Re: I asked ChatGPT to prove that Hafele-Keating 1971 experiment was A HOAX.

On 04/30/2025 12:44 PM, gharnagel wrote:

On Wed, 30 Apr 2025 14:18:34 +0000, Ross Finlayson wrote:

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On 04/30/2025 06:41 AM, gharnagel wrote:

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I find the AI discourse rather shallow.  There were no mentions of
more recent experiments which support relativity not at all dependent
on muons:
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https://www.nist.gov/news-events/news/2010/09/nist-pair-aluminum-atomic-clocks-reveal-einsteins-relativity-personal-scale
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https://pmc.ncbi.nlm.nih.gov/articles/PMC5253894/
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"Relativity in the Global Positioning System"
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https://www.nature.com/articles/nature01997
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"A test of general relativity using radio links with the Cassini
spacecraft"
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On Wed, 30 Apr 2025 3:42:29 +0000, Ross Finlayson wrote:

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Gravitational singularities rather exist, even if as regards to
the "cosmic censorship" or "raw singularities", the wobbles as
they may be result an unboundedly large concentration even if
with a vanishingly small extent or duration.

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Singularities only appear in theories, not in reality.  Their
presence indicates that the theory has exceeded its domain of
applicability.

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Mathematics _owes_ physics better mathematics of infinities
and singularities, because infinitesimals and multiplicities
are in effect in dynamics of continuous change.

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There has been considerable interplay between mathematicians and
physicists.  Mathematicians invented complex analysis and Laplace
transforms. which are used by physicists and engineers.  The Euler
function had no practical use until physicists noticed that it
seemed to predict baryon masses, which then led to string theory
and brane theory.
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Singularity theories are just half-accounts of multiplicity theories.

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“as far as the laws of mathematics refer to reality, they are
not certain; and as far as they are certain, they do not refer
to reality” -- Albert Einstein
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When they asked Einstein "is the universe infinite" he said
something along the lines of "it isn't not".

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"Only two things are infinite, the universe and human stupidity,
and I'm not sure about the former."  -- Albert Einstein
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It's pretty well agreed we're looking at a field theory
and a gauge theory and over a continuous manifold,

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I'm not sure about that.  Those are mathematical models
of reality (see the first Einstein quote above).
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.....
So, the "domain of applicability" here is "a physics",

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Actually, it's a limit on a model.  If you want a larger
domain, get a new model.

Well, there are a lot of empirical models.
Consider something like, "visco elasticity". It's two
complementary, opposite things, modeled together.
How about "integral equations and their plane curves"
versus "differential equations and their solutions".
Now, the vast majority of the dynamical modeling industry,
that being analysis say, largely concerns itself with
systems of differential equations. Yet, integral equations
and differential equations have the singular solutions, as it
were, where they meet, then all kinds where they don't,
while it results from the inside and outside, they model
the same things.
When you say model, it refers to the setup or the ansaetze,
then in proof theory it also refers to the model theory,
as with regards to mathematical models of physical models,
and, structural and logical models of objects in relation,
mathematics' objects.
So, before even getting into mathematical models and physical
models, and the mathematical interpretation and the physical
interpretation, and what's "real" as it's in the physical
interpretation, there's all of mathematical model theory
to figure out, or at least as with regards to continuity,
and here, infinity.
Then, something like the path integral, built as via Jordan
measure, or, the complete metrizing ultrafilter, about the
Dirichlet problem, for these to even exist as models of
continuous domains, has that in the standard linear way
they don't, so of course that requires extra-ordinary set
theory if everything's going to result a set theory, and
that results extra-ordinary and ubiquitous ordinals,
about set theory and ordering theory, two different "theories
of mathematics' objects of one relation", where as well
part theory and something different as well, are "theories
of mathematics' objects of one relation".
Then, "descriptive set theory" as "model theory's models
of mathematics", sort of has its own baggage, and, results
in physics, built way, way above that, have ready derivations
of their contradictions together. So, without fixing that,
then, mathematics is a bit short delivering more and better
mathematics of continuity and infinity, to physics, which needs it.
Adding points does not make lines and dividing lines does
not make points, in the finitist, inductive account. "Claiming"
the completions of these things, instead of providing deductively
why they can complete, eventually runs out as un-complete.
Then, at least standard mathematics the 20'th century enterprise
is, "incomplete", so, something needs to get _under_ it instead
of _above_ it.
The other day I was reading some from Tullio Levi-Civita,
has a sort of thorough development called "absolute differential"
calculus, an interesting section on "the indefiniteness of ds^2",
which is all about the quadratic and later the triangle inequality
of Cauchy-Schwartz which about everywhere in physics is the law.
Yet, in things like "the cube wall", or the event horizon of
a gravitational singularity, it's two laws.
All one theory: it's a continuum mechanics.
The overwhelming consensus is there being a gauge theory
about a continuous manifold, ..., it's a continuum mechanics.
Then, equipping mathematics with more about better, or less
and fuller, mathematics of continuity and infinity, here
convergence and emergence, automatically equips the physical
models, which otherwise are such the, "severe abstraction",
that they've become, "too simple".
When asked if the universe was infinite, Einstein was like
"after all my successes, I'm working on a total field theory".
Dirac delta, Heaviside step, Fourier series for that matter,
examples where physics made mathematics that then mathematics
the enterprise had to justify for its own justification.
Dirichlet problem, Jordan measure, the measure problem:
open problems both ways.
QM and GR don't agree _120 orders of decimal magnitude_.
Neither has gravity, which would be a constant violation
of energy conservation in them, and the Arago spot
definitely makes that light is not corpuscular.
So, foundations and all.
The larger reasoning agents are pretty receptive to thorough reasoning.
There are a lot of empirical models: there's only one data.