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The Aharonov – Bohm effect illustrates the physicality of electromagnetic potentials, Φ and A, whereas previously it was possible to argue that only the electromagnetic fields, E and B, were physical and that the electromagnetic potentials, Φ and A, were purely mathematical constructs ( Φ and A being non-unique, in addition to not appearing in the Lorentz Force formula ).
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Aharonov and –
The Aharonov – Bohm effect, sometimes called the Ehrenberg – Siday – Aharonov – Bohm effect, is a quantum mechanical phenomenon in which an electrically charged particle is affected by an electromagnetic field ( E, B ), despite being confined to a region in which both the magnetic field B and electric field E are zero.
The underlying mechanism is the coupling of the electromagnetic potential with the complex phase of a charged particle's wavefunction, and the Aharonov – Bohm effect is accordingly illustrated by interference experiments.
The most commonly described case, sometimes called the Aharonov – Bohm solenoid effect, takes place when the wave function of a charged particle passing around a long solenoid experiences a phase shift as a result of the enclosed magnetic field, despite the magnetic field being negligible in the region through which the particle passes and the particle's wavefunction being negligible inside the solenoid.
There are also magnetic Aharonov – Bohm effects on bound energies and scattering cross sections, but these cases have not been experimentally tested.
An electric Aharonov – Bohm phenomenon was also predicted, in which a charged particle is affected by regions with different electrical potentials but zero electric field, but this has no experimental confirmation yet.
A separate " molecular " Aharonov – Bohm effect was proposed for nuclear motion in multiply connected regions, but this has been argued to be a different kind of geometric phase as it is " neither nonlocal nor topological ", depending only on local quantities along the nuclear path.
The Aharonov – Bohm effect is important conceptually because it bears on three issues apparent in the recasting of ( Maxwell's ) classical electromagnetic theory as a gauge theory, which before the advent of quantum mechanics could be argued to be a mathematical reformulation with no physical consequences.
Because of reasons like these, the Aharonov – Bohm effect was chosen by the New Scientist magazine as one of the " seven wonders of the quantum world ".
Similarly, the Aharonov – Bohm effect illustrates that the Lagrangian approach to dynamics, based on energies, is not just a computational aid to the Newtonian approach, based on forces.
Thus the Aharonov – Bohm effect validates the view that forces are an incomplete way to formulate physics, and potential energies must be used instead.
The Aharonov – Bohm effect shows that the local E and B fields do not contain full information about the electromagnetic field, and the electromagnetic four-potential, ( Φ, A ), must be used instead.
By Stokes ' theorem, the magnitude of the Aharonov – Bohm effect can be calculated using the E and B fields alone, or using the ( Φ, A ) 4-potential alone.
The magnetic Aharonov – Bohm effect can be seen as a result of the requirement that quantum physics be invariant with respect to the gauge choice for the electromagnetic potential, of which the magnetic vector potential A forms part.
Schematic of double-slit experiment in which Aharonov – Bohm effect can be observed: electrons pass through two slits, interfering at an observation screen, with the interference pattern shifted when a magnetic field B is turned on in the cylindrical solenoid.
The magnetic Aharonov – Bohm effect was experimentally confirmed by Osakabe et al.
( 1985 ) demonstrated Aharonov – Bohm oscillations in ordinary, non-superconducting metallic rings ; for a discussion, see Schwarzschild ( 1986 ) and Imry & Webb ( 1989 ).
The magnetic Aharonov – Bohm effect is also closely related to Dirac's argument that the existence of a magnetic monopole can be accommodated by the existing magnetic source-free Maxwell's equations if both electric and magnetic charges are quantized.
Aharonov and Bohm
* 1959 Yakir Aharonov and David Bohm predict the Aharonov-Bohm effect
Werner Ehrenberg and Raymond E. Siday first predicted the effect in 1949, and similar effects were later published by Yakir Aharonov and David Bohm in 1959.
The superconducting flux quantum was actually predicted prior to Aharonov and Bohm, by F. London in 1948 using a phenomenological model.
By constructing a situation in which the electrostatic potential varies for two paths of a particle, through regions of zero electric field, an observable Aharonov – Bohm interference phenomenon from the phase shift has been predicted ; again, the absence of an electric field means that, classically, there would be no effect.
Aharonov and effect
They have interesting optical properties associated with excitons and the Aharonov – Bohm effect.
In the terms of modern differential geometry, the Aharonov – Bohm effect can be understood to be the monodromy of a flat complex line bundle.
