Bohm interpretation

The Bohm interpretation of quantum mechanics, sometimes called the Causal interpretation, or Ontological interpretation, is an interpretation postulated by David Bohm in which the existence of a non-local universal wavefunction (Schrödinger equation) allows distant particles to interact instantaneously.

The interpretation generalizes Louis de Broglie's pilot wave theory from 1927, which posits that both wave and particle are real. The wave function evolves according to the Schrödinger equation and somehow 'guides' the particle. It assumes a single, nonsplitting universe (unlike the Everett many-worlds interpretation) and is deterministic (unlike the Copenhagen interpretation). It says the state of the universe evolves smoothly through time, without the collapsing of wavefunctions when a measurement occurs, as in the Copenhagen interpretation. However, it does this by assuming a huge number of hidden variables, which can never be measured directly.

Background

The Bohm interpretation can be thought of as taking its cue from what one sees in the laboratory, say, in a two-slit experiment with electrons. We can see localized flashes whenever an electron is detected at some place on the screen. The overall pattern made by many such flashes is governed by a pattern closely matched by simple wave dynamics. Bohm and de Broglie posited that in the world of quantum phenomena, every kind of particle is accompanied by a wave which guides the motion of the particle, hence the term pilot wave. Mathematically, the pilot wave is described by the wavefunction of conventional quantum mechanics, but with an added piloting influence on the motion of the particles.

We can formulate the pilot wave's influence using a wavefunction-derived potential called the quantum potential, which acts upon the particles in a manner analogous to the interaction of particles and fields in classical physics. The pilot wave governs the motion of the particle and evolves according to the Schrödinger equation. Unlike the Everett many-worlds interpretation, the Bohm interpretation does not assume that the universe splits when a measurement occurs, and unlike the Copenhagen interpretation it is both objective and deterministic. It says the state of the universe evolves smoothly through time, with no collapsing of wavefunctions. Thus, Bohm called the hidden variable or pilot wave the quantum potential force.

Two-slit experiment

In this theory all fundamental entities, such as electrons, are point-like particles that occupy precisely defined regions of space at all times. When one performs a double-slit experiment (see wave-particle duality? ), one is concerned with noting the positions on a screen at which electrons arrive individually, one at a time. Over time, the positions at which the electrons are detected build up a pattern characteristic of wave interference. The usual Copenhagen interpretation is puzzling in that a single entity, the electron, is said to exhibit characteristics of both particle and wave. The Bohm interpretation accounts for the same phenomena by saying that both a particle and a wave do exist. The particle aspect is present because each electron traverses one slit or another, but never both. The wave aspect is present because the electron's pilot wave traverses both slits.

Thus, the Bohm interpretation resolves the puzzle quite simply and naturally. The electron's motion is guided — both in its choice of slits and its subsequent trajectory towards the screen — by the wave. The characteristic wave-interference pattern seen in the detection of the electrons arises by considering that the guiding wave exhibits interference in the familiar way one learns in the elementary physics of waves.

One might also note that what is measured in such an experiment — the position on the screen at which each electron arrives — is itself none other than the "hidden variable" the Bohm interpretation adds to the description, as we show in the formulation below. It might seem that the term "hidden variables" is an inappropriate name for the positions of particles, the quantity that is apparently most conspicuously manifested in the experiment. However, the particle's position has no influence on the guiding wave and hence is unobservable or "hidden" in some sense (see criticisms).

Nonlocality

Now we must address the question of nonlocality? . Within Bohm's interpretation, it can occur that events happening at one location in space instantaneously influence other events which might be at large distances: thus we say that the theory fails to obey locality, i.e., it is non-local. The response many physicists have to Bohm's theory is often related to how they regard this concept.

The question of nonlocality hinges upon the attitude one takes towards the Einstein-Podolsky-Rosen paradox[1] and Bell's theorem (see p.14 in[2]). There are often two camps into which people fall regarding the issue.

According to one camp, it has been shown that quantum mechanics itself is nonlocal and that this cannot be avoided by appealing to any alternative interpretation. The same Bell responsible for Bell's theorem was a member of this group (p. 196 in[3]): "It is known that with Bohm's example of EPR correlations, involving particles with spin, there is an irreducible nonlocality." If this is indeed the case, then the nonlocality of the Bohm interpretation can hardly be regarded as a strike against it.

Others see the consequences of EPR and Bell's theorem in a different way. They regard the correct conclusion to be related not so much to quantum theory itself, but only to deterministic interpretations of the same (i.e., to hidden-variable theories such as Bohm's interpretation). According to the people who think this way, what has been shown is that all deterministic theories must be nonlocal. For example, Niels Bohr was a member of this group. This group would claim that retaining orthodox quantum mechanics — with its nondeterministic character — permits one to retain locality, or at least to avoid the EPR type of nonlocality, at the expense of having no way to picture particles as objective elements of reality that occupy definite regions of space at all times. Armed with such a viewpoint, these physicists tend to be less receptive to Bohm's interpretation.

In contrast to this, others argue[4] that non-locality is independent of determinism, counterfactual definiteness and probability factorization, and notes that H.P. Stapp concludes that QM contradicts the locality postulate alone.

