Bohm interpretation

The Bohm interpretation assumes that the interaction between measuring apparatus and observed system breaks the wave function into a series of classically separated wave packets, corresponding to the possible outcomes of a measurement. The particle enters one of the packets and remains in that packet. All other packets can now be neglected and the complete wave function is replaced by a simplified one corresponding to the actual result of the measurement. The fluctuations in the fluid are never large enough to move the particle from one packet to another. 

Elucidation of the non-local holistic nature of quantum theory, first discerned by Einstein [3] and interpreted as a defect of the theory, is probably the most important feature of Bohm s interpretation. Two other major innovations that flow from the Bohm interpretation are a definition of particle trajectories directed by a pilot wave and the physical picture of a stationary state. 

Small wonder that Sommerfeld and Welker [76], when they first encountered this state for hydrogen, identified it as a situation in need of further investigation. The fact of the matter is that no logical description of this electronic state exists within conventional quantum theory. It makes sense only in the framework of the Bohm interpretation. 

The possibility that conformation as an inherent molecular property is revealed within the Bohm interpretation has never been tested. The fact that double bonds show an experimentally measurable barrier to rotation strongly suggests that there is a conformational factor at work and this could serve as a starting point for examination of the broader issue. 

It is not difficult to see that every scheme is strongly equivalent to a WHILE scheme relative to some fixed subinterpretation. Just add switch variables to indicate which statement is now being executed and let the interpretation to which you are relativized include constants and tests for constants. This is essentially the Bohm-Jacoppini result. 

In Equation 4.56, the real quantities p, v, and j are the charge density, velocity field, and current density, respectively. The above equations provide the basis for the fluid dynamical approach to quantum mechanics. In this approach, the time evolution of a quantum system in any state can be completely interpreted in terms of a continuous, flowing fluid of charge density p(r,t) and the current density j(r,t), subjected to forces arising from not only the classical potential V(r, t) but also from an additional potential VqU(r, t), called the quantum or Bohm potential the latter arises from the kinetic energy and depends on the density as well as its gradients. The current... 

Gas-phase reactions which result in nucleophilic displacement at a saturated, or an unsaturated, carbon centre have been observed in positive and negative ion chemistry. By far, the most widely occurring case is the formal analog of the Sn2 reaction initially reported by Bohme and Young (1970). The experimental determination of rate constants for SN2 reactions has received a great deal of attention as has the mechanistic point of view including the interpretation of the potential energy surface for the gas-phase reaction. 

The holonomy represents a parallel-transport operator around C assuming values in a non-Abelian Lie group G. (Interestingly, in the Abelian case, the holonomy has a physical role it is an object playing the role of the phase that can be observed in the Aharonov-Bohm experiment, whereas ,- itself does not have such an interpretation.)... 

The famous experiment proposed by Aharonov and Bohm [53,54] is schematically represented in Fig. 6. In such an experiment, a source emits an electron beam directed toward a wall in which two slits, located on each side of the beam axis, are located. A photographic plate (film) placed behind the slits records impacting electrons. After the emission of a large number of electrons by the source, the aforementioned film exhibits neat, clear, and dark fringes that are parallel to the slits. This result is interpreted as a manifestation of the wave nature of electrons. 

In search for an explanation, Aharonov and Bohm worked out quantum mechanics equations based on the measurable physical effect of the vector potential, which is nonnull in a region outside the solenoid. Like many other paradoxes in physics, including the twin paradox, the interpretation of this experiment proposed in 1959 was the subject of an intense controversy among researchers. This controversy is well summarized in a review article [55] and in other references of interest [56-67]. 

The interpretation of the original Aharonov-Bohm experiment implies mathematical considerations to be taken into account concerning ... 

Physicists have proposed several mechanisms to interpret the Aharonov-Bohm effect. We shall focus here on the most interesting of them. We shall first examine the case of the classical solenoid so as to define the problem on a sound... 

The first interpretation of the Aharonov-Bohm effect is based on the system of equations given by Olariu and Popescu [55, p. 423] where charge density and current density are suppressed ... 

A second interpretation of the Aharonov-Bohm effect was devised by Boyer [65,66], who used matter waves associated to moving electrons. Waves coming from each slit interfere with a phase shift = 2jidistance between two slits. If P is the impulse of an electron in the beam, the de Broglie relation gives us P 2nh/X. This results in the fact that the phase... 

