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Coverup of Antigravity: Problem of H-bar or the Reduced Planck's Constant: noncommutative coherence
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"Further, by emphasising the constancy of h-bar in the relation [change of]X times [change of]P approximates h-bar one tends to be led to the notion that the 'disturbance' is dependent only on the size of the cell in phase space. In this way the overall experimental conditions were tacitly dismissed as irrelevant."
Emphasis on "size" in original, p. 186, B.J. Hiley, "Phase Space and Cohomology Theory" in 1971, Quantum Theory and Beyond,
What is Planck constant?
"This is made possible by exploiting sequential weak measurements, allowing to measure non-commuting observables in sequence on the same state, on each entangled particle.... dynamical nonlocality seems to manifest the system’s dependence on future configurations in a two-time picture."
"...this implies the possibility of gravitational repulsion rather than attraction within the weak reality. Moreover, not only the gravitational mass, but also the inertial mass will be shown to admit a negative sign."
From Basil J. Hiley: ""the Baker bracket [Jordan product] does not reduce to the usual commutative product. ...The bracket plays an important role when energy (Hiley 2015) is involved. A careful study of Pauli’s (1926) application of the algebraic approach to the energy level structure of the hydrogen atom shows how a Jordan product enters into the calculation.v. As we have already pointed out, one of the advantages of the Moyal approach is that it contains classical physics as a limiting case as is clearly seen from equation (12). There is no need to look for a one-to-one correspondence between commutator brackets and Poisson brackets, a process which fails as was demonstrated by the well-known Groenewold-van Hove “no-go” theorem (Guillemin and Sternberg 1984). "Proceedings of the Royal Society of New South Wales Journal Article December 2021
The Moyal-Dirac controversy revisited
B J Hiley "In conventional relativistic quantum mechanics, the Clifford algebra made its appearance indirectly as an attempt to remove the negative energy that arises in the relativistic expression for the energy, E = ±√p2 + m2. (We use natural units throughout).... However what Dirac had actually discovered was that α and β were elements of the Clifford algebra C1,3. The Pauli spin matrices had already alerted us to a possible role for the Clifford algebra, but the Schr¨odinger theory seemed not to require a Clifford algebra. . we see that the Schr¨odinger theory can also be discussed in terms of a Clifford algebra. ...instead use an element of a minimal left ideal to carry the information normally carried by the wave function. Thus once again we can work entirely within the algebra with no need to introduce an external Hilbert space structure."
This, of course, not only provides us with an alternative approach to the Dirac theory itself, but it also provides a way to generalise the Bohm model so that it can be applied to all relativistic particle situations."
"Here we have chosen to start this sequence with the conformal Clifford C2,4 since this contains the Penrose twistors [25]....This condition is sometimes known as the guidance condition, but here we have no ‘waves’, only process, so this phrase is inappropriate in this context."
And in relation to Penrose:
"this h-bar squared with a q and he calls this q the quantum potential"
"And Roger this talk is aimed at some of the work you are doing..."
"For a single particle it fails Einstein criteria of reality and completeness. The experiment proposed here requires heralded single photon counting."
Herbert J. Bernstein
" there are two topological types of closed curves γ on the surface of a sphere; those that encircle the rotation axis and those that do not. Since singularities are present, the above method of deriving the Lagrange bracket no longer holds and so any method using Poisson brackets will not hold." Hiley
Emphasis on "size" in original, p. 186, B.J. Hiley, "Phase Space and Cohomology Theory" in 1971, Quantum Theory and Beyond,
What is Planck constant?
"This is made possible by exploiting sequential weak measurements, allowing to measure non-commuting observables in sequence on the same state, on each entangled particle.... dynamical nonlocality seems to manifest the system’s dependence on future configurations in a two-time picture."
"...this implies the possibility of gravitational repulsion rather than attraction within the weak reality. Moreover, not only the gravitational mass, but also the inertial mass will be shown to admit a negative sign."
From Basil J. Hiley: ""the Baker bracket [Jordan product] does not reduce to the usual commutative product. ...The bracket plays an important role when energy (Hiley 2015) is involved. A careful study of Pauli’s (1926) application of the algebraic approach to the energy level structure of the hydrogen atom shows how a Jordan product enters into the calculation.v. As we have already pointed out, one of the advantages of the Moyal approach is that it contains classical physics as a limiting case as is clearly seen from equation (12). There is no need to look for a one-to-one correspondence between commutator brackets and Poisson brackets, a process which fails as was demonstrated by the well-known Groenewold-van Hove “no-go” theorem (Guillemin and Sternberg 1984). "Proceedings of the Royal Society of New South Wales Journal Article December 2021
The Moyal-Dirac controversy revisited
B J Hiley "In conventional relativistic quantum mechanics, the Clifford algebra made its appearance indirectly as an attempt to remove the negative energy that arises in the relativistic expression for the energy, E = ±√p2 + m2. (We use natural units throughout).... However what Dirac had actually discovered was that α and β were elements of the Clifford algebra C1,3. The Pauli spin matrices had already alerted us to a possible role for the Clifford algebra, but the Schr¨odinger theory seemed not to require a Clifford algebra. . we see that the Schr¨odinger theory can also be discussed in terms of a Clifford algebra. ...instead use an element of a minimal left ideal to carry the information normally carried by the wave function. Thus once again we can work entirely within the algebra with no need to introduce an external Hilbert space structure."
This, of course, not only provides us with an alternative approach to the Dirac theory itself, but it also provides a way to generalise the Bohm model so that it can be applied to all relativistic particle situations."
"Here we have chosen to start this sequence with the conformal Clifford C2,4 since this contains the Penrose twistors [25]....This condition is sometimes known as the guidance condition, but here we have no ‘waves’, only process, so this phrase is inappropriate in this context."
And in relation to Penrose:
"this h-bar squared with a q and he calls this q the quantum potential"
"And Roger this talk is aimed at some of the work you are doing..."
"For a single particle it fails Einstein criteria of reality and completeness. The experiment proposed here requires heralded single photon counting."
Herbert J. Bernstein
" there are two topological types of closed curves γ on the surface of a sphere; those that encircle the rotation axis and those that do not. Since singularities are present, the above method of deriving the Lagrange bracket no longer holds and so any method using Poisson brackets will not hold." Hiley
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