Re: Scalar waves

On 05/11/2024 06:59 AM, Ross Finlayson wrote:

On 05/10/2024 11:12 PM, Thomas Heger wrote:

Am Mittwoch000008, 08.05.2024 um 10:20 schrieb Tamerlane Oldfart Lefévre:

Thomas Heger wrote:
>

"entire wire"?? you must be kidding, this usenet user doesn't know
what
a current is in physics. But that's also related to time, said above,
and you cannot "ignore" anything, once directly not related, but
connected. Just as a translation of pig from engilsh to swine in
gearmon. It's the same pig,
you eat alot. How many pigs did you eat along your journey?

>
Well, actually I mean: the Ampere addresses the current in a conductor,
which is usually a wire.
There Ampere does not say, whether the wire is thick or thin, or
whether
or not the current distributes evenly within the wire.
If you have a wire with a current of 1 A, you don't mean the
distribution of the current within the conductor, but the sum of all
small partial currents within that wire.

>
me frendo, that's irrelevant for the problem in case, at any point at
any
time you measure the same current along a wire. That you think that more
Coulombs go through a wire "where is thinner", this is false. But that's
not the point. As I remember Q=It, which is charge equals the current
times
time. I related to space, t related to time.
>

I actaually wrote, that the thickness of a wire is irrelevant for the
measure 'current strength'.
>
If you like to include the diameter of the wire, you get a different
measure, which is called 'current density'.
>
Both measures are -btw- not always constant in time.
>
...
>
TH
>

>
It's true that "bulk" or "current", Ampere physics,
and "test particle", or electron physics,
are two different things, that attain to the same thing.
>
It's like mathematics and "make a line from points" or
"break a line into points", either way results an
infinite comprehension.
>
The Democritan or atomic theory, of course is great,
it's fantastic, and results in the classical, the
entire notion of the stoichiometric in ratio, of the
effectively unboundedly-small what to it is the
effectively unboundedly-large, about infinities.
>
It's like, if you look at the definition of "hysteresis"
these days on the Wiki, it's among examples of terms
that are collected all such manners of differences between
the fundamental and the empirical, the "anomalies",
what are going into the non-standard analysis in mathematics,
of probabilities as mostly in use to reflect statistical ensembles,
and the quasi-invariant measure theory for continuum mechanics,
that it's getting back into the foundations of mathematics,
the continuum mechanics, how to arrive at the quasi-invariant,
for the pseudo-differential, what adds back up,
"classical in the limit".
>
https://en.wikipedia.org/wiki/Hysteresis
>
Current, is an integration, of cross-sections, of a path.
It's a contour integral of a path. (And needn't necessarily
include complex analysis or the Eulerian-Gaussian at all.)
>
https://en.wikipedia.org/wiki/Contour_integration
>
There's much to be studied in a heat equation,
and the theory of heat equations, or Fourier-style.
>
https://en.wikipedia.org/wiki/Heat_equation
>
Then, usual notions like "Lienard-Wiechert and
the test-particle", are the usual fundamental
derivation these days.
>
https://en.wikipedia.org/wiki/Li%C3%A9nard%E2%80%93Wiechert_potential
>
Then, Einstein gets into things like "Einstein's bridge"
and "Einstein's final formalism", and these days there's
a lot of "well Gauss is biased so let's just log-normal",
then about things like Maugin and the monomode process,
for things like Fritz London and superclassical models.
>
https://en.wikipedia.org/wiki/Law_of_the_wall
>
>

Dimensional analysis is not to be confused with a usual sort
of "dimensionless analysis" which follows a sort of echelon
reduction about the Pi-theorem of Buckingham et alia,
which I've been reading about from the Wiki and for example
"Symmetry and Integration Methods for Differential Equations".
Dimensional analysis is the development quantitatively and
in units of the physical model at all, and the corresponding
attachment to the mathematical model, in terms of the
coordinate setting, and its what are "dimensions", in units,
in units of measure, in its space(s), about its metric and norm(s),
the ansaetze or setup.
Natural units, are synthetic, vis-a-vis the mathematical units,
which combine being arithmetical, algebraic, and, geometric,
in the arithmetization, algebraization, and geometrization,
which usually enough coincide, yet according to a deconstructive
account, result each other in the (continuum) limit.
So, "a dimensional analysis after the style of Buckingham Pi-theorem",
a "dimensionless" or "reduced dimension" setup, is just part of
methods, sitting atop the usual methods of the linear algebra,
as part of usual approaches to rank reduction, as part of usual
approaches to reducing the problem space, in the usual approaches
to resulting the linearly independent, and establishing the fixed
and free degrees.
The dimensions of the mathematical model, aren't so necessarily
linear, and neither are the dimensions of the physical model,
about what are "running constants" and about things like
"the highly non-linear of the asymptotic" yet much more simply
about "the infinitely-many higher orders of acceleration in
moments of motion", or simply "the rotational".
Then methods like symmetries are introduced to help peel the onion.