In 1979, Bohm and Hiley discussed the Aharonov–Bohm effect which had recently found experimental confirmation Hiley's follow-up paper on the AB effect, 2013
Both Ehrenberg and Siday (1946) found this result very strange and totally
contrary to what they would expect. At that stage the vector potential A
was simply regarded as a mathematical symbol with no observable conse-
quences. Yet here, in quantum mechanics, it has an observable consequence.
So Hiley traces the discovery of this "effect" to 1939 in theory and to 1946 in experiment.
Recall that at this time, Siday was working at Edinburgh University in
Norman Fowler’s laboratory, while Born was then Tait professor of Natural
Philosophy at the same university, so he decided to invite Max Born to
his laboratory. David Butt2 shared the same laboratory with Siday and at
the time of the meeting, was sitting in the corner of the lab while Siday
and Born discussed the effect. Unfortunately he could not hear the actual
conversation, which lasted about 45 minutes, but he did see Born shaking
his head from side to side every so often, seemingly with incomprehension.
Butt was one of the Birkbeck group that carried out one of the first experiments to test for quantum non-locality holding over distances of up to 6m. [20 in 1975].
At that stage, the vector potential A was still
regarded as merely a mathematical convenience and could be gauge trans-
formed away. Therefore it should produce no physical effect. Furthermore
the effect was presented in a context that it appeared to be a problem in
designing electron lenses, not a general new effect.
On the other hand, the wave properties follow from the
covering group, namely, the [noncommutative] metaplectic group. What Ehrenberg and Siday
had discovered in their own way was that the homotopy group of the cov-
ering space was non-trivial and were on the way to discovering the notion
of a winding number. Alas being experimentalists, they would not have
known about these advanced mathematical structures, then or even later
when these techniques became more well known.
however because of the unexpected nature of the effect, people argued that as the magnetic
whisker produced an unshielded field, the effect may be due, after all, to
the field rather than the potential. This was wishful thinking. However the
appearance of Bayh’s results immediately showed that any arguments about
stray fields causing the effect could be ruled out. Since those early days a
number of more refined experiments have all confirmed the effect. The full
details of all these experiments can be found in a review article by Olariu
and Popescu [18]. Olariu, S. and Popescu, I. I., The quantum effects of electromagnetic
fluxes, Rev. Mod. Phys., 57, (1985) 339-436.
Wow - a Ph.D. thesis on metaplectic supervised by Hiley!
2006
Nonexistence of the AB Effect 1979
So that author is also published in the 1987 book , "Again About Old Stuff: The Aharonov-Bohm Effect" by A. Loinger (1987) insisting the AB effect is a "magical nonlocal" effect that doesn't exist in reality - it's conjured up by bad physics.
Therefore, there is no (magic or) nonlocal action of... on the electron....
But this argument amounts to the "Quantum Measurement" problem [difference between a discrete collapse and a continuous wave function probability] that is solved by noncommutivity!
In general the noncommutative correction (29) oscillates with respect to time. Here we use the maximum value to illustrate the method of probing the spatial noncommutativity, and estimate the experimental sensitivity to the noncommutative parameter. Because there is no phase shift on the commutative space, therefore, the observation of the phase shift means there is spatial noncommutativity.
Time-dependent Aharonov–Bohm effect on the noncommutative space
Fundamental Aspects of Quantum Theory
Vittorio Gorini, Alberto Frigerio
| Fundamental Aspects of Quantum Theory Volume 144 of NATO ASI B Series Volume 144 of NATO ASI series: Physics, ISSN 0258-1221 Volume 144 of NATO Science Series B: Volume 144 of NATO advanced study institutes series: Physics, B | |
| Editors | Vittorio Gorini, Alberto Frigerio |
| Contributor | North Atlantic Treaty Organization. Scientific Affairs Division |
| Edition | illustrated |
| Publisher | Springer US, 1986 |
| Original from | the University of California |
| Digitized | Sep 16, 2008 |
I just got the NATO science series on "fundamentals of quantum theory" containing a fascinating article by future Nobel Prize physicist (Zeilinger) who worked with the NSF administrator, my professor Herbert J. Bernstein. Zeilinger was the experimentialist while Bernstein was the theorist. So Bernstein isn't cited in Zeilinger's book chapter but Zeilinger cites the MIT lab where Bernstein was administrating the NSF grant through Hampshire.