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Commentary

The Bohm interpretation is not popular among physicists for a number of scientific and sociological reasons that would be fascinating but long to study, but perhaps we can at least say here it is considered very inelegant by some (it was considered as "unnecessary superstructure" even by Einstein who dreamed about a deterministic replacement for the Copenhagen interpretation). Presumably Einstein, and others, disliked the non-locality of most interpretations of quantum mechanics, as he tried to show its incompleteness in the EPR paradox. The Bohm theory is unavoidably non-local, which counted as a strike against it; but this is less so now, now that non-locality has become more compelling due to experimental verification of Bell's Inequality. However the theory was used by others as the basis of a number of books such as the Dancing Wu-li Masters, which purport to link modern physics with Eastern religions. This, as well as Bohm's long standing philosophical friendship with J. Krishnamurti, may have led some to discount it.

Bohm's interpretation vs. Copenhagen (or quasi-Copenhagen as defined by Von Neumann and Dirac) is different in crucial points: ontological vs. epistemological; quantum potential or active information vs. ordinary wave-particle and probability waves; nonlocality vs. locality (it should be noted that standard QM is also non-local, see EPR paradox); wholeness vs. regular segmentary approach. In his posthumous book The Undivided Universe, Bohm has (with Hiley, and, of course, in numerous previous papers) presented an elegant and complete description of the physical world. This description is in many aspects more satisfying than the prevailing one, at least to Bohm and Hiley. According to the Copenhagen interpretation, there is a classical realm of reality, of large objects and large quantum numbers, and a separate quantum realm. There is not a single bit of quantum theory in the description of "the classical world"- unlike the situation one encounters in Bohmian version of quantum mechanics. It also differs in a few matters that are experimentally tested with no consensus whether the Copenhagen. or other, interpretation has been proven inadequate (and this inadequacy just glossed over due to inertia in physicist circles- not unlike the situation with cold fusion or any other ambiguous human situation. Most physicists are human.); or the results are too vague to be interpreted unambiguously. The papers in question are listed at the bottom of the page, and their main contention is that quantum effects, as predicted by Bohm, are observed in classical world- something unthinkable in the dominant Copenhagen version.

The Bohmian interpretation of Quantum Mechanics is characterized by the following features:

• it is based on concepts of non-local quantum potential and active information. Just as an aside-one should mention that Bohmian approach is not new with regard to mathematical formalism, but a reinterpretation of the ordinary quantum mechanical Schrödinger equation (which under a certain approximation is the same as the classical Hamilton-Jacobi equation), which simply, in the process of calculation, gives an additional term Bohm had interpreted as a quantum potential and developed a new view on quantum mechanics. So, Bohm's is (as anyone familiar with The Undivided Universe knows) not original mathematical formalism (it's just a wave function in radial form, and Schrodinger equation applied on it) -- but in interpretation that denies central features of ordinary quantum mechanics: no wave-particle dualism (electron is a real particle guided by a real quantum potential field); no epistemological approach (i.e., quantum realism and ontology).
• maybe the most interesting part about Bohm's approach is its formalism: it gives a new version of microworld, not only a new (albeit radical) interpretation. It describes a world where concepts such as causality, position and trajectory have concrete physical meanings. Putting aside possible objections with regard to non-locality, and possible triumphs of Bohmian view (for instance, no need for anything like complementarity principle) - one is left with impression that what Bohm offers is perhaps a new paradigm and absolutely a boldy rephrased version of the old and established quantum mechanics.
• Bohm emphasized that experiment and experimenter comprise an undivided whole. There is nothing separate from this undiv ided whole. The quantum potential Q does not go to zero at infinity.

Criticisms

The main points of critics may be summarized to the following points:

• the wavefunction must "disappear" after the measurement, and this process seems highly unnatural in the Bohmian models
• the theory artificially picks privileged observables: while the orthodox quantum mechanics admits many observables on the Hilbert space that are treated almost equivalently (much like the bases composed of their eigenvectors), Bohm's interpretation requires one to pick a set of "privileged" observables that are treated classically - namely the position. There is no experimental reason to think that some observables are fundamentally different from others.
• the Bohmian models are truly non-local: this non-locality is likely to violate the Lorentz invariance; contradictions with special relativity are therefore expected; they make it highly nontrivial to reconcile the Bohmian models with up-to-date models of particle physics, such as quantum field theory or string theory, and with some very accurate experimental tests of special relativity, without some additional explanation. On the other hand, other interpretations of quantum mechanics - such as Consistent Histories or Many-worlds interpretation allow us to explain the experimental tests of quantum entanglement without any non-locality whatsoever.
• the Bohmian interpretation has subtle problems to incorporate the spin and other concepts of quantum physics: the eigenvalues of the spin are discrete, and therefore contradict the rotational invariance unless the probabilistic interpretation is accepted
• the Bohmian interpretation also seems incompatible with the modern insights about decoherence that allow one to calculate the "boundary" between the "quantum microworld" and the "classical macroworld"; according to decoherence, the observables that exhibit classical behavior are determined dynamically, not by an assumption

Source: http://en.wikipedia.org/wiki/Bohm_interpretation (Note: Explore external links here)