So when Penrose says Frequency = Mass, he is not clarifying that frequency goes DOWN (red-shifts) for a particle as time slows down (gets bigger in wavelength) towards the speed of light but the quantum frequency goes UP since all matter is made of LIGHT. So what Penrose is emphasizing that even though light as a NULL geodesic in relativity it is still in two places in TIME as the 5th dimension due to noncommutative phase. Penrose then states since he's a geometer then he's not good as noncommutative quantum algebra. haha.
Still Frequency=Mass is a nice "sound byte" or "meme" that people can use since it embraces BOTH relativity and quantum physics - as Penrose emphasizes the secret of consciousness is NOT just quantum but also relativity. haha.
So this paper The Hopf-Fibration and Hidden Variables in Quantum and Classical Mechanics
is demonstrating that the Quaternion equation in quantum mechanics inherently is noncommutative but in the normal Copenhagen Interpretation, the "global phase" hides the "dynamic phase" that is noncommutative - hides it by averaging it as a geometric mean (just as in music theory!).
Under the hopf-fibration the global phase is 'curled up' as a natural hidden variable...global phase is not explicitly present in the bloch vector as a parameter, it is encoded in the 3-D kinematics through the global, geometric and dynamic phases - it is implicitly present.
Whereas the 1/2 spin means that reality is inherently 2 dimensional even at the 1 dimensional "path" of the spinor - requiring a 720 degrees to complete the noncommutative phase as global phase.
So this means that 3 dimensional space is actually 4 dimensions.
So this is what Dr. Andrija Puharich was referring to as the subharmonic or ELF Psi-plasma of reality - the backwards precession as the magnetic moment between the proton and electron. So each particle as an angular momentum or external spin and then an intrinsic momentum or internal spin. For electrons the internal spin is 1/2 so that it is noncommutative but then the global phase of the electron to the proton is also noncommutative (meaning the angular momentum as defined in relation to the proton). So it is literally the nuclear magnetic resonance value - that I have cited - as the ELF frequency for water splitting via ultrasound. So the intrinsic spin is then the supermomentum as virtual photons that also have a reverse time as anti-matter mass - as the precession that is backwards against the angular momentum.
So then the supermomentum as virtual photons is also the "binding" energy from relativity as the magnetic moment of the whole atom.
So this is the new Noncommutative version of the Pythagorean Theorem!
So then what does the Noncommutative Phase version of the Pythagorean Theorem look like?
http://quantumostinato.blogspot.com/2014/07/brainwashed-by-pythagoras-theorem-and.html
As I stated - I never accepted the Pythagorean Theorem proof when I was 14 years old because I already knew that music was noncommutative. Of course I could not explain this to anyone so I kept it to myself so that people wouldn't think I was wacko.
The standard model from the metric point of view: how noncommutative geometry provides extra-dimensions from Pythagoras theorem pdf
So each point already has this 720 degree spin in it that is noncommutative.
So therefore:
And so reality is inherently 4 dimensional!
So this below was pointed out to me by my internet correspondent in Brazil - we began corresponding from my original blog on guerrillanewsnetwork - back around 2004 or so....
This is also the point of Chinese Nobel physicist Yang.
So as I have quoted him - he emphasizes that this spin force was covered up by Heaviside. The Tesla enthusiasts have made the same point as well - the Tesla was relying on this spin force.
And de Broglie discovered this as well - before spin was formulated as a concept!
And this is why my quantum mechanics professor uses the "donut" as a noncommutative torus for the fiber bundle of spin - because in the Bloch Sphere normally used for spin - the global phase hides the noncommutative spin - as a null geodesic. Geometric phase from Aharonov–Bohm to Pancharatnam–Berry and beyond
The general form of geometric phase was introduced by Michael Berry nearly 35 years ago36. He noticed that when the parameters of a quantum system are slowly cycled around a closed path, the phase of its state may not return to its original value.
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