Fundamental aspects of quantum theory
A Zeilinger, M Zukowski, MA Horne, HJ Bernstein, DM Greenbergerby V
So Bernstein lists this in his published research but in the actual book chapter/article he is not referenced.
This book chapter is followed up by two chapters (articles) dismissing the Aharonov-Bohm Effect as simply a misunderstanding of quantum physics. This book, then, reveals the deep chasm at the heart of quantum physics.
in QM, the WF's DOF/phase is typically ignored.
https://www.reddit.com/r/quantum/comments/ek6qiz/how_best_to_understand_the_aharonovbohm_effect/
This Reddit thread nicely describes the Aharonov-Bohm Effect in "layman" terms.
It's kind of boring to have to get weighed down in the technical details of physics - especially since I don't do math or equations or anything. I just study the concepts and enjoy the debate!
I find it fascinating that in this book I am now reading - the scientists are freaking out about the nonlocality being "magical." hahahaha. Because I know from my meditation training that magic is indeed real and is indeed nonlocal!! That's why I read this science.
Of course if science has been so wrong then the fact that our civilization is destroying life on Earth also should not be such a surprise, nor should the complete psychological denial that it is happening then surprise anyone.
We can do activism to try to stop the corporate-state elite attack on basic survival of life but what happens when so-called rational science can not agree on the foundation of reality?
The celebrated manifestation of a quantum wave func-
tion for a combined system is the nonlocal correlations
which are generated by entangled states. The AB effect
is conceptually different, since it can appear even if in the
state (8) there is almost no entanglement at all times....I hope that a general formal-
ism of quantum mechanics based on local fields will be
developed. It will provide a solution to the problem of
motion of a quantum particle in a force field even if there
is no potential from which it can be derived. Meanwhile
my assertion provides one useful corollary: If the fields
vanish at locations of all particles then these fields yield
no observable effect.
the AB phase which has observable manifestation is ac-
quired inside the interferometer in spite of the fact that
there is no particular place or time where this happens.
I have shown that this peculiarity disappears when all
relevant parts of the system are considered: the phase is
gradually acquired by the source of the electromagnetic
potential.
This result does not question the validity of the AB
effect and does not diminish the importance of its numer-
ous applications. It removes, however, conceptual claims
associated with the AB effect regarding non-locality and
the meaning of potentials. The AB effect does not prove
that the evolution of a composite system of charged parti-
cles cannot be described completely by fields at locations
of all particles. The potentials might be just a useful
auxiliary mathematical tool after all
Wow so Vaidman doesn't believe in the AB Effect either! dang
That's what Basil J. Hiley developed through noncommutativity!! A quantum local momentum.
the noncommutative Aharonov-Bohm, being a 2+1 dimensional
effect on the noncommutative plane (or punctured plane), is of great importance. In fact
the Aharonov-Bohm phase is the phase which appears in front of the wave-function of two
charged particles upon their exchange (for a review, see [18]).
The Aharonov-Bohm effect concerns the shift of the interference pattern in the double-slit
experiment, due to the presence of a thin long solenoid placed just between the two slits
[20, 21]. Although the magnetic field B is present only inside the solenoid, the corresponding Schroedinger equation depends explicitly on the magnetic potential A (non-vanishing outside the solenoid). Therefore, the wave function depends on A and consequently the interference
pattern shifts. However, due to the gauge invariance, the shift in the phase of the particles
propagator, δφ0, is gauge invariant itself and can be expressed in non-local terms of B.
Moreover, we have found that in the case of the NC-torus, the Casimir energy is positive, in contrast to the case of a usual commutative space. This can be very important in the large
extra-dimensional models [32]: The repulsive Casimir force can compensate for the attractive forces originating from the Kaluza-Klein modes and hence this can provide a stabilization of the compactification radius for extra dimensions.
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