Finally, some authors [71-75] proposed an interpretation of the Aharonov-Bohm effect based on the interaction between the electrons of the beam and electrons of the solenoid. The Aharonov-Bohm effect looses its mystery if we acknowledge that Newton s third principle is transgressed here. Indeed, if electrons within the solenoid cannot act on electron of the beams, electron beams can act on the electrons of the solenoid, by means of the momentum equations [70]... 

If the velocity U of an electron within the beam is constant outside the solenoid, the variation of the vector potential A as a function of time in the medium, and thus also in the solenoid, will induce a modification of the phase, as indicated by the equations written above. This will produce a modification of the boundary conditions on the boundary of the solenoid for the quantities a and b. We must also stress that the modification of the vector potential outside the solenoid is generated by either an external or an internal source feeding the solenoid. This can explain the existence of the Aharonov-Bohm effect for toroidal, permanent magnets. The interpretation of the Aharonov-Bohm effect is therefore classic, but the observation of this effect requires the principle of interference of quantum mechanics, which enables a phase effect to be measured. 

As is well known, de Broglie abandoned his attempts at a realistic account of quantum phenomena for many years until David Bohm s discovery of a solution of Schrodinger s equation that lends itself to an interpretation involving a physical particle traveling under the influence of a so-called quantum potential. 

J. P. Vigier, Derivation of inertial forces from the Einstein-de Broglie-Bohm causal stochastic interpretation of quantum mechanics, Found. Phys. 25(10), 1461-1494 (1995). 

J. P. Vigier, D. Bohm, and G. Lochack, Interpretation de l equation de Dirac comme approximation lineaire de 1 equation d une onde se propageant dans un fluide tourbillonnaire en agitation chaotique du type ether de Dirac, Seminaire de L. De Broglie, Institut Henri Poincare, Paris, 1956. 

J. P. Vigier and D. Bohm, Model of the causal interpretation of quantum theory in terms of a fluid with irregular fluctuations, Phys. Rev. 2(96), 208-216 (1955). 

The Hamilton-Jacobi form of the classical equations of motion has been shown to have provided the basis for the quantum-mechanical formulations according to Sommerfeld, Heisenberg, Schrodinger and Bohm. Each of these formulations inspired its own peculiar interpretation of quantum effects, despite their common basis. Each of the different points of view still has its adherents and the debates about their relative merits continue. Closer scrutiny shows that the Sommerfeld and Heisenberg systems assume quanta to be particles in the classical sense, although Heisenberg considered electronic positions to be fundamentally unobservable. 

Schrodinger and Bohm both accepted that quantum motion follows a wave pattern. To account for wave-particle dualism the interpretation of matrix mechanics, developed by Heisenberg and others, was extended on the assumption of probability densities. Schrodinger developed the notion of wave structures to simulate particle behaviour, but this model has been rejected almost universally and apparently irretrievably, in favour of proba-bities, arguably prematurely and for questionable reasons. Bohm s attempt to revive the wave interpretation advocated a literary interpretation of wave-particle dualism in the form of a classical particle accompanied and piloted by a quantum wave. 

Schrodinger, Einstein, Bohm and others who may have happened to support aspects of the model outlined here, were invariably accused of trying to revive a classical interpretation of non-classical events. The implied sin is that these individuals dared to recognize a causal structure where it is expressly forbidden by the Copenhagen doctrine. The exact opposite is probably closer to the truth What is more non-classical than a particle that consists of vibrations in the aether a particle with the ability to adapt its shape as dictated by the environment a particle that disappears into, or appears from, the wave structure of another particle a particle with continuous non-local mass and charge densities or a particle which is different from the mass points of classical mechanics However, this is an irrelevant argument. Whether a model is classical or quantal is of no consequence -what is important is that it leads to a reasonable interpretation of chemical phenomena. 

David Bohm gave new direction to Madelung s proposal by using the decomposition of the wave equation for a radically new interpretation of quantum theory. He emphasized the similarity between the Madelung and Hamilton-Jacobi equations of motion, the only difference between them being the quantum potential energy term,... 

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