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NNTP-Posting-Date: Sun, 30 Jun 2024 03:59:17 +0000
Subject: Re: REASONS RELATIVISTS GIVE FOR DOUBLED DEFLECTION OF NEWTON'S:
Newsgroups: sci.physics.relativity
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From: Ross Finlayson <ross.a.finlayson@gmail.com>
Date: Sat, 29 Jun 2024 20:59:19 -0700
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On 06/29/2024 08:36 PM, LaurenceClarkCrossen wrote:
> Doubling Newtonan affect of gravity for light violates Galileo's finding
> that all masses are affected the same and Eotvos finding that all
> materials are affected the same. This has never been justified by
> relativity and cannot be. It is extremely ad hoc.

You figure mathematics must explain it somehow.

Vitali was a geometer when analytic geometry was the thing
and algebraic geometry was becoming the thing in the days of
the rigorous formalization of real analysis and when measure
theory was becoming a thing. So, what he showed, was, you
take the unit interval, and split it up into infinitesimals,
and re-composing those, it results having a length between
1 and 3, or 2, instead of 1.

So, that was made the first example of "non-measurable sets",
yet, also it's the first sort of example of "doubling space".

The "doubling space" and "doubling measure" is most popularized
as the Banach-Tarski equi-decomposability of a ball into two,
yet really it's Vitali and Hausdorff who did that first in
geometry, then later the algebraists approached it from the
side of words of algebra instead of the side of points of
geometry.

So, these days that's much involved in "invariant" theory,
which is about symmetries and conservation and Noether's theorem,
about invariants. So, these "doubling measures" for doubling
spaces are a thing in measure theory, "quasi-invariant", measure
theory.

Now, what this is is a very relevant and salient fact about
discretization and quantization, and about why for root-mean
and these kinds of things, are introduced the term "1/2",
about the doubling space and halving space, and doubling
measure and halving measure, as a simpler sort of fact from
mathematics, about the nature of discretizing the continuous
and vice-versa, why it's so.

Thus, "re-Vitali-izing measure theory" is the thing.

These days it's talked about as "the measure problem",
because standard measure theory arrives at wanting to
talk about things yet it's "measure zero", then what
results is a lot of Hausdorff-style buildouts the
other way arriving at an "almost everywhere", then
forgetting that in the derivation, instead of resolving
it as some "re-Vitali-izing" measure theory.



Then there's also Fresnel and "large lensing".