1952: Bohm Interpretation

1The Bohm interpretation can be linked to deBroglie’s earlier idea of ‘pilot waves that guides elementary particles, such as electrons. In the context of deBroglie’s original idea, particles are guided by a wave function, which evolves according to the Schrödinger wave equation that never collapses. Thus, in this theory, electrons have a physical reality as particles, where in terms of the double-slit experiment, the particle must go through one slit or the other. However, the slit selected is not a random process, as it is governed by the pilot wave, which then results in the observed interference pattern. This said, the simultaneous determination of a particle's position and momentum is still subject to the usual uncertainty principle constraint. As already stated, the initial acceptance of the Copenhagen interpretation seemed to just side-step the issue of wave-particle duality by reducing all discussions to the probabilistic nature of quantum mechanics. However, in 1952, David Bohm rekindled the wider debate by suggesting that there was not just one ‘entity’, which might sometimes be described in terms of a particle and, at others, as a wave, but two ‘entities’ that simultaneously exist as a particle and a wave. Within this concept, the particle is said to exist within the region defined by the wave function [ψ], such that some might claim that the Bohm interpretation is more representative of a deterministic objective model. However, while this interpretation was capable of predicting the outcome of a quantum measurement and, to some extent, the implied superposition within the wave equations; the theory was dependent on the idea of ‘hidden variables’  and the subsequent idea of ‘non-locality’ in order to satisfy Bell's inequality.

The principle of locality states that an object is only influenced directly by its immediate surroundings. However, experiments were beginning to suggest that quantum entangled particles must violate either the principle of locality or question the scope of objective reality.

The validity of Bell's theorem, published in 1964, suggested that any classical hidden-variable theory, which is still consistent with quantum mechanics, would have to be non-local, requiring instantaneous or faster-than-light ‘interaction’ between physically separated entities.

Today, the Bohm or Bohmian interpretation, which Bohm himself described as a causal or ontological interpretation, is possibly still considered to be the main alternative to the Copenhagen interpretation. The Bohm interpretation is based on the following principles:

  • Every particle has a definite trajectory, although details of the trajectories position and momentum remain hidden.

  • The state of a N-particle ensemble is affected by a 3N-dimensional field, which guides the motion of the particles.

  • While deBroglie called this the pilot wave, Bohm referred to it as the ψ-field. This field influences the motion of the particles in the form of a quantum potential derived from the ψ-field.

  • This 3N-dimensional field is defined by a wave function that evolves according to the Schrödinger equation, although the positions of the particles do not affect the wave function.

  • The particles form a statistical ensemble with a given probability density.

In recent years there has been a resurgence of interest in Bohm’s interpretation. Initially, based on mathematical conjecture and limited experimental evidence, it appeared that Bohm's interpretation should be rejected. However, over time, there is an increasing school of thought, which has argued for the possibility of a causally hidden variables.

  • Double-Slit Experiment:
    In general terms, the Bohmian interpretation addresses the duality of both particle and wave properties raised within the double-slit experiment in quite an obvious way, based on its description above. The physical trajectory associated with each particle can only pass through only one slit, but Bohm’s 3N-dimensional [ψ] field, i.e. deBroglie’s pilot wave, can pass through both slits and, in so doing, guides the trajectory of particle to its final position within the observed inference pattern. However, while the description might be ‘quite’ obvious, the reality of this description is another matter entirely, as most aspects are still essentially conceptual.

  • EPR Experiment:
    In contrast, even the conceptual resolution of the entanglement within the standard Bohm interpretation is far from obvious, although not necessarily impossible. While some might question aspects of Bell’s theorem, the general consensus is that quantum entanglement is not compatible with local reality. Now just saying that the Bohm interpretation is non-local does not really explain anything. For example, there is an implicit suggestion that the non-local correlation of entangled particle states must be associated with some sort of superluminal, i.e., faster than light, signalling, which appears to contradict the theory of special relativity. In recent years, there have been several attempts to upgrade the Bohm interpretation within a relativistic framework by showing that special relativity does not explicitly reject the possibility of superluminal velocities under certain circumstances. While understanding these arguments goes beyond the scope of this discussion, it is argued that within a generalized form of relativistic mechanics, the particle is not only influenced by gravitational and electromagnetic potentials, but also by a scalar potential, e.g. as defined by Bohm. The exact dynamics of this field are, of course, conceptual, but speculate on the possibility of negative field values that could then lead to superluminal velocities.