In fact for the Aharonov – Bohm effect we can work in two simply connected regions with cuts that pass from the tube towards or away from the detection screen.
For example, in classical statistical physics, quantization of a molecular motor motion in a stochastic environment can be interpreted as an Aharonov – Bohm effect induced by a gauge field acting in the space of control parameters.
Aharonov and was
This situation results in an Aharonov – Bohm phase shift as above, and was observed experimentally in 1998.
Recently, the debate reached the level of a journal publication, interpretation of the Josephson effect here was performed on the basis of the alternative theory of superconductivity as a manifestation of Aharonov – Bohm effect.
The argument of EPR was in 1957 picked up by David Bohm and Yakir Aharonov in a paper published in Physical Review with the title Discussion of Experimental Proof for the Paradox of Einstein, Rosen, and Podolsky.
Aharonov and B
Schematic of double-slit experiment in which Aharonov – Bohm effect can be observed: electrons pass through two slits, interfering at an observation screen, with the interference pattern shifted when a magnetic field B is turned on in the cylindrical solenoid, marked in blue on the diagram.
Aharonov and ).
In the case of the Aharonov – Bohm effect, the adiabatic parameter is the magnetic field inside the solenoid, and cyclic means that the difference involved in measuring the effect by interference corresponds to a closed loop, in the usual way ( see below ).
– and Bohm
* De Broglie – Bohm theory
* 1917 – David Bohm, American-born physicist, philosopher, and neuropsychologist ( d. 1992 )
* de Broglie – Bohm – Bell pilot wave formulation of quantum mechanics
In the resulting representation, also called the de Broglie – Bohm theory or Bohmian mechanics ,, the wave – particle duality is not a property of matter itself, but an appearance generated by the particle's motion subject to a guiding equation or quantum potential.
* December 20 – David Bohm, American-born physicist, philosopher, and neuropsychologist ( d. 1992 )
* April 14 – Oliver Bohm, Swedish ice hockey player
* October 27 – David Bohm, American-born physicist, philosopher, and neuropsychologist ( b. 1917 )
The de Broglie – Bohm theory, also called the pilot-wave theory, Bohmian mechanics, and the causal interpretation, is an interpretation of quantum theory.
The de Broglie – Bohm theory is explicitly non-local: The velocity of any one particle depends on the value of the wavefunction, which depends on the whole configuration of the universe.
De Broglie – Bohm theory is based on the following:
In de Broglie – Bohm theory, the wavefunction travels through both slits, but each particle has a well-defined trajectory and passes through exactly one of the slits.
While the ontology of classical mechanics is part of the ontology of de Broglie – Bohm theory, the dynamics are very different.
In de Broglie – Bohm theory, the velocities of the particles are given by the wavefunction.
In Bohm's original papers 1952, he discusses how de Broglie – Bohm theory results in the usual measurement results of quantum mechanics.
In summary, in a universe governed by the de Broglie – Bohm dynamics, Born rule behavior is typical.
Similarly, in the de Broglie – Bohm theory, there are anomalous initial conditions which would produce measurement statistics in violation of the Born rule ( i. e., in conflict with the predictions of standard quantum theory ).
It is in that qualified sense that Born rule is, for the de Broglie – Bohm theory, a theorem rather than ( as in ordinary quantum theory ) an additional postulate.
In the formulation of the De Broglie – Bohm theory, there is only a wave function for the entire universe ( which always evolves by the Schrödinger equation ).
To extend de Broglie – Bohm theory to curved space ( Riemannian manifolds in mathematical parlance ), one simply notes that all of the elements of these equations make sense, such as gradients and Laplacians.
For a de Broglie – Bohm theory on curved space with spin, the spin space becomes a vector bundle over configuration space and the potential in Schrödinger's equation becomes a local self-adjoint operator acting on that space.
In Dürr et al., the authors describe an extension of de Broglie – Bohm theory for handling creation and annihilation operators, which they refer to as " Bell-type quantum field theories ".
Hrvoje Nikolić introduces a purely deterministic de Broglie – Bohm theory of particle creation and destruction, according to which particle trajectories are continuous, but particle detectors behave as if particles have been created or destroyed even when a true creation or destruction of particles does not take place.
Antony Valentini has extended the de Broglie – Bohm theory to include signal nonlocality that would allow entanglement to be used as a stand-alone communication channel without a secondary classical " key " signal to " unlock " the message encoded in the entanglement.
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