Re: Scalar waves

On 04/29/2024 11:10 PM, Thomas Heger wrote:

Am Dienstag000030, 30.04.2024 um 07:55 schrieb Thomas Heger:

Am Montag000029, 29.04.2024 um 15:28 schrieb Ross Finlayson:
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It's rather as there's a physical constant.
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It's 1.0. In natural units, it's infinity.
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Or, there's a physical constant.
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It's infinity. In natural units, it's 1.0.

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I don't like this 'c=1 thing', because 1 is a natural number, while
speed/velocity have physical dimensions with v = dx/dt.
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Because time and distance are not measured with the same units, c had
to have units.
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Now 1 has no units whatsoever (because it is just a number) you cannot
say, that c is one.
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Actually meant were:
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lightyears and years.
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And c = 1 lightyear/year
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This is (trivially) true, but has units.
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TH
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The reason to require a unit for c:
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EVERY physical quantity is composed from a numerical value and a unit!
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In case you would like to use something called 'natural unit(-s)' as
unit, this would be perfectly ok, but only if - say - 'nu' is properly
defined.
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If you like to define 'nu' you would end up in a dilemma, because c is
assumed to be 1 one these natural units.
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That would be a definititon, which is based on itself (what is not
allowed).
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Such a 'circular' definition is something, which is referring to itself.
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Such definitions violate important principles of logic.
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TH
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The dimensional analysis of course is the attachment of a mathematical
model to a physical model at all, then with regards to usual
"dimensions" being quantitative and geometrical.
The dimensionless really does have any number of "balanced implicits"
in it. Any sort of "1 unit/unit" is a thing, and as well in the
quantities, "1 goes-to-1-from-the-left/goes-to-1-from-the-right",
sort of arrives at the same thing.
Here in this podcast, is mentioned
first, Dirac delta, "the only non-standard function",
second, in singular integrals where 1 <= p <= infinity, inclusive,
then getting into geometric equations, Scheveningen, Zygmund,
Einstein, and the scalar.
https://www.youtube.com/watch?v=IkRqd6Zohe0&list=PLb7rLSBiE7F4eHy5vT61UYFR7_BIhwcOY&index=22&t=2440s
It gets right into talking about relativity theory
since Scheveningen.
https://inspirehep.net/conferences/966266
Lately I've been introducing notions for mechanics of motion
"dimensionless resonator" and "dimensionless alternator",
extensions to mathematics for explaining classical mechanics
and for providing Einstein his request "zero-eth law(s) of
motion" as from a passage in "Out of My Later Years" where
Einstein introduces his "Einstein's bridge" concept.
These are the kinds of definitions that mathematics
needs to provide physics a resolution between
vis-motrix and vis-viva.