientist means. This isn't some obscure or
>controversial concept. The principle of relativity asserts that all the equations of
>physics take their simple homogeneous and isotropic form in terms of any (local)
>system of inertia-based coordinates. This is an extremely restrictive principle,
>such that there is only a single degree of freedom in the transformations that
>must relate inertia-based coordinate systems.
>
>oddbodkin wrote:
>>Robert Mills used the principle of relativity and the MMX as a starting point
>
>The combination of those two things is not sufficient to serve as a starting point,
>because the Michelson experiment, by itself, doesn't constrain the single degree
>of freedom. Remember, Einstein cited failure of the ether drift experiments not in
>support of his light speed principle, but merely in support of the relativity principle.
>He did not make the mistake of confusing them. Hopefully Mills doesn't really
>make the mistake that you attribute to him.

I am getting the feeling that the notion of rigorous mathematical
proof is alien to most of the posters here. Well, Newton and Einstein
have long been criticized for often being deficient in that area too.
No contemporary mathematician would accept Newton's laws of motion and
Einstein's relativity postulates, as their authors stated them, as
mathematical axioms. The best that can be said about them, from such
a point of view, is that they are intuitive modeling principles that
might guide one in writing down real axioms that can be used in
setting up a mathematical model.

Re: A Precise Statement of Time Dilation

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 by: Tom Roberts - Sun, 1 May 2022 23:00 UTC

On 5/1/22 5:35 PM, Ricardo Jimenez wrote:
> I am getting the feeling that the notion of rigorous mathematical
> proof is alien to most of the posters here.

Hmmmm. Those of us who demonstrate a clear understanding of modern
physics are all familiar with mathematical proofs. But we are certainly
not "most of the posters here".

In physics, mathematical proofs only apply within the context of a
specific theory. Theorems can be derived from axioms (postulates), but
that has nothing whatsoever to do with whether or not those theorems
correspond to physical phenomena in the world we inhabit -- for that one
needs experiments. Physics is not math.

> Well, Newton and Einstein
> have long been criticized for often being deficient in that area too.

Hmmmm.... The standards of rigor are DIFFERENT in physics than in math.

> No contemporary mathematician would accept Newton's laws of motion and
> Einstein's relativity postulates, as their authors stated them, as
> mathematical axioms.

Of course they aren't intended to be mathematical axioms. The standards
of rigor are DIFFERENT in physics than in math.

> The best that can be said about them, from such
> a point of view, is that they are intuitive modeling principles that
> might guide one in writing down real axioms that can be used in
> setting up a mathematical model.

Current theories of physics are all mathematical models. The standards
of rigor are DIFFERENT in physics than in math.

Tom Roberts

Re: A Precise Statement of Time Dilation

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Subject: Re: A Precise Statement of Time Dilation
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 by: Stan Fultoni - Sun, 1 May 2022 23:15 UTC

On Sunday, May 1, 2022 at 3:35:56 PM UTC-7, Ricardo Jimenez wrote:
> >

> I am getting the feeling that the notion of rigorous mathematical
> proof is alien to most of the posters here.

Your "feeling" is unfounded. Mathematical proof always proceeds from some
axiomatic basis, and for special relativity the axiomatic basis has been provided
to you, namely, the principle of relativity and (say) the light speed principle. From
this (and isotropy, memorylessness, etc) the Lorentz transformation follows rigorously.

> No contemporary mathematician would accept Newton's laws of motion
> and Einstein's relativity postulates, as their authors stated them, as
> mathematical axioms.

Not true, many mathematicians have and do work in the axiomatic foundations
of relativity. May whole books have been written about it by many mathematicians.
I think your difficulty stems from the fact that you don't understand the basic
concepts, such as inertia-based coordinate systems, well enough to grasp the
content of the axioms that are expressed in terms of those concepts.

oddbodkin wrote:
> The principle of relativity is assumed. The result of the MMX is taken as true.

That's garbled already... Michelson's result is one of the empirical bases
of the principle of relativity. If you stipulate the principle of relativity, then
Michelson's result is superfluous. Remember, Einstein cited failure of the ether
drift experiments purely in support of the relativity principle, not as evidence for
(say) the light speed principle.

> A hypothesis of time dilation (or alternatively length contraction)

That makes no sense at all. If you are hypothesizing time dilation and/or
length contraction, then this is tantamount to hypothesizing the Lorentz
transformation.

