Re: Scalar waves

On 05/05/2024 02:18 PM, J. J. Lodder wrote:

Ross Finlayson <ross.a.finlayson@gmail.com> wrote:
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On 05/02/2024 11:56 PM, Thomas Heger wrote:

Am Mittwoch000001, 01.05.2024 um 09:46 schrieb J. J. Lodder:

Thomas Heger <ttt_heg@web.de> wrote:
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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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You really need to work on your misunderstandings about units and
dimensions.
In particular, physical quantities do not -have- a dimension.
Conversely dimension is not a property of physical quantity.
You cannot measure a dimension.

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Sure, you measure physical quantities.
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Lets say: you measure a current in Amperes.
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Then the measurement of - say- 100 mA means, that a certain electrical
current has a current strength of 100 mA.
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Now 'current strength' is the quantity which is measured. This current
strength is then the dimension of the measurement and the value depends
on the used units, which are Ampere in this case.
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Now all measured quantities need some kind of dimension and unit, if
they should make sense in physics.
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Even pure numbers have a dimension this way.
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E.g. if you count eggs, the result would be a number. But the number
alone would not make sense, since 'number of eggs' can also be a dimension.
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Dimensions are human constructs that can be assigned arbitrarily,
limited only by the need to be consistent about it.

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'Human contruct' is ok, while to 'arbitrary' I would not agree.
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E.g. if you measure a distance, than the measure has the dimension
'length', even if you don't use the meter as unit, but angström,
light-years or fourlongs instead.
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...
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TH

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In mathematical logic, often there's something like a quantifier,
that there are explicit quantifiers, and implicit quantifiers.
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So, sort of like dimensional analysis, is a quantifier analysis,
representing fixed or free parameters, and the implicitly
infinitely-many quantifiers, in front of a given classical
quantifier.
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The quantities, are results of derivations, to represent measurables,
or the "real" and "virtual" quantities that result real quantities
that are measurables.
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So, quantities are often results of infinite expressions and
thusly completions of infinite limits or continuum limits.
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The dimensional analysis and what results the dimensionless,
gets into degrees of freedom as independent parameters, then
also gets into the implicits. The quantities are not purely
algebraic, yet ensconced in their derivations.
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Consider the length of a body vis-a-vis the distance it
travels: both in units of length, yet distance as only
after a derivation of all the higher orders of acceleration
and deceleration whether it results a distance at rest, or,
a distance marking motion, that the other factors of the
dimensional analysis, go along with it, though algebraically,
at each point dimensionless.

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Right. A system of dimensions is just a consistent mapping
of a system of equations into a finite-dimensional algebra,
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Jan
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It's more the point that classical mechanics has a richer
system of implicitly involved dimensions with regards to
the derivations of the equations or formulas of systems
of moving bodies and the dynamics of change, in the
orbifold of the orbits of the geodesy of moving bodies
their world-lines and trajectories, that length and
distance and metric and norm have separate derivational
attributes as systemic.
"Algebras", as generically "magmas", have that just like
anything else in the non-linear or singular, that there
are sometimes systems of equations in algebras,
and sometimes completions of limits of systems of inequalities,
what represent dimensional passage, in the implicits,
what result the simplified results, the classical linear impulse,
vis-a-vis the entire sum-of-histories and sum-of-potentials,
all the higher order moments in effect.
Or: force is a function of time.
So, metric and norm, for length and distance,
aren't the same thing.