Evolving out of this interpretation is a basic description of ‘Bohmian’ mechanics, which was originally rooted in a non-relativistic framework, despite the speculative discussion of non-locality above. However, originally, Bohmian mechanics might be said to have failed to address other aspects of modern theory, such as particle creation and annihilation characteristics, which is now defined within a relativistic quantum field theory. Such statements do not amount to a rejection of the Bohm interpretation, only a recognition of its limitations, as original published by Bohm in 1957, and the need to provide specific proposals, as per entanglement above, by which the Bohm interpretation might be upgraded. In this context, there now appears to be some renewed interest in challenging all of the original objections, raised by some of the most notable names in the development of quantum physics, e.g.

Bohr: 1934
"The quantum postulate implies a renunciation of the causal space-time coordinates."

 Born: 1949
"No concealed parameters can be introduced with the help of which the indeterministic description could be transformed into a deterministic one. Hence if a future theory should be deterministic, it cannot be a modification of the present one but must be essentially different. How this could be possible without sacrificing a whole treasure of well-established results I leave to the determinists to worry about."

Feynman: 1965
"How does it really work? What machinery is actually producing this thing? Nobody knows any machinery. Nobody can give you a deeper explanation of this phenomenon than I have given; that is, a description of it."

 Wheeler: 1983
"Every attempt, theoretical or observational, to defend such a hypothesis (the notion of hidden variables supplementing the wave function description) has been struck down."

Clearly, even today, the source of these quotes carries a considerable weight of authority, which those wishing to pursue a career in this field might well take into consideration before publicly disagreeing with them, as suggested by this next quote:

Mike Towler: 2009
Those who do not agree are unable to face the facts and disagreeing with the masters of the universe thus becomes bad for your career..

However, today, any search of the Internet related to the Bohmian interpretation will now throw up any number of papers that appear to support this basic concept, although many now extend or refine some of the arguments of Bohm's original interpretation. The following extracts from a paper by  Marius Oltean, in 2011, entitled: De Broglie-Bohm and Feynman Path Integrals, is cited purely by way of an example:

Abstract:
The de Broglie-Bohm theory offers what is arguably the clearest and most conceptually coherent formulation of nonrelativistic quantum mechanics known today. It not only renders entirely unnecessary all of the unresolved paradoxes at the heart of orthodox quantum theory, but moreover, it provides the simplest imaginable explanation for its entire (phenomenologically successful) mathematical formalism. All this, with only one modest requirement: the inclusion of precise particle positions as part of a complete quantum mechanical description. In this paper, we propose an alternative proof to a little known result—what we shall refer to as the de Broglie-Bohm path integral. Furthermore, we will show explicitly how the more famous Feynman path integral emerges and is, in fact, best understood as a consequence thereof..............

Conclusion:
The Feynman path integral is conventionally understood as a sum over all (infinite) possible paths connecting (q,t) and (q0,t0), each of these contributing with an amplitude found by integrating the classical Lagrangian. However, these paths are understood not to be real paths, i.e. along which the particle actually moves. (Of course, in orthodox quantum theory, such a concept does not even exist). Rather, they are seen merely as mathematical tools useful for computing the evolution of the wavefunction. In this sense, the Feynman path integral is nothing more than a reformulation of the Schrodinger equation. However, de Broglie-Bohm theory requires a bit more than this to make the quantum picture complete: namely, that the particle actually does move along one of the possible paths, in accordance with the guiding equation. As we have seen, the evolution of the wavefunction can in this case be calculated, quite elegantly, by integrating the quantum Lagrangian along this one single path i.e. the particle’s de Broglie-Bohm trajectory. It should then come as no surprise that the Feynman method of summing over all paths can be constructed with the de Broglie-Bohm theory at its basis.

While noting the possible shift in position on what might be described as the edge of mainstream physics, it is unclear how any 'hidden variable' interpretation puts quantum theory on any firmer ground than the Copenhagen interpretation, when it comes to the issue of empirical verification.