> is shown to be consistent with those results

That doesn't make sense either, because (again) Michelson's result isn't
saying anything other than supporting the principle of relativity, so all you are
saying is that time dilation and length contraction (i.e., the Lorentz transformation)
are consistent with the principle of relativity. Of course they are, but so is
Galilean relativity, and we need some principle to select Lorentz invariance
over Galilean invariance. I really hope Mills' book isn't as bad as you are
portraying it.

Re: A Precise Statement of Time Dilation

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 by: Thomas 'Pointed - Sun, 1 May 2022 23:26 UTC

Ricardo Jimenez wrote:

> I am getting the feeling that the notion of rigorous mathematical
> proof is alien to most of the posters here.

That might be so, but would only be due to a lack of proper education.

> Well, Newton and Einstein have long been criticized for often being
> deficient in that area too.

By clueless people perhaps.

> No contemporary mathematician would accept Newton's laws of motion and
> Einstein's relativity postulates, as their authors stated them, as
> mathematical axioms.

Nobody but you said that anyone should.

> The best that can be said about them, from such a point of view, is that
> they are intuitive modeling principles that might guide one in writing
> down real axioms that can be used in setting up a mathematical model.

But that would be an argument that could only be made by people as clueless
as yourself. In order to educate yourself, about “The Relation of
Mathematics and Physics”, you should watch

<https://www.feynmanlectures.caltech.edu/messenger.html>

PointedEars
--
Heisenberg is out for a drive when he's stopped by a traffic cop.
The officer asks him "Do you know how fast you were going?"
Heisenberg replies "No, but I know where I am."
(from: WolframAlpha)

Re: A Precise Statement of Time Dilation

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 by: Odd Bodkin - Mon, 2 May 2022 03:17 UTC

Ricardo Jimenez <rickyjim@earthlink.net> wrote:

>
> I am getting the feeling that the notion of rigorous mathematical
> proof is alien to most of the posters here. Well, Newton and Einstein
> have long been criticized for often being deficient in that area too.
> No contemporary mathematician would accept Newton's laws of motion and
> Einstein's relativity postulates, as their authors stated them, as
> mathematical axioms. The best that can be said about them, from such
> a point of view, is that they are intuitive modeling principles that
> might guide one in writing down real axioms that can be used in
> setting up a mathematical model.
>

Congratulations for landing on the difference between mathematics and
physics.

In mathematics, one starts with a set of axiomatic statements and then
deductively find conclusions that stem from them, without actual reference
to any reality check as to whether the things you discover are actually
instantiated in nature.

Physics, on the other hand, is always going to test axioms and hypotheses
against experimental test. In this way, even if the axioms seem plausible
and the deductive reasoning is flawless, if it does not agree with
measurements and observations, then they are wrong. On the other hand,
experimental validation does not serve as a proof in any formal sense that
the hypotheses are correct. Rather, the hypotheses are provisionally
supported by the evidence, and no proof is ever obtainable by this
comparison.

If you thought that physics could be subject to the same methodologies as
mathematical analysis, then I’m afraid you have the wrong idea of what
science is about.

--
Odd Bodkin -- maker of fine toys, tools, tables

Re: A Precise Statement of Time Dilation

<t4nigs$1b4c$2@gioia.aioe.org>

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https://www.novabbs.com/tech/article-flat.php?id=89574&group=sci.physics.relativity#89574

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From: bodkin...@gmail.com (Odd Bodkin)
Newsgroups: sci.physics.relativity
Subject: Re: A Precise Statement of Time Dilation
Date: Mon, 2 May 2022 03:17:48 -0000 (UTC)
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 by: Odd Bodkin - Mon, 2 May 2022 03:17 UTC

