Re: Scalar waves

On 05/04/2024 11:00 PM, Thomas Heger wrote:

Am Samstag000004, 04.05.2024 um 17:38 schrieb Ross Finlayson:
>

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.
>

>
A physical system has attributes.
>
These attributes can be measured.
>
The measure of this measurement has a dimension and a value.
>
>
The pyhsical system is space in this case.
>
In this space we have two points, which are somehow identifiable.
>
The distance is the length of a connecting streight line.
>
This length has the dimension 'length', which is quantified by
approriate units (meters in case of SI-units).
>
So the measure of that distance has a certain value (say 2) and certain
units (meters) and a certain dimension (length).
>
>
TH

Space has a metric and a norm, this of course makes for
all the application of triangle or Cauchy/Schwartz inequality,
which is used throughout the application of tensor products,
what results that the vectors after tensors,
are commensurable (measurable together).
Saying that distance-measurable and distance-measured,
or distance-measurable and distance-traveled,
have different implicit units yet same explicit units,
has that the units come and go in the derivation,
the "dimensionless" implicits and "dimensioned" explicits.
The sum-of-histories sum-of-potentials, is an idea that
all the notions of least-action and so on just result
that state is sum-of-histories, and the gradient is sum-of-potentials.
(This is the gradient that's the geodesy the world-lines.)
Many empirical settings start to require this extra book-keeping
of the derivations and their implicits, while that each formula
or step of the derivation the system of equations or system of
inequalities is readable in its "least" dimensioned units, the
derivation indicates also the "implicit" dimensioned units.
Then as with regards to which of those are negligeable,
is for all the higher orders of acceleration,
of which of those that all above are zero.
So, the singular and its branches
and non-linear and multi-pole,
and even the plain starting/stopping
and stop/walk and run/pause,
have this sort of fuller dimensional analysis,
about dimensional/dimensionless resonator/alternator,
that mathematically book-keeps the moments of the motion.
I've been studying this in my recent podcasts,
see "Moment and Motion" under "Philosophical Foreground",
recently about "vis-motrix" and "vis-viva",
and about Einstein's goal of understanding classical motion.
- https://www.youtube.com/@rossfinlayson
It's a field theory, it's a gauge theory, it has an "R" gauge,
"R" for "Real".