A Noncommutative critique of Planck's Constant....the ear drum two orders of magnitude smaller than the diameter of a hydrogen atom.

 https://inspirehep.net/literature/1392081

Inconstant Planck’s constant

• Gianpiero Mangano(

  • INFN, Naples

  )
  ,
• Fedele Lizzi(

  • INFN, Naples and
  • Naples U. and
  • Barcelona U., ECM

  )
  ,
• Alberto Porzio(

  • CNR-SPIN, Naples

  )

Sep 7, 2015

 Motivated by the Dirac idea that fundamental constants are dynamical variables....

 ok

 https://arxiv.org/abs/0910.2949

Distortion of the Poisson Bracket by the Noncommutative Planck Constants

Artur E. Ruuge, Freddy van Oystaeyen

In this paper we introduce a kind of "noncommutative neighbourhood" of a semiclassical parameter corresponding to the Planck constant.

https://link.springer.com/article/10.1140/epjc/s10052-019-6794-4 

  The resulting equation reduces in the small energy limit to the standard quantum mechanical one, while for large energies the effects of the noncommutativity become important. We investigate in detail three cases, in which the noncommutative strengths are determined by an independent energy scale, related to the vacuum quantum fluctuations, by the particle energy, and by a quantum operator representation, respectively. Specifically, in our study we assume an arbitrary power-law energy dependence of the noncommutative strength parameters, and of their algebra. 

Moreover, some drastic changes are expected in the physics near the Planck scale, with one important and intriguing effect being the emergence of the noncommutative structure of the spacetime

  an effective energy-dependent Planck constant, which is a function of the noncommutativity parameters θ(E) and η(E)

, and it is given by [21]

ℏeff=ℏ[1+ζ(E)] ,

(25)

where ζ≡θ(E)η(E)/4ℏ2

. Such a scaling can be used to make the Planck constant a true constant.

who does the scaling and why?

On the other hand, in [21] it was shown that by assuming that θ√, giving the fundamental length scale in noncommutative geometry, is smaller than the average neutron size, having an order of magnitude of around 1 fm, it follows that (ℏeffℏ)/ℏ≤O(10). Hence, in practical calculations one can ignore the deviations between the numerical values of the effective Planck constant and the usual Planck constant.

 Oh I get it...

So as long as we keep at a safe distance to the foundation of reality then....

the ear drum two orders of magnitude smaller than the diameter of a hydrogen atom.

 So it's still NOT as small as the neutron... yet....

let's see what B.G. Siddharth has to say about this.

We also considered B.G. Sidharth's theory of cosmological constant based on the non-commutative geometry of the Planck scale space-time, what gives an extremely small DE density providing the accelerating expansion of the Universe.

 

 

 so this is very fascinating....

 

 This is the joke that God is a Weak-Left-Hander....

Pauli couldn’t be happier that he was proven wrong — he later wrote to Jung that “God is a weak left-hander after all”.

 

 

Energy Vector and Time Vector in the Dirac Theory

Christian Rakotonirina ^*

Version 1 : Received: 16 July 2020 / Approved: 21 July 2020 / Online: 21 July 2020 (03:16:16 CEST)
Version 2 : Received: 1 October 2020 / Approved: 5 October 2020 / Online: 5 October 2020 (11:07:17 CEST)
Version 3 : Received: 25 May 2021 / Approved: 26 May 2021 / Online: 26 May 2021 (14:17:55 CEST)

How to cite: Rakotonirina, C. Energy Vector and Time Vector in the Dirac Theory. Preprints 2020, 2020070472 Rakotonirina, C. Energy Vector and Time Vector in the Dirac Theory. Preprints 2020, 2020070472

Abstract

We have introduced a sign operator of energy, analogous to the operator helicity, but in the direction of what we call energy vector. However, this energy vector needs a time vector. To give physical senses to the components of such a time vector, we try to explain the time dilation in special relativity and try to relate the components of the time vector to the tunneling times when an electron crosses a potential barrier.

Subject Areas

Tunnelling time; helicity; time dilation; Dirac equation; superluminal velocity 

https://www.preprints.org/manuscript/202007.0472/v3 

 

https://www.worldscientific.com/doi/abs/10.1142/S0217751X14500365 

 The instantaneous rate of change of the position expectation value with respect to the simultaneous expectation value of the dynamical time operator is shown to be the phase velocity, in agreement with de Broglie's hypothesis of a particle associated wave whose phase velocity is larger than c. Thus, these two elements of the original basis and interpretation of quantum mechanics are integrated into its formal mathematical structure. Pauli's objection is shown to be resolved or circumvented. Possible relevance to current developments in electron channeling, in interference in time, in Zitterbewegung-like effects in spintronics, graphene and superconducting systems and in cosmology is noted.

 The dynamical time operator here proposed is the appropriate one to define the time
of passage or arrival time at a specific point. In contrast, as pointed earlier, in many
of the interpretations of a time-energy uncertainty relation the
t corresponds to a time
6
interval, not to an instantaneous value of the uncertainty. Dwell times, tunneling times,
i.e., time intervals, should be expressed as differences of average values of the time operator
taken at two different points of the trajectory, and consequently related to parametric time
differences (Appendix C). Their time uncertainties would need to combine the instantaneous
uncertainties of the end points.

 

 

 https://arxiv.org/pdf/2002.11463.pdf

 

 

 Precisely!!!

Noncommutative Planck Oscillators - pdf of B.G. Siddharth