Stan Fultoni <fultonistan@gmail.com> wrote:
> On Sunday, May 1, 2022 at 3:35:56 PM UTC-7, Ricardo Jimenez wrote:
>>>
>
>> I am getting the feeling that the notion of rigorous mathematical
>> proof is alien to most of the posters here.
>
> Your "feeling" is unfounded. Mathematical proof always proceeds from some
> axiomatic basis, and for special relativity the axiomatic basis has been provided
> to you, namely, the principle of relativity and (say) the light speed principle. From
> this (and isotropy, memorylessness, etc) the Lorentz transformation follows rigorously.
>
>> No contemporary mathematician would accept Newton's laws of motion
>> and Einstein's relativity postulates, as their authors stated them, as
>> mathematical axioms.
>
> Not true, many mathematicians have and do work in the axiomatic foundations
> of relativity. May whole books have been written about it by many mathematicians.
> I think your difficulty stems from the fact that you don't understand the basic
> concepts, such as inertia-based coordinate systems, well enough to grasp the
> content of the axioms that are expressed in terms of those concepts.
>
> oddbodkin wrote:
>> The principle of relativity is assumed. The result of the MMX is taken as true.
>
> That's garbled already... Michelson's result is one of the empirical bases
> of the principle of relativity. If you stipulate the principle of relativity, then
> Michelson's result is superfluous. Remember, Einstein cited failure of the ether
> drift experiments purely in support of the relativity principle, not as evidence for
> (say) the light speed principle.
>
>> A hypothesis of time dilation (or alternatively length contraction)
>
> That makes no sense at all. If you are hypothesizing time dilation and/or
> length contraction, then this is tantamount to hypothesizing the Lorentz
> transformation.
>
>> is shown to be consistent with those results
>
> That doesn't make sense either, because (again) Michelson's result isn't
> saying anything other than supporting the principle of relativity, so all you are
> saying is that time dilation and length contraction (i.e., the Lorentz transformation)
> are consistent with the principle of relativity. Of course they are, but so is
> Galilean relativity, and we need some principle to select Lorentz invariance
> over Galilean invariance. I really hope Mills' book isn't as bad as you are
> portraying it.
>

It is not clear whether you are claiming that Mills’ presentation makes no
sense, even without looking at his presentation; or whether you are
claiming that my representation of his approach must surely be wrong, again
without bothering to even look at what it is he actually said. Either way,
it seems silly to critique something you don’t have first-hand acquaintance
of.

Perhaps it would be easier if in these discussions you would just refer to
your own book on the subject. Since you are so enamored with the
flawlessness of your approach, surely you have published it for the benefit
of all, not just the readers here.

--
Odd Bodkin -- maker of fine toys, tools, tables

Re: A Precise Statement of Time Dilation

<d6b8639a-2999-4bff-8096-b1e60fb703e0n@googlegroups.com>

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Subject: Re: A Precise Statement of Time Dilation
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 by: patdolan - Mon, 2 May 2022 03:30 UTC

On Sunday, May 1, 2022 at 8:17:54 PM UTC-7, bodk...@gmail.com wrote:
> Stan Fultoni <fulto...@gmail.com> wrote:
> > On Sunday, May 1, 2022 at 3:35:56 PM UTC-7, Ricardo Jimenez wrote:
> >>>
> >
> >> I am getting the feeling that the notion of rigorous mathematical
> >> proof is alien to most of the posters here.
> >
> > Your "feeling" is unfounded. Mathematical proof always proceeds from some
> > axiomatic basis, and for special relativity the axiomatic basis has been provided
> > to you, namely, the principle of relativity and (say) the light speed principle. From
> > this (and isotropy, memorylessness, etc) the Lorentz transformation follows rigorously.
> >
> >> No contemporary mathematician would accept Newton's laws of motion
> >> and Einstein's relativity postulates, as their authors stated them, as
> >> mathematical axioms.
> >
> > Not true, many mathematicians have and do work in the axiomatic foundations
> > of relativity. May whole books have been written about it by many mathematicians.
> > I think your difficulty stems from the fact that you don't understand the basic
> > concepts, such as inertia-based coordinate systems, well enough to grasp the
> > content of the axioms that are expressed in terms of those concepts.
> >
> > oddbodkin wrote:
> >> The principle of relativity is assumed. The result of the MMX is taken as true.
> >
> > That's garbled already... Michelson's result is one of the empirical bases
> > of the principle of relativity. If you stipulate the principle of relativity, then
> > Michelson's result is superfluous. Remember, Einstein cited failure of the ether
> > drift experiments purely in support of the relativity principle, not as evidence for
> > (say) the light speed principle.
> >
> >> A hypothesis of time dilation (or alternatively length contraction)
> >
> > That makes no sense at all. If you are hypothesizing time dilation and/or
> > length contraction, then this is tantamount to hypothesizing the Lorentz
> > transformation.
> >
> >> is shown to be consistent with those results
> >
> > That doesn't make sense either, because (again) Michelson's result isn't
> > saying anything other than supporting the principle of relativity, so all you are
> > saying is that time dilation and length contraction (i.e., the Lorentz transformation)
> > are consistent with the principle of relativity. Of course they are, but so is
> > Galilean relativity, and we need some principle to select Lorentz invariance
> > over Galilean invariance. I really hope Mills' book isn't as bad as you are
> > portraying it.
> >
> It is not clear whether you are claiming that Mills’ presentation makes no
> sense, even without looking at his presentation; or whether you are
> claiming that my representation of his approach must surely be wrong, again
> without bothering to even look at what it is he actually said. Either way,
> it seems silly to critique something you don’t have first-hand acquaintance
> of.
>
> Perhaps it would be easier if in these discussions you would just refer to
> your own book on the subject. Since you are so enamored with the
> flawlessness of your approach, surely you have published it for the benefit
> of all, not just the readers here.
> --
> Odd Bodkin -- maker of fine toys, tools, tables

