de Broglie Law of Phase Harmony='a very special synchronization' Lou Kauffman='2, 3, ∞' Connes music

This is the secret of the Law of Phase Harmony also being noncommutative as John G. Williamson explains:
A new theory of relativistic quantum mechanics explains that Law of Phase Harmony is noncommutative. So in reality this is quantum biology that is relativistic nonlocality as the Tao and the "three gunas."

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The crucial difference in the quantum case is that the fre-
quencies do not combine in the same way as the classical
harmonics, but rather in accordance with the Ritz combina-
tion principle: which is consistent with Eq. ~1!.

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If we fix θ and project the motion onto the x − y plane, we find the spin up
state rotates anti-clockwise, while the spin down state rotates clockwise.
Since the charge current is simply related to the velocity of the electron
by vi = ji/|Ψ|2, we immediately see that the relativistic electron is moving
in the relativistic Bohm model. It clearly rotates either anti-clockwise if its
spin is up, or clockwise if it is in the spin down state. Thus in the case of
muonium, we see that the muon is also moving and therefore subject to a
time dilation. This then explains why we see the muon live longer in the
atomic state.

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Understanding Heisenberg’s “magical” paper of July 1925: A new look at
the calculational details
Ian J. R. Aitchison, David A. MacManus, and Thomas M. Snyder
Citation: Am. J. Phys. 72, 1370 (2004); doi: 10.1119/1.1775243
In the quantum theory, however, the transition frequency cor-
responding to the classical a v(n) is, in general, not a simple
multiple of a fundamental frequency, but is given by Eq. ~1!,
so that a v(n) is replaced by v(n, n-a)...It is the transition amplitudes X(n, n2
a) which Heisenberg took to be ‘‘observable;’’ like the transition frequencies, they
depend on two discrete variables.

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In this paper we have shown how it is possible to
write the content of the Schr ̈odinger equation in algebraic
form without reference to either Hilbert space or to any
specific representation. The resulting two equations are
respectively the Liouville equation, equation (19), and
an equation that describes the time development of the
phase, equation (20), which we have called the quan-
tum phase equation. Furthermore, we have shown that
this equation is gauge invariant and from it we calcu-
lated the Aharonov-Bohm, the Aharonov-Casher and the
Berry phases in a simple and straight forward way.
We have also shown that it is possible to write the
probability currents as algebraic operator forms. This
allows us to define probability currents in any arbitrary
representation. All of these results follow from the quan-
tum formalism without the need to appeal to any classical
On the other hand, if we take the quantum formalism
as primary then we must place our emphasis on the non-
commutative structure of the algebra of formalism. If we
do this then attempts to focus on a single phase space,
which is equivalent to giving primary relevance to space-
time, will fail.

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But in the quantum theory, Heisenberg wrote29 that a
‘‘similar combination of the corresponding quantum-
theoretical quantities seems to be impossible in a unique
manner and therefore not meaningful, in view of the equal
weight of the variables n and n2 a @that is, in the amplitude
x(t)... .’’ This way of representing x(t), that is, as we would
now say, by a matrix, is the first of Heisenberg’s ‘‘magical
jumps, ’’ and surely a very large one. Representing x(t) in
this way seems to be the sense in which Heisenberg consid-
ered that he was offering a ‘‘reinterpretation of kinematic
relations.’’