How Phase Velocity is faster than Group Velocity (de Broglie Law of Phase Harmony) via Guenther Nimtz superluminal phonons: Universal Tunneling time= Law of Phase Harmony

 

 This is the hidden noncommutative phase that is lost by converting frequency to a "2pi" circle symmetry phase.

 For their analysis, Sommerfeld and Brillouin examined the propagation of ‘square’ pulses, for which, “in almost any case the beginning of the signal is a discontinuity in the signal envelope or in a higher derivative.” It was to be in this step-like front velocity, vF, - which may not exceed c in order to preserve causality - that the fiducial role of c as the limit of the front velocity of a wave packet “is deduced from the Lorentz invariance of the Maxwell equations.” (Heitmann & Nimtz 1994, p. 155)

 Wow - fascinating.

 So the phase velocity is TWICE the group velocity.

The previously "infinite" front velocity is not valid due to the inherent noncommutative phase as the origin of Planck's Constant.

 So the Quantum of Action is inherently limited as h-bar time the angular frequency.

But HIDDEN within the Quantum of Action is the 1/2 spin that is superluminal - as noncommutative phase of time-frequency.

 So here it is again. The phase velocity is FASTER than the group velocity.

 the group velocity, vGr, - and analogously described as the ‘centre of gravity’ of a wave packet. Insofar as “the group velocity was then believed to be identical to the energy propagation,” careful definition became important. (Jackson, Lande & Lautrup 2001, p. 1).

https://researchbank.swinburne.edu.au/file/261593b6-a3e7-4ddb-b042-8ceec25d1838/1/Gareth%20Boardman%20Thesis.pdf 

So his point is that since the energy as amplitude is the "second order" as a squaring of frequency and time - therefore the energy signal hides the wave packet as Law of Phase Harmony.

Mozart is sent INTO THE FUTURE!!

So because the tunneling is in the "imaginary" time then it is superluminal.

So the Universal Tunneling Time is simply the Pythagorean Principle of time inverse to frequency!

Only it is the negative commutative phase at the same time for a "zero" tunneling time.

Central to the ensuing inquest was disquiet as to whether such observed pulses were, in fact, signals as carriers of information within the ambit of information theory and the prevailing interpretations of special relativity. Such contentions evoked the Italian researchers’ concession that “the question as to whether a wave packet can be considered a signal is a much debated and complicated one.” (Mugnai, Ranfagni & Ruggeri 2000, p. 4830).

tunneling:

Sommerfeld committed suicide - was it because this result didn't get accepted?!

So the reflection arrival time is the SAME as the tunneled signal.

Any realistic wave packet, or envelope employed as a signal, is of necessity frequency limited and in consequence cannot exhibit a sharp and accurately step-like front.

in the now ubiquitous world of electronic data handling, information often derives from the half-height detection of the practical approximation of a square wave pulse. Heitmann and Nimtz point out that application of such practicalities to evanescent and tunneling phenomena would validate claims of information superluminality in their cases.

So this is the SQUARE wave "signal" assumption of Sommerfeld. Amazing.

So the wave becomes infinite frequency due to zero time as a square wave.