Survey for sci.physics.foundations: infinities and infinitesimals in models of physics

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Ross A. Finlayson

Nov 4, 2015, 12:40:03 PM11/4/15

We know of values in physics that besides the
running constants of physics (that work up to
finite bounds 1/oo and 1/0) there yet remain
vanishing or unbounded quantities (eg, Einstein's
cosmological constant and Planck's little c as vanishing/
infinitesimal and Planck's big C as unbounded/infinite).

There is normalization which is in a sense re-un-de-
normalization (normalization is an operation following
de-normalization), rather, unintuitively in the nomenclature.

So I'm wondering what physicists here would make note
and use of a system that provides a mathematical foundation
for "real" or "concrete" (say, for scalar and gauge) infinitesimals
and infinities as values in our formula. This is where, without
changing the formula, augmenting the underlying mathematical
model would automatically equip these equations with features
in effect as would follow, for example, "discretization" of what
is otherwise usually a model of the vector fields that are the
mathematical, physical objects.

I wonder this as I've found some features in effect of discretization
that give a factor of two for a line configuration or 3/4/5 for a planar
configuration, and would be looking for experiments and data as
would correlate more neatly with having these factors to so cancel
otherwise from their cluttered notation.

This is my research direction: for novel mathematical features to
so equip extant physical models, for the resulting features in effect
in mathematical physics to highlight hypothetical corrections in
the interpretation of configuration of experiment.

So, and I'll thank you, it would be of interest that interested
physicists here might note such examples as may otherwise
be explained these days, of configurations demanding integer
factors of what is otherwise about the continuous and discrete, or the
measurement/observer effect(s) as about "numbering" for

Also I'd be interested in direct or apocryphal results as of the
path integral of the travel of particles, with regards to usual
terms in the fitting models seeing various integer factors
introduced in various configurations and energies of

There are also a variety of central and fundamental simple
features of statistics in probability that may be so founded.

Good day, Ross Finlayson, B.S. Mathematics, USA

Nov 5, 2015, 12:50:06 PM11/5/15
Op woensdag 4 november 2015 18:40:03 UTC+1 schreef Ross A. Finlayson:
Dear Ross,
May be you can find some interesting views in the paper "On the Origins of Physical Fields", ,which goes deep into the foundations of how reality might use number systems and differential calculus.

Ross A. Finlayson

Nov 6, 2015, 2:40:02 AM11/6/15
Beginning to read.
Quotes follow from your paper.

Looking to follow "The type of the point- like object
corresponds to the type of the controlling mechanism. "

Most of this development is initially familiar as Cartesian
and Cartanian (Cartanian as super-Cartesian).

"The difference originates from the artifacts that cause the
discontinuities of the fields. " ... "Since the elementary point-
like objects reside inside their individual symmetry center, the
embedding continuum will also be affected by what happens to
the symmetry centers."

These seem significant touchstones of the development.

"Apart from the way that they are affected by point-like artifacts
that disrupt the continuity of the field, both fields obey, under not
too violent conditions and over not too large ranges, the same
differential calculus. However, especially field 𝔄 is known to show
wave behavior that cannot properly be described by quaternionic
differential calculus. For that reason we will also investigate what
a change of parameter space brings for the defining functions of
the basic fields 𝔄 and ℭ ."

Section 10 "Regeneration and detection" seems particularly relevant
to effects of discretization, eg as of measurement/observer effects
and as so correlating otherwise with systematic effect.

"A virtual map images the completely regeneration set {𝑎𝑖𝑥} onto
parameter space ℛ⓪. This involves the reordering from the stochastic
generation order to the ordering of this new parameter space. This first
map turns the location swarm into the eigenspace of a virtual operator 𝒷.
A continuous location density distribution 𝜉(𝑞) describes the virtual map
of the swarm into parameter space ℜ⓪. Actually each element of the
original swarm is embedded into the deformable embedding continuum
ℭ where that element is blurred with the Green’s function of this embedding
continuum. This indirectly converts the operator ℴ, which describes the
regeneration in the symmetry center 𝕾𝑥 into a differently ordered operator
𝜉 that resides in the Gelfand triple ℋ. The defining function 𝜉(𝑞) of operator
𝜉 describes the triggers in the non- homogeneous quaternionic second order
partial differential equation, which describes the embedding behavior of ℭ. "

Section 11 "Photons" describes some features of _configuration of experiment_,
vis-a-vis usual running constants as of _energy of experiment_.

"In his paper “On the Origin of Inertia”, Denis Sciama used the idea of Mach in
order to construct the rather flat field that results from uniformly distributed
charges [10]. He then uses the constructed field in order to generate the vector
potential, which is experienced by the uniformly moving observer. Here we use
the embedding field as the rather flat background field. "

>From S.13 "Conclusion": "This indicates that elementary particles inherit these
properties from the space in which they reside" in "distinguish[ing] between
Cartesian ordering and spherical ordering [and] reveal[ing] that these ordered
versions of the number systems exist in several distinct symmetry flavors."

Thank you, thank you very much, I think that's relevant and have some foundational
support from mathematics to directly declare some of these features as then may be
useful for you.

You might indicate some examples of where your design is better than others, or
where it is particular in the modelling of otherwise noisy data.

Hans Van Leunen

Apr 5, 2016, 1:20:02 PM4/5/16
Op woensdag 4 november 2015 18:40:03 UTC+1 schreef Ross A. Finlayson:
The considered paper is a report of an ongoing research project. The author (me) will regularly update the papers and when the number of revisions becomes rather high, then a new paper is written with a new title. The current paper is called "The Hilbert Book Test Model" ;
I mostly write these papers in order to order my ideas and in order to support discussions.

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