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Subject: Re: Steel Man of Einstein & Relativity.
Newsgroups: sci.physics.relativity
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From: Ross Finlayson <ross.a.finlayson@gmail.com>
Date: Sat, 14 Sep 2024 11:59:43 -0700
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On 09/14/2024 09:20 AM, Ross Finlayson wrote:
> On 09/13/2024 08:58 PM, Volney wrote:
>> On 9/13/2024 2:00 AM, rhertz wrote:
>>
>>> α = 8π² a³/[c² T²]  = 2 GM/c² (curiously, it's the Schwarzschild radius
>>> for the Sun).
>>
>> Not "curiously", the GR formula for deflection depends on the
>> Schwarzschild radius. Look what happens when you calculate deflection of
>> light grazing a Schwarzschild radius object.
>>>
>>> The only possible explanation is that he commited FRAUD, in order to
>>> obtain the 43"/cy.
>>>
>>> Finally, I'm shure that his ADVISOR Schwarzschild had a cut in the 1915
>>> paper that he presented to the Prussian Academy of Science. Even when he
>>> was serving as a Lieutenant on the Eastern Front (WWI),  Schwarzschild
>>> made sure to be present on that day (Nov. 18, 1915). After all, he was
>>> not at the vanguard of the eastern front.
>>>
>>> Just ONE MONTH AFTER THIS PRESENTATION, Schwarzschild came out with his
>>> analytical solution that formally introduced what is known today as the
>>> Schwarzschild´s radius formula.
>>>
>>> TOO MANY COINCIDENCES AND TOO MUCH ROTTEN FISH AROUND GR INTRODUCTION IN
>>> SOCIETY.
>>
>> Nobody cares about your obvious paranoia created delusions.
>
> Here that's considered with respect to the "cube wall", as with
> regards to systems of coordinates, what there is of the tensorial
> preserving the affine for otherwise the "not-coordinate-free",
> and under torsions, then as with regards to the Kerr, Kruzkeles (sp.),
> and turtle coordinates, with regards to Schw. and Chandrasekhar.
>
> Einstein's work on the centrally symmetrical and his
> "second most-famous mass-energy equivalency relation
> that nobody's ever heard of", also enter the picture
> as with regards to the laws of motion and classical,
> and the sum-of-histories sum-of-potentials as what's
> considered "real", for realists, today.
>
> Then, as with regards to doubling-spaces and doubling-measures,
> and halving-spaces and halving-measures, gets involved with
> the continuum mathematically, as with regards to the
> individuation of parts, or points, a.k.a. quantization,
> with regards to models of flow and the fluid, and flux
> and the super-fluid.
>
> So, when doubling or halving really very is according to
> ponderance of derivation, capricious, to make it fit,
> then gets into these days what's called quasi-invariance
> and the quasi-invariant in the measure theory, as with
> regards to the measure problem, and why mathematics has
> required a "re-Vitali-ization", of the measurable really
> of Vitali's example, and why Vitali and Hausdorff are at
> least as good geometers as Banach and Tarski algebraists,
> that mathematics _owes_ physics more about why this is so,
> and as with regards to the usual notions of stress and
> strain tensors, about Green and Euler and Cauchy and Dirac,
> and Piola-Kirchhoff, with regards to Birkhoff and the lacunary
> and the Ramsey theory, why there are more than the standard
> laws of large numbers, for it to result that and when the
> doubling and halving are _not_ capricious, conscientiously.
>
> It's like, "Einstein, what coordinates maintain continuity
> among and between these systems of coordinates", and it's
> like, "whatever works, one of the major aspects of my later
> researches into the total field theory of the differential-system
> of the inertial-system that's real gets involved the centrally
> symmetric with regards to the un-linear", while physics yet
> doesn't even have a model of "the infinitely-many higher orders
> of acceleration, nominally non-zero yet vanishing", then it's
> like, "you know, the cosmological constant is about that".
>
> ... Which of course is available to reason. Poincare and Dirichlet
> are pretty great, and, one of Hilbert's greater ideas is that
> "you know, geometry needs a postulate of continuity or one made".
>
>


The Vitali's construction is about the most usual example
of a doubling-space, where a unit interval is infinitely
divided and results when re-composed as for equi-decomposability
that it results an interval of length L 1 < L < 3, or here L = 2,
as with regards to the "one-sidedness" of points _in_ a line,
and "two-sidedness" of points _on_ a line, as with regards
then thirdly to the signal-analysis of points _about_ a line.

So, Vitali's example was in the early days of point-set topology,
with the idea that for the standard formalism of real analysis,
that "least-upper-bound" a.k.a. Dedekind completeness is
axiomatized, stipulated so that the ordered field the rationals
fulfills being the complete ordered field the field-reals or "R"
usually in the standard formalism, that Vitali's result made
a mumbling consternation in the algebraists, who resulted
introducing "non-measurability" of sets of points the point-sets,
as what results the day's "measure problem", that these days
is because the Planckian eventually results "either no straight
lines or no right angles", i.e., no metric, no norm.

So, then another quite amazing example is the very simple
case mathematically:

f(n) = n/d, natural n, natural d, 0 <= n <= d, d -> \infty

where it results that this looks like an equi-partitioning
of the unit interval and as a function is constant monotone
strictly increasing. (In the limit, the infinite limit,
the continuum limit.)


What's great is that it's both a discrete function though
modeled in the continuum limit, and, it's integrable, and,
it has a definite integral over the entire domain, and,
it's not 1/2, instead 1.

So, these are features of numbers that make for after
everybody's first non-standard function with real
analytical character, Dirac delta, that way before that,
is this sort of "Natural/Unit Equivalency Function",
which meets most people's exact intuition, of the
continuous infinitely-divided to the discrete,
and, vice-versa, then with a bunch of uniqueness
and distinctness results, in the seat of real analysis.


So, "re-Vitali-ization of measure theory", is making a
place for this as it's natural and fundamental,
and pivotal, and crucial, and all.