But Fritz London exposed the problem with Planck's Constant!!
additively-periodic with a whole-number multiple of the Planck constant as its period.
When one gets serious about the radical continuum conception of matter, with the solution of the discontinuously-bounded electron in field quantities that vary continuously in space and time, as was suggested by de Broglie’s theory and more consistently by the theory that Schrödinger considered later (1), one will arrive at an especially-definitive complication when one examines the sense that one might assign to metric statements inside of the undulatory continuum, if at all.
That is because in that oscillating and fluctuating infinitely-broad medium that enters in place of the bounded electron, one finds no discontinuities that cannot be understood nor rigid bodies that might permit one to establish a metric as a reproducible yardstick.
It is known to lead to compelling reasons for reinterpreting the entire undulatory formalism statistically, which was proposed by, above all, Born and his collaborators. To the extent that the charge density can be reinterpreted as a statistical weighting function, it is not difficult to see that this indeterminacy in regard to the applicability of the law of identity to which we will refer here must be translated accordingly. However, since that conception initially rejects any interpretation in space and time, there is little of interest in its relation to Weyl’s theory of space.
The law of identity is not applicable to the πάντα ῥεῖ (†) of standing and travelling waves, since there are no features of a continuum that would be suitable for defining a reproducible measurement.
However, I would not like to pause to discuss here whatever it should mean that every line segment is regarded as a complex quantity and what it should mean that the entire Weyl variability of the measure of the line segment is presented as a change in only the phase while preserving the absolute value.
One can now foresee already how that difficulty must be resolved: Quantum theory allows matter to have only a discrete series of equations of motion, and one suspects that those distinguished motions will allow one transport the gauge only in such a way that the phase will have made precisely a whole number of circuits upon returning to the starting point, such that despite the non-integrability of the transport of line segments, the gauge will always be realized in a single-valued way at every location.
despite the non-integrability of the transport of line segments, the gauge
will always be realized in a single-valued way at every location. In fact, one recalls the resonance property of the de Broglie waves, which is the same way that the older Sommerfeld-Enstein quantum condition first reinterpreted the de Broglie condition so successfully. That is generally coupled with the phase velocity, but as a result of the five-dimensional extension of the wave function, the oscillation process will be dispersion-less, and as a result, our current velocity will be identical to the phase velocity.
Fritz London's paper translated from
London, F. Quantenmechanische Deutung der Theorie von Weyl. Z. Physik 42, 375–389 (1927)
London, F. Quantenmechanische Deutung der Theorie von Weyl. Z. Physik 42, 375–389 (1927). https://doi.org/10.1007/BF01397316
Basil J. Hiley and David Bohm proved that energy is NOT quantized but rather energy is a nonlocal noncommutative discrete algebraic process as explained by Alain Connes, Fields Medal math professor talk on music!!
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