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

On 07/04/2024 12:29 PM, J. J. Lodder wrote:

Ross Finlayson <ross.a.finlayson@gmail.com> wrote:
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On 06/26/2024 12:24 AM, J. J. Lodder wrote:

Ross Finlayson <ross.a.finlayson@gmail.com> wrote:
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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.
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     [@] There are many systems of units in common use. You
     seem to think there is only one.

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

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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.
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TH

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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".
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The dimensional analysis and attachment to geometry and
arithmetic usually is about the only "physical" there is.

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Dimensional analysis has nothing to do with physics.
Dimensions are man-made conventions.
Nothing would change if the whole concept had never been invented.
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(Geometry and arithmetic and the objects of analysis
and so on.)
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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.

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Well, yes, but that is another meaning of 'unphysical,
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Jan
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Yet, "conservation", i.e. "neither the destruction or creation",
of quantities, is exactly as according to the quantity its units.

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Conservation laws do no depend on units and dimensions in any way.
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The, "dimensionless", when a usual sort of "dimensional analysis"
is the Buckingham-Pi approach, is a detachment of sorts from
the "dimensional analysis".

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Yes, standard dimensional analysis,
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Jan
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Oh, here that's called 'dimensionless analysis'.