Bodkin,

Citizen Jimenez has already publish much remarkable work in this forum. I am eager to study this latest production of his. But the argument for which posterity will remember Citizen Jimenez is the one he made a few months back concerning the absolute nature of relative motion. According to the LTs, relative motion [ the "v" in the LTs ] is an absolute quantity not subject the the principle of relativity. This is quite curious (and quite ad hoc) when you consider that the constituent parts of motion, x and t, are easily transformed into x' and t'. So why not transform v into v' ? There is no v' in relativity, by fiat and nothing more. Even though it is easy to calculate v':

v' = ∆x'/∆t' = g(x-vt)/g(t-vx/c^2)

But to calculate v' is to deliver a fatal blow to the entire relativistic enterprise; which is left as an exercise for the reader.

The clear thinking world thanks you for your insight Citizen Jimenez.

Re: A Precise Statement of Time Dilation

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Subject: Re: A Precise Statement of Time Dilation
From: fultonis...@gmail.com (Stan Fultoni)
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 by: Stan Fultoni - Mon, 2 May 2022 04:24 UTC

On Sunday, May 1, 2022 at 8:17:54 PM UTC-7, bodk...@gmail.com wrote:
> It is not clear whether you are claiming that Mills’ presentation makes no
> sense, or that my representation of his approach must surely be wrong...

Neither one. I've said quite clearly (see the posts above) that your
representation of Mills' presentation makes no sense, and I explained
in detail why.

Re: A Precise Statement of Time Dilation

<t4np65$1068$1@gioia.aioe.org>

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Newsgroups: sci.physics.relativity
Subject: Re: A Precise Statement of Time Dilation
Date: Mon, 2 May 2022 05:11:33 -0000 (UTC)
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 by: Odd Bodkin - Mon, 2 May 2022 05:11 UTC

Stan Fultoni <fultonistan@gmail.com> wrote:
> On Sunday, May 1, 2022 at 8:17:54 PM UTC-7, bodk...@gmail.com wrote:
>> It is not clear whether you are claiming that Mills’ presentation makes no
>> sense, or that my representation of his approach must surely be wrong...
>
> Neither one. I've said quite clearly (see the posts above) that your
> representation of Mills' presentation makes no sense, and I explained
> in detail why.
>

Whether it makes sense to you is of no concern of mine.

You have only to look at Robert Mills’ book yourself, and then at least
your comments will be about what it is that he said. And if you find that
his presentation is lacking in your estimation, I’m sure his heirs will be
pleased to hear your critique. Perhaps you could point them to your book
and your own best-possible presentation.

--
Odd Bodkin -- maker of fine toys, tools, tables

Re: A Precise Statement of Time Dilation

<f8a8c02d-bf02-4673-94bc-63a674cd51d3n@googlegroups.com>

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 by: Maciej Wozniak - Mon, 2 May 2022 05:52 UTC

On Monday, 2 May 2022 at 05:17:50 UTC+2, bodk...@gmail.com wrote:

> Congratulations for landing on the difference between mathematics and
> physics.
>
> In mathematics, one starts with a set of axiomatic statements and then
> deductively find conclusions that stem from them, without actual reference
> to any reality check as to whether the things you discover are actually
> instantiated in nature.
>
> Physics, on the other hand, is always going to test axioms and hypotheses
> against experimental test.

