Re: The failure of the unified field theory means general relativity fails.

On 06/24/2024 11:49 PM, Thomas Heger wrote:

Am Dienstag000025, 25.06.2024 um 05:57 schrieb Tom Roberts:
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Nope. YOU have imposed specific units onto the formula/equation. The
equation itself does not impose any particular units on its variables
and constants [@], it merely requires that they be self-consistent.
>
   [@] There are many systems of units in common use. You
   seem to think there is only one.

>
A forteriori, any result that depends on any particular choice
of units (or dimensions) is unphysical.

>
Yes, of course. Good point. Similarly, any result that depends on
choice of coordinates is unphysical.
>

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Not quite...
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Because velocity is 'relative' (relative in respect to what you regard
as 'stationary'), kinetic energy is frame dependent.
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Since the used coordinate system defines 'stationary', you need a
coordinate system for kinetic energy and that for practically everything
else.
>
TH

When I hear "unphysical" I think it means "in the mathematical
representation and having no attachment to the physical representation,
in the system of units of the dimensional analysis in the
geometric setting".
The dimensional analysis and attachment to geometry and
arithmetic usually is about the only "physical" there is.
(Geometry and arithmetic and the objects of analysis
and so on.)
Things like "negative time" and "anti-deSitter space" are
unphysical, as are the non-real parts of complex analysis,
usually, though for example if you consider the Cartanian
as essentially different from the Gaussian-Eulerian,
complex analysis, then the Majorana spinor makes an
example of a detectable observable, though, one might
aver that that's its real part, in the hypercomplex.
The Gaussian-Eulerian deserves a real break-down of
a deconstructive account about Euler's identity and
Gauss' integral and so on, about the regular singular
points of the hyper-geometric and so on (0, 1, infinity).
That wave mechanics have super-classical real parts
is a thing.
If it's a geodesy, it's a geometry. The "coordinate-free"
are just "hidden coordinates", patched together piece-wise.