So Martin van der Mark points out that the subtraction of frequencies is a multiplication and thus nonlinear. It's not just nonlinear - it is noncommutative!
the principle of equivalence tells us that light must also have a gravitational mass mg, and consequently it must be attracted by heavy bodies...The reason that we find Mg = M0 is that we have a closed system with the centre of mass of all the particles at rest.
P5-P4= 3/2 x 3/4=9/8 or major 2nd. C to G (3/2 as frequency) x C to F (3/4 as frequency) = C to D as 9/8 frequency. The F frequency is derived from 2/3 as frequency that is 4/3 as wavelength (larger than the 1) while 3/2 as wavelength is G as frequency.
So the Wave in quantum physics assumes a 1 value for the circle from 2pi but with the addition of the imaginary number you get a noncommutative 5th dimensional "flip" to the photon and election as inherent 1/2 spin.
This is the result of Martin van der Mark's paper but he does not call it noncommutative!
Why not? As Alain Conne points out the "time" originates from the noncommutativity as the inner automorphism that is nonlocal and thus beyond linear time. So it is "off the diagonal" of the Matrices in quantum algebra. This "off the diagonal" is before any external measurement collapses the wavefunction and this is inherently from the future!!
matter’s most basic building blocks, the elementary particles, all have non-zero spin, intrinsic angular momentum, which seems to imply that they all must have some sort of intrinsic dynamics. Hypothetical structures which do not have internal dynamics, such as point particles and hard spheres, do not exist. So what is matter really made of then? In the Dirac theory, the electron is like electromagnetic energy quivering at light speed, just like a photon in a box [5]. If really so, matter is light.
So the conversion of time and frequency to wavelength as linear time inherently implies the future already exists as precognition and an anti-gravitation repulsive force!!
The rest mass of the box is not equal to the sum of the rest masses of its contents. The reason that we find Mg = M0 is that we have a closed system with the centre of mass of all the particles at rest.
So this means you get a Klein Bottle that can not be visualized in 3D directly or even 4D spacetime - because of that internal flip in the 5th dimension.
Martin van der Mark called it a "Spinning Breather"
https://quicycle.com/wp-content/uploads/2020/05/Mark_2019_J._Phys.__Conf._Ser._1251_0120491.pdf
the form of breathers (oscillating/spinning solitons), displaying simultaneous particle-like and wave-like behaviour.
https://arxiv.org/pdf/0909.4195
The particle ’feels’ the distant environment through its vibrating ’tail’ (7), which navigates the particle in compliance with the far-field geometry. Note, that while the particle velocity is clearly subluminal its communication with the environment is superluminal, which is not incompatible with the Lorentz-invariance of the system.
I just emailed Prof. Gregory Sivashinsky
https://arxiv.org/pdf/1003.2542
his first paper was never published.
https://arxiv.org/pdf/0912.5156
Not sure about the 2 follow-up papers - but Martin van der Mark never cited Sivashinksy.
de Broglie wave thus acquires the meaning of a localized excitation of the action func-
tion displaying simultaneous particle-like and wave-like behavior.
the secret spinor of the photon that creates matter....
"A much stronger force than the strong reaction...it explains what the electron is inside."
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