Repeating this bullshit won't make it true, and the
thinkers more competent than poor idiot Popper
(Poincare, Kuhn, Lakatos) knew better.

Re: A Precise Statement of Time Dilation

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Subject: Re: A Precise Statement of Time Dilation
From: fultonis...@gmail.com (Stan Fultoni)
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 by: Stan Fultoni - Mon, 2 May 2022 06:56 UTC

On Sunday, May 1, 2022 at 10:11:36 PM UTC-7, bodk...@gmail.com wrote:
>Robert Mills used the principle of relativity and the MMX as a starting point

The combination of those two things is not sufficient to serve as a starting point,
because the Michelson experiment is merely evidence for the relativity principle,
which doesn't distinguish between Galilean and Lorentzian relativity. Remember,
Einstein cited failure of the ether drift experiments not in support of his light
speed principle, but merely in support of the relativity principle. He did not make
the mistake of confusing them. Hopefully Mills doesn't really make the mistake
that you attribute to him.

> The principle of relativity is assumed. The result of the MMX is taken as true.

That's garbled already... Michelson's result is one of the empirical bases
of the principle of relativity. If you stipulate the principle of relativity, then
Michelson's result is superfluous.

> A hypothesis of time dilation (or alternatively length contraction)

That makes no sense at all. If you are hypothesizing time dilation and/or
length contraction, then this is tantamount to hypothesizing the Lorentz
transformation, not deriving it.

> is shown to be consistent with those results

That doesn't make sense either, because (again) Michelson's result isn't
doing anything other than supporting the principle of relativity, so all you are
saying is that time dilation and length contraction (i.e., the Lorentz transformation)
are consistent with the principle of relativity. Of course they are, but so is
Galilean relativity, and we need some principle to select Lorentz invariance
over Galilean invariance. I hope Mills' book isn't as bad as you are
portraying it.

> It is not clear whether you are claiming that Mills’ presentation makes no
> sense, or that my representation of his approach must surely be wrong...

Neither one. I've said quite clearly (see above) that your representation of Mills'
presentation makes no sense, and I explained in detail why, as appropriate for
a discussion group on the subject of relativity. When crackpots like yourself
post nonsense, you have to expect to sometimes be told that you have posted
nonsense, and to have your misconceptions debunked, regardless of whether
the corrections are "of concern" to you.

Re: A Precise Statement of Time Dilation

<1prbrrt.1npkou81nw9w9nN%nospam@de-ster.demon.nl>

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https://www.novabbs.com/tech/article-flat.php?id=89597&group=sci.physics.relativity#89597

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From: nos...@de-ster.demon.nl (J. J. Lodder)
Newsgroups: sci.physics.relativity
Subject: Re: A Precise Statement of Time Dilation
Date: Mon, 2 May 2022 13:27:37 +0200
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Reply-To: jjlax32@xs4all.nl (J. J. Lodder)
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 by: J. J. Lodder - Mon, 2 May 2022 11:27 UTC

Ricardo Jimenez <rickyjim@earthlink.net> wrote:

> Assume the standard configuration where (t,x) are the coordinates in
> the rest frame. Thus the origin's world line is x=0 in the rest
> frame. There is also an inertial moving frame with coordinates
> (t',x'). It shares a common origin (event (0,0)) with the rest frame
> and it's origin's world line is x=vt, |v| < c, in the rest frame. Then
> for any event on the world line x=vt, the respective time coordinates
> have the relationship, t=gamma*t'.
>
> Does this statement have any non trivial generalizations? Is there an
> easy proof that doesn't appeal to adding a third dimension to make a
> light clock argument? TIA.

There is nothing to prove, it is an a-priori.
Space-time has local Lorentz invariance by postulate. (Einstein 1905)
This means that space and time must be measured in such a way
that local Lorentz invariance holds.
If you measure something else, that only means
that you have set up your measurements
in a way that is somehow wrong.

A forteriori, this doesn't hold just for length and time measurements,
it holds for all of physics.
Conversely, all of physics show that this is the right postulate.

We live in a universe like that, and you need to get used to it.
If you don't like it, invent not just another theory,
but another universe entirely,

Jan

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