Basil J. Hiley on Heisenberg: "Let me call that phase [of the amplitude] frequency"

 https://www.youtube.com/watch?v=jl00BY8kopw&t=181s

 

 "Why? Because atoms are quantized and we have these spectral lines, rather than the continuum."

 Hiley is referring to Heisenberg's "transitional frequencies" of the Ritz-Rydberg combination principle.

And the rule that the found, if you go from, E(n) to E(m), take the energy difference, it gives you a frequency. That frequency is the same as the sum of the transition from there to there [n to k and k to m].  If you put that in the exponential as multiplication, because it's squared terms that gives you the energy, you add the frequencies. And that's why Heisenberg did this.

 

 So the phase of the amplitude is assumed to be a commutative exponential just as it is wrongly assumed that the Perfect Fifth PLUS the Perfect Fourth = the Octave (as the very first logarithmic equation).

So the statistical average for amplitude actually is derived from this simpler, nonlocal, noncommutative process of time-frequency. So then Feynman just said the Path is still continuous but does not have derivatives.

Feynman was doing what was Dirac was doing - and so his focus on kinetic energy caused an infinity or singularity of energy! So Feynman changed the rest mass as renormalization.

Since kinetic energy is a squared term then it has to use Planck's constant squared!

"So what he [Feynman] is missing here is the quantum potential"

So the quantum potential only emerges when using Planck's Constant squared.

De Broglie (1960) has already realized that "the appearance of the quantum potential makes it look as if the mass has changed."

 So the "enfolding" and "unfolding" process is the future and past overlapping - as shown in the image! This is then averaged to become "deterministic" as the Bohm momentum. That deterministic momentum is wrongly called "Bohmian mechanics" that still ignores this underlying noncommutative.

"a deeper [algebraic] structure that gives rise to a noncommutative phase space - it's a dynamical geometry."

"You take all the structure in X [position] and you transform it all over the momentum space and vice versa - in other words, the whole process is a nonlocal process from the start....The process itself can not be described in local terms."

 David [Bohm] was talking about thought ultimately.

 as the "the quantum potential is an informational potential...a formative causality...the mathematical structure of the quantum potential - it contains information about the experimental environment - about whether it's a one-slit, two-slit, whether it's diffracting grating, etc. etc. It's encoded in this extra energy, this new quality of energy, the quantum potential energy... you actually take the quantum potential energy from the classical kinetic energy."

-it's ENCODED in to the quantum potential energy.