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On 11/03/2024 11:53 PM, Thomas Heger wrote:DesArgues <-> DesCartesAm Sonntag000003, 03.11.2024 um 18:28 schrieb Ross Finlayson:>On 11/02/2024 11:19 PM, Thomas Heger wrote:I like a certain mathematical principle called 'geometric algebra' andAm Samstag000002, 02.11.2024 um 01:39 schrieb Ross Finlayson:>On 11/01/2024 11:13 AM, rhertz wrote:>A definition of mass, as found in Google:>
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"Mass is a measurement of the amount of matter or substance in an
object.
It's the total amount of protons, neutrons, and electrons in an
object."
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It's "accepted" since the 60s that protons and neutrons are not
elementary particles anymore. As stated in the Standard Model of
Elementary Particles, protons and neutrons are composed of quarks,
with
different flavors.
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https://www.quantumdiaries.org/wp-content/uploads/2014/03/2000px-
Standard_Model_of_Elementary_Particles.svg_.jpg
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But electrons are thought as elementary particles, so they can't be
formed by a collection of other elementary particles. Even quarks are
currently thought as working together with elementary gluons (QCD,
Gauge
Bossons).
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So, what is THE MATTER that electrons contain?
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This is one of many FAILS of the current SMEP.
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Is that the electron's mass is composed of unknown matter? Maybe of
electromagnetic nature?
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After all, modern civilization is based on what electrons can do,
isn't
it?
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THEY KNOW NOTHING, AS IN RELATIVISM!.
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You got there a deconstructive, elementary account, into
what's called the trans-Planckian regime, from what's
called the Democritan regime, where Democritus or
Demokrites is who championed "atomism" the theory
while Aristotle or Aristoteles while outlining either
the "infinitely-divisible" or "infinitely-divided",
picked "not atomism because no vacuums", as with regards
to that electrons, protons, neutrons are elementary matter
while photon is still the usual particle in terms of
the quanta of energy, as to how energy is quantized,
at the atomic scale, or as with regards to Avogadro.
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For some people, charge is primary, others, matter.
I assume a certain mechanism, which belongs to a self-developed concept
called 'structured spacetime'.
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(
https://docs.google.com/presentation/
d/1Ur3_giuk2l439fxUa8QHX4wTDxBEaM6lOlgVUa0cFU4/edit?usp=sharing
)
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In this the electron is not a particle, but denotes a hypothetical
'creation operator', which does not really exists, but if it would, it
would create a certain structure (in spacetime).
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As example I take waves on the surface of a pond.
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E.g. I could assume a little demon, that pull up the water surface and
wanders around over the pond.
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In the microscopic realm of elementry particles we have, of course, no
pond and no demon.
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But we could assume a thing would exist, if we see certain paterns
repeatedly.
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Those we give the name 'particle' (or 'quantum object' if you prefer
that).
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But such 'particles' violate simple requirements for material objects,
like being at some position at a certain time and existing continously.
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They would also violate several other principles and observations.
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For instance the particle concept violates 'Growing Earth', so called
pair production, the big bang theory and 'transmutation'.
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Best would be, to abandon real lasting particles altogether and replace
them by something else.
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This 'something else' could be 'timelike stable patterns'.
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The relation is not at all obvious and you certainly have not heard
about this before.
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But think about a standing 'rotation wave'.
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This is somehow similar to the path of a yo-yo.
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Then we could call the outer edge of this path 'potential' and the
inner
turning point 'mass'.
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The outer edge had in this scheme a geometric relation and is somehow
'attracted' by the inner turning point, which has mass instead of
rotational velocity.
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TH
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...
Aristotle has an idea like "un-moved mover", so it's generally
figured that "physics is an open system", while any sort of
usual classical ansaetze/gendanke, the setup/problem, is
defined as either the initiation of an action, "closed",
that there are no closed systems in physics as the entire
system of physics is an open system.
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So, you can usually ascribe in systems of physics, the
idea of mechanical advantage after "information advantage",
that an arbitrarily small reasoning can result an arbitrarily
large mechanical change, as with regards to systems in
physics being open to actors, according to information.
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Then, the linear and rotational is a very excellent example
of this, with regards to a usual sort of notion that
"the lever" is the simplest machine and also represents
any sort of mechanical interaction, even the usual
equal/opposite of inelastic conditions, that it's always
so that "the world turns", with regards to theories like
those of DesCartes and Kelvin, of the vortex, as a necessary
complement to the classical and linear (and partial and incomplete)
of what is _not_ the "closed".
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assume, that nature does also behave like this on a fundamental level.
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So, nature is kind of mathematical, if you regard geometry as math.
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Now the difficult trick is, to find the correct type of math, which
nature actually uses.
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I had bi-quaternions in mind previously, but think, that another type of
clifford algebras perform actually better.
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This system consists of indempotent and nilpotent operators and is
called 'dual quaternions'.
https://en.wikipedia.org/wiki/Dual_quaternion
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This is actually a system of geometric algebra, which is in common use
in robotics (but hardly anywhere else).
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The benefit of this system is, that it allows relatively simple
translations and rotations of rigid bodies (in computers).
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'Nilpotent' means, that such entities square to zero.
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This requirement for a description of nature was first used by Prof.
Peter Rowlands of Liverpool in his book 'From Zero to Infinity'.
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That book is very hard to read and also very expensive.
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But there exist a pdf 'What is Vacuum' from the same author, which is
availible on the internet.
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Dual quaternions are actually very old and known by Clifford since 1882
(as far as I know).
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These are very similar to bi-quaternions, but behave better for
translatory movemnts.
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The connection to nature could be seen in in my own 'book' about
'structured spacetime':
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https://docs.google.com/presentation/d/1Ur3_giuk2l439fxUa8QHX4wTDxBEaM6lOlgVUa0cFU4/edit?usp=sharing
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TH
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We might look to "algebraic geometry" a la Hodge as leading into
geometric algebra, with regards to bi-rational forms, for example,
and the convolutional setting, with regards to _symmetries_,
that _symmetries_ as with regards to symmetries and _rotations_,
make for the Cartan-ian about reflections and rotations after
"geometric algebra", with regards to the inner and outer products,
what result for forms, why "geometric algebra" seems so great
because it solves some singular issues in modeling rotation
with matrix manipulation.
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When 25 years ago I thought geometric algebra was about the
best and greatest mathematics, it's also that it arrives
from algebraic geometry and also ring theory (Normel rings)
after van der Waerden then Zariski and Kodaira, Hodge, de Rham,
then into Lounesto and the modern late-20'th century geometric algebra,
from Picard and Sevari after "the Italian geometers" and to Lefschetz,
with regards to: "analysis situs".
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So, mentioning analysis situs, then is Poincare. The great Poincare,
much appreciated that the usual linear formalism, was lacking.
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Then, for ideas like topological surgery after analysis situs,
is that much like "geometric algebra" is after "algebraic geometry",
and must be to _include_ it, also the differential analysis and
the integral analysis point at two quite different approaches.
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Then, overall here it is a _geometric_ approach, that then the
_algebraic_ or _analytic_ approach, must attain to it, then
that for space contraction, fall gravity, real wave collapse,
and so on, mathematics _owes_ physics a thorough account.
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Then there's Feynman for example, "how about 4-vectors, or
about mass-less charge-less virtual-ons and virtual-inos
which are unscientific in the un-observable sense yet add up",
instead, to figuring out how scattering and tunneling theory
must be continuum mechanics again. Feynman would be like
"that would be great, I wish we had that when."
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