"The reason time is passing, and passing in a way that we don’t control at all, is precisely the lack of reproducibility of the quantum." https://celebratio.org/Connes_A/article/842/
Hi Myke: thanks for your reply. Nobel Physicist Gerard 't Hooft with Martin van der Mark explain in their classic paper, "Light is Heavy" that all matter is actually made of light! https://arxiv.org/abs/1508.06478 In the de Broglie-Bohm model of reality this light, also proven in the weak measurement experiments of Yakir Aharonov's research group - this light is not a photon but rather created from a deeper noncommutative time-frequency nonlocality. So there is no "center of mass" for light even though light has gravitational mass! This is due to the 1/2 spin of matter originating from virtual photons. In the standard model the virtual photons do NOT exist but rather are just a mathematical fiction of renormalization. Basil J. Hiley proves that this is incorrect! Feynman's renormalization made an error - as did Dirac - as Hiley explains - since Planck's Constant has to be squared and also the Schroedringer wave equation using the Hamiltonian has to be converted to Polar form using both real and imaginary components. So this imaginary component then has a noncommtuative nonlocal time-frequency of negative frequency and time-reversed signal from the future that overlaps.
the "transition frequency" of cesium that defines the "second" has an inherent "uncertainty" that is noncommutative as nonlocality. Alain Connes: "the definition from the wavelength of the cesium spectrum, this is exactly the transition between old geometry and non-commutative geometry. It’s exactly that. It is a spectral type geometry, spectral in nature. And so, that’s it, the change is the change in the unit of length. So, it’s a spectral geometry in nature and in addition, if you want, there is non-commutativity of algebra, it is practically imposed by what are called the gauge theories." http://denisevellachemla.eu/mai15-en.pdf Alain Connes again: It is cesium because cesium is very easily available and sold, and moreover, the wavelength of cesium which is used is a microwave. So it’s like when you put something in the microwave oven, it’s a wavelength that is of the order of 3 centimeters. And it’s an instrument which allows you to measure length up to 12 decimals, so I mean, it’s abolutely incredible. And this is now what is taken as the unit of length. Of course, people will tell you it’s not a unit of length it’a a unit of time but because of the constancy of speed of light, speed of light has been fixed to a very specific number. So things have evolved and now, what you see from that is that there was a complete change in the paradigm because the unit of length is no longer a localized object, which is somewhere, but it’s a spectral data. And it turns out tha the new paradigm which comes from quantum mechanics, which is the paradigm of non-commutative geometry, which is called spectral geometry if you want, is exactly parallel to this change of paradigm in physics. So it’s very concrete. It’s something which is very very concrete and the enormous advantage is that if we had, for instance, to unify the metric system, not on Earth, but in the galaxy, for instance, if you tell to people, “ok, come to Paris and compare your unit of length to the unit of length we have defined there...” (laughs), they would laugh at you, they would roar, because they would say “we have our unit of length”, whereas if you tell to people “take a chemical element”. Of course, cesium is a little bit complicated because....the advantage of hyperfine splitting which is used for cesium is that an hyperfine splitting is a difference of energy which is very, very small, and that would in the inverse law, when you pass to the wavelength, it will generate microwaves, which is much more practical, whereas if you take a huge difference of frequency, like for a transition, you will get a very, very tiny unit of length and that would not ( ?) be good. " http://denisevellachemla.eu/mai10.pdf So the momentum is to wavelength as the frequency is to time (as period). The frequency and time are noncommutative and nonlocal and thus have inherent "uncertainty" as a quadrature - going from the future to the past and vice versa. That is then squared for the wavelength. https://alainconnes.org/wp-content/uploads/bookwebfinal-2.pdf "the transition between two hyperfine levels of the Cesium 133 atom....as a consequence of relativity, c does not depend upon the frequency of the light, a property that is the object of crucial experimental probing. ...It is natural to adapt the basic paradigm of geometry to the new standard of length. We explain briefly below that this is indeed achieved by noncommutative geometry, which shows moreover how geometric spaces emerge naturally from purely spectral data.... "one should not confuse the “line element” ds with the unit of length."
Thus there is an intrinsic “variability” in the quantum world which is so far
not reducible to anything classical. The results of observations are intrinsically variable
quantities, and this to the point that their values cannot be reproduced from one experiment
to the next, but which, when taken altogether, form a q-number.
Heisenberg’s discovery shows that the phase-space of microscopic systems is noncommutative
inasmuch as the coordinates on that space no longer satisfy the commutative rule of ordinary
algebra. This example of the phase space can be regarded as the historic origin of noncom-
mutative geometry. But what about spacetime itself ? We now show why it is a natural step
to pass from a commutative spacetime to a noncommutative one....
The point is simple to understand:
these spaces are constructed by the process of passing to the quotient and this cannot be
done at once since it is impossible to select a representative in each equivalence class. Thus
the quotient is encoded by the equivalence relation itself and this generates the noncommu-
tativity, exactly as in the case of the original discovery of Heisenberg from the Ritz-Rydberg composition law.
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