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

On 07/05/2024 12:00 PM, J. J. Lodder wrote:

Ross Finlayson <ross.a.finlayson@gmail.com> wrote:
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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'.

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That's either an error or a silly neologism,
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Jan
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It's kind of like Higgs field.
"Hey, have you heard of Higgs' field?"
"Yeah, I suppose."
"You know, it's not a field."
"....  What's that supposed to mean?"
"It's not a field according to the usual definition
in physics of what a field is, it's just an interface."
"Whuh - why don't they call it that?"
"You know there's a Higgs classical field?"
"Well now I'm wondering."
"It's a field, in physics."
"Oh, well, so, there is a Higgs field?"
"No, it's just the usual field."
Quantities, and their derivations, have implicit units,
about them.
Any changes, model infinite formations of expressions,
in algebraic terms, canceling variously to 1 above and
below the divisor and 0 left and right the equals sign,
that each little formula looks like quantities, yet is
just a term in an infinite expressions of terms,
with no beginning and no end.
Then, classically of course it's considered classical
and a constant, more than less, yet the "quantities"
are all their derivations all their terms.
So, "implicits", and that's their name, "implicits",
or for reformulation or parameterization or extensionality
resulting whatever isn't a closed form resulting a term,
or for whatever aren't trivial result terms, make for
a real solid reflection that "the theory" is a
sum-of-histories sum-of-potentials, the potential fields
are real, the classical field is really itself a potential
field again, and, there are approaches to dimensional
analysis of the usual sort, project into greater dimensions
to affect to reflect where the terms come from, then for
example little algebraizations like Buckingham-Pi "dimensionless".