Re: I dare to relativists to explain local time: t-vx/c²

On Thu, 3 Oct 2024 2:19:13 +0000, Ross Finlayson wrote:
<snip my OP, for clarity>

I think it gets involved as even things like
the difference between numbering and counting,
or for example, what result dimensionless quantities,
and in the linear are simple not dimensioned quantities,
yet in the angular result dimensioned then dimensionless,
and so on, about quantities and derivations, what reflect
that the very laws of motion, those being rest/rest
motion/motion equal/opposite then f=ma then gravity tossed in,
are underdefined, and such notions as "infinitely-many higher
orders of acceleration", clearly and obviously and according
to all the usual consideration of who-moves-who what _must_
be non-zero, yet _must_ be vanishing, has that then
there's that mechanics is under-defined.
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Dis-placement and di-stance are two different things.
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Numbering and counting are two different things.
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So, then local time as just counting ticks or beats
of the clock, has whatever clock is closest is "local".
Yet, in physics there are theories where every point
in space-time has one, so, then getting into the
perceived receipt of continuous information, has
that time is _always_ an extended quantity.
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Then, relativity, after absolutism, is just fine,
Einstein has a particularly relativity of motion
as that's what he figures changes the most, that
in the _severe abstraction_ of theory and the
_mechanical reduction_ of theory that relativity
itself the idea is quite most usual as "this is
the place I've chosen to stand and try this lever",
where "the place" is an ideal and "to stand" means
to let out what would otherwise be ideals in all
the absolute, helps explain that there are wider
ideals like a clock-hypothesis, and while it took
a while and some still haven't heard, Einstein at
least himself already arrived at "SR is local"
with respect to "SR is spacial, not spatial, and
the L-principle", and with regards to Einstein's
bridge and Einstein's second-most famous mass-energy
formula, why at least Einstein left "the brief theory
Einstein's relativity theory, a relativity theory
in a theory of absolutes", sort of simply.
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Here your usual notion of "proper time" is almost
entirely acoustic, pretty much Doppler. I.e.,
that's right after the Galilean and perspective
and parallax, it's pretty much just parallax,
then for something like a "peripheral parallax",
as with regards to the optical, light in the angular.

I'm sorry, but you didn't explain anything. It's mostly gobbledygook.
Here is the sequence of how such ARTIFACT appeared with the years.
***********************************************
LOCAL TIME FOR LORENTZ, INTRODUCED IN 1901
t' = t - vx/c² ;  This is Voigt's Local Time, from 1897.
No explanations given by Voigt, Lorentz or Einstein about the
MATHEMATICAL ARTIFACT vx/c².  This the equivalent of NOISE in
mathematics, an undesired effect.
t' = t - vx/c² ;  This is Lorentz Local Time, from 1901, presented to
Poincaré.
..............
β² = c²/(c² - v²)  ; Lorentz Eq. 3 (plagiarized from 1897 Voigt), and
inserted without explanations on his 1904 paper.
Lorentz, since formulae 4 and 5 on his 1904 paper.
1904 ORIGINAL LORENTZ TRANSFORMS
x' = β x  ;  Lorentz Eq. 4
t' = t/β - β vx/c² ;  Lorentz Eq. 5
1905 MODIFIED LORENTZ TRANSFORMS
In 1905, Einstein introduced (TRICK, out of the blue)  x = X - vt, in
order to get rid of ether.
t' = β (t/β² - vx/c²)
t' = β/c² (t (c² - v²) - vx)
t' = β/c² (t (c² - v²) - vX + v² t) = β/c² (tc² - tv² - vX + v² t)
t' = β (t - vX/c²)
1905 EINSTEIN'S MODIFIED LORENTZ TRANSFORMS
t' = β (t - vX/c²)
x' = β (X - vt)
You may recognize the later formulae as the "modern" Lorentz transforms.
In order to understand how the ARTIFACT vx/c² appeared on this history,
you HAVE TO READ the original 1897 Voigt's paper. I put a link on the
OP.
You'll be disappointed to learn that the linear transformations that
Voigt proposed at the beginning of his paper produces, after his
manipulations, the appearance of such ARTIFACT in the expression of t'.
Voigt didn't provide any justification for it. Actually, he wrote that
he was "enchanted" with the beauty of the transforms.
NO EXPLANATIONS ABOUT WHAT LOCAL TIME t' = t - vx/c² EXISTS AS OF TODAY.
ACTUALLY, THERE ARE MANY ATTEMPTS WRITTEN IN THE LAST CENTURY, MANY
INVOKING A ROLE OF MINKOWSKI'S SPACETIME, AND OTHERS MERELY
PHILOSOPHICAL OR METAPHYSICAL.
But, as it's a BYPRODUCT of SR, its presence (most of the time dismissed
in calculations) remain UNQUESTIONED. Because IF SUCH TERM DO NOT EXIST,
THEN THE ENTIRE MATHEMATICAL STRUCTURE OF SR COLLAPSES.
To understand my above assertion, you have to read carefully the
mathematical derivation performed by Einstein in 1905, and you'll
CONFIRM that the appearance of such a term is IMPOSSIBLE TO AVOID, even
when it means NOTHING.
Read here what Lorentz considered for "local time" use, which was
(somehow) validated by Poincaré, who was his mathematical "tutor" for
many years, which Lorentz acknowledged in writing.
https://en.wikipedia.org/wiki/Lorentz_ether_theory