So I've been studying the "weak measurements" - from the perspective of Basil J. Hiley and I recently did a video on the negative time of superluminal phase that can be interpreted as either a group velocity or a "weak measurement." So with the "weak measurement" you have an entangled photon(s) and you do the measurement before the "collapse" of the noncommutative variables which are called conjugate variables. So it would be either time and frequency or position and momentum or spin. So you do something called "post-selection" which means the "weak measurement" is turned into a "strong measurement" as a post-selection, which then determines that the position noncommutative to the momentum.
But they are using photons and so Basil J. Hiley's criticism was that the photon, since it has zero mass, then you're dealing with just velocity at the speed of light and not momentum. So you end up getting a zero point in spacetime as a singularity with an infinite...well it ends up being a singularity because of that zero rest mass. So that's why Basil J. Hiley wanted to redo the weak measurement with mass using a particle - and this is what his collaboration was going to be with Robert Flack and their Ph.D. research students. But then the pandemic kicked in and they lost their funding.
So you have this fascinating difference between what is velocity vs. momentum because momentum means you have to have mass or speed because the speed of light invariance for relativity is assuming a symmetric magnitude for the wavelength. But what the "negative time" experiments have shown with the weak measurement is that you have a phase that is superluminal. So if it is superluminal it is faster than the wavelength divided by the speed of light, which means the time is not dependent on a physical medium of spacetime. So it proves that time exists before spacetime and this precisely the point of David Bohm and Basil J. Hiley were making - is that there is a deeper process that this the "quantum potential" that exists as pure time and frequency before spacetime exists. And that is why it is a "negative frequency" and time-reversed signal but technically it can't be a signal but the Bell's Inequality showed that you're getting a "spooky-action-at-a-distance."
And Professor Jean Bricmont says that even though it's technically not a signal because there's no amplitude yet as energy it is information because not random, it's correlated. And what's fascinating about that is when you are using the statistics as probability you're assuming a unitarity as one. So you go to the Bloch Sphere; so you are assuming a magnitude of one. But with the Bloch Sphere you have the inherent noncommutativity as Eddie Oshins showed. So you're flipping around the Z, Y and X axis. So you when you have a singularity the "Z" is the negative infinite time. So that would be like a vertical Z axis. And when you have that negative infinite time that is when you have the inherent nonlocality because that would create a singularity in terms of spacetime.
And so that's why math professor Lou Kauffman says that, and along with Roger Penrose, say that time inherently has the imaginary number to it. So it's what they call "primitive time" or "primordial time" or "fundamental time." So time is inherently an asymmetric eternal nonlocal energy - a force to it that is a newly discovered force that is also the formative cause of matter. And so this was the point in music theory because you are assuming the One when you listen to the source of the One in music theory it's also the source of the I-thought. But what happens is that in order to create a symmetric octave for the resonance of the overtone as the 1/2 wavelength and 2 as a frequency, if you keep doing that resonance as 3 then all of a sudden, since 3 doesn't go into 2 then you're forced to change the 1. So you change the 1 which would be a zero to one and you have to use the common denominator. So what Philolaus did is he expanded that to 12 because when you use 12 then you can have the ratio of 3/4 and 2/3 with the common denominator as using 6/8 and then 8/12 and 9/12 and then 9/8.
So what happens is all of a sudden you are covering up the fact that you change what the "one" is. So you turn the one into a magnitude that is irrational and it no longer has an arithmetic value. So in that case you change the one from 0 to 12 to 0 to 8 and then you reverse the direction of time. And you cover that up, so you're just saying "oh no it's just X as an irrational magnitude" and so by doing that you are covering up the inherent nonlocality or noncommutativity as the source of the One, which is actually the Perfect Fifth which would be C to F as an undertone which would be 2/3 and then C to G as an overtone which would be 3/2. So this is why Alain Connes calls it "two, three and infinity" as the simplest example of noncommutativity of time and frequency.
So this exists before you have any momentum because you're not squaring any amplitude as the probability. You don't even need amplitude because the force is coming directly just from time and frequency before you're assuming any kind of symmetric spacetime to square in order to have amplitude. So if you're not squaring for amplitude then you no longer have a probability of one as your unitarity - what they call the identity matrix. So even when Heisenberg discovered the "order of the overtones" changes the value of the energy for the photon since the photon has no mass, then you are working directly just with velocity. But because you have that noncommutative overtone then all of a sudden you have the superluminal signal that's based on just the time and frequency.
But classical physics says no it can't be a signal because you don't have the amplitude as energy and you need the amplitude as energy to have the signal as information. But in Bell's Inequality they're saying no, it's instantaneous correlation in the probability. But the probability is already assuming again this inherent unitary identity matrix between noncommutativity of the position and the momentum. So what Basil J. Hiley is pointing out is that you don't even need that probability; you don't need any kind of collapse of the wavefunction until you have a "strong measurement." Because when you compare the Moyal product and the Baker - what does he call it? Basically the [Pascual] Jordan Product is that inherent noncommutativity.
So it's what von Neumann discovered and Dirac - it gets turned into the Poisson Bracket which is essentially is this inherent noncommutativity because you're subtracting the position and the momentum and then you end up getting the inherent imaginary number times Planck's Constant. And Planck's Constant is the average energy of light but Planck himself was directly inspired by the equal-tempered music tuning. So when he created Planck's Constant he divided out time as a dimensionless radian, so he's assuming time as second which inherently defines time as a symmetric circle, you know pi over two. So then you end up having to rely what they call h-bar which is actually pi over four because you have that inherent noncommutativity to the measurement.
In other words when you just use Planck's Constant (h) by itself you end up having this inherent nonlocality that is noncommutative with the time and the frequency. So then you're forced to use h-bar so mainstream physics just assumes it's an h-bar measurement as if Planck's Constant doesn't exist on its own. But you still have the imaginary even with h-bar so you end up having Planck's Constant times the imaginary number divided by two and that ends up being your noncommutative unitarity Poisson Bracket. But when you do that you're covering up Jordan Product which is essentially - you are adding together the difference (of position and momentum) - in terms of music theory I suppose this would be the same you know it's either the exponential or the logarithm.
So as Alain Connes points out, you know, when you have the Pythagorean Comma it's 2 to the 19th against 3 to the 12th. And then when you put that back into logarithms for the octave music scale of twelve notes then you have 2 to the (1/12th) against 3 to the (1/19th). So you have that noncommutativity because it's covering up the fact that the 2 is actually assuming the octave is symmetric against the 3/2 which it's inherently not, cause you can't have that, since 3 doesn't go into 2. So you end up getting this eternal listening process to the source of the One whereby the source of sound in your mind is actually pure time itself that has no physical medium of spacetime as an external measurement. So Lou Kauffman's point is that everytime you make an external measurement it takes a certain amount of time and therefore the imaginary number is this algebraic process of X= negative 1 or positive one/X, so you have that inherent 1 and negative 1 at the same time.
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