An Alternative Quantum Theory?

David Bohm: Introduction to Bohmian Mechanics

David Bohm. Source.

There is no doubt that quantum mechanics is one of the most irrefutably successful theories in the history of our existence. In the eighty years since its introduction, it has helped to explain phenomena ranging from Cooper pairs in superconductors to the detonation of stars. We have paid a price for these advances, however. We have abandoned some of our most basic assumptions about reality.

According to the orthodox interpretation of quantum mechanics, subatomic entities such as electrons or photons are either waves or particles — depending on how the physicist chooses to observe them. Actually, until they are observed, quantum entities have no real existence; they exist in a probabilistic limbo of many possible ‘superposed’ states. This did not sit right with many scientists for the better half of the 20th Century. However, no physicist was more dedicated to these conundrums or worked harder to resolve them than David Bohm who spent 40 years promoting an alternative to the orthodox interpretation.

As Scientific American notes, Bohm began questioning the Copenhagen interpretation in the late 1940s. According to the Copenhagen interpretation, a quantum entity such as an electron has no definite existence apart from our observation of it. We cannot say with certainty whether it is either a wave or a particle. The interpretation also rejects the possibility that the seemingly probabilistic behavior of quantum systems stems from underlying, deterministic mechanisms.

Bohm found this view unacceptable. He believed that the whole idea of science has been to say that underlying the phenomenon is some reality that explains things. It was not that the existing interpretation denied reality, but it merely said quantum mechanics implied there was nothing more that could be said about it. That we could very quickly exhaust all the information about a quantum system. Such a view reduced quantum mechanics to “a system of formulas”.

Bohm’s theory envisages a world of particles that all have definite momenta and positions, albeit the values of which are generally inaccessible. It is important to point out that the concept of momentum in Bohm’s theory is not straightforward. We will get to this in a bit. The fact that we can assign a value of mv to a particle is not directly related to what we would find if we performed a quantum mechanical measurement of momentum. The particles are deterministically “steered” or “guided” by a universal field which is described by the quantum wave function. It is sometimes said that Bohm’s view is a return to a classical picture of the world, embracing atomistic particularity and determinism. But it is also sometimes accepted that Bohm’s view offers a more complete description of reality.

In addition to the wavefunction, Bohm also postulates an actual configuration of particles that exist even when unobserved. The evolution over time of the configuration of all particles is defined by a guiding equation. The evolution of the wave function over time is given by the Schrödinger equation. Together, they come together to form the Bohmian interpretation.

The governing equation for Bohmian mechanics. In its non-relativistic form, the theory asserts the following: N material points (“particles”) move in 3-dimensional Euclidean space (denoted for simplicity as R³) in a way governed by a field-like entity that is mathematically given by a wave function ψ (as familiar from standard quantum mechanics). More precisely, the position Qk(t) of particle number k at time t obeys the above Bohm’s equation of motion. Where Q(t) = (Q1(t), . . . ,QN (t)) ∈ R³N denotes the configuration of the particle system at time t, mk is the mass of particle k, Im the imaginary part of a complex number, ψ is the wave function

Here, Psi is the standard complex-valued wavefunction known from quantum theory, which evolves according to Schrödinger’s equation.

Schrödinger’s equation

In 1952 Bohm proposed that particles are indeed particles — and at all times, not just when they are observed in a certain way. Their behavior is determined by a force that Bohm called the “pilot wave.” Any effort to observe a particle alters its behavior by disturbing the pilot wave. Bohm thus gave the uncertainty principle a purely physical rather than metaphysical meaning. In the sense that observing a particle induces an inherent uncertainty by interfering with the pilot wave.

Bohm’s interpretation gets rid of one quantum paradox, wave-particle duality, but it preserves and even highlights another: nonlocality, the capacity of one particle to influence another instantaneously across vast distances. Einstein had drawn attention to nonlocality in 1935 in an effort to show that quantum mechanics must be flawed. The Einstein-Podolsky-Rosen paradox rested on the idea that physics may never violate the principles of locality. The orthodox perspective of quantum mechanics, however, showed that it would be completely possible for a system of entangled states to act at a distance.

A letter by Albert Einstein to David Bohm when he was at Sao Paolo University and seeking a position in Israel. Credit.

Bohm’s account of quantum mechanics introduces some new ideas and a radically different general outlook on nature. However, it does not make any empirical difference: Bohmian predictions are identical to those of the Copenhagen interpretation. Bohm’s interpretation assumes that the initial conditions of a system satisfy the quantum equilibrium condition, that is, the probability distribution of the initial positions of the particles is given by the modulus of the wavefunction squared. It is conceivable that (parts of) the universe do not abide by this condition. It has also been argued that, although Bohmian theory matches quantum mechanics statistically, it could vary from it in individual cases, and this divergence might not be absolutely impossible to measure. It thus joins the ranks of a host of alternative interpretations and turns into a metaphysics of nature.

But just like any other theory, Bohm raises a paradox as well. Although he tried to make the world more sensible with his pilot-wave model, he also argued that complete clarity is impossible. Applying this concept to the quantum realm, Bohm proposed that the implicate order is a field consisting of an infinite number of fluctuating pilot waves. The overlapping of these waves generates what appears to us as particles, which constitute the explicate order. In a lot of senses, Bohm was tired of fitting nature’s circle into a square.

In Scientific American’s article, Bohm’s ideas are better motivated. I would suggest checking that out for a more complete understanding.,

Bohm rejected the claim of physicists such as Hawking and Weinberg that physics can achieve a final “theory of everything” that explains the world. Science is an infinite, “inexhaustible process,” he said. “The form of knowledge is to have at any moment something essential, and the appearance can be explained. But then when we look deeper at these essential things they turn out to have some feature of appearances. We’re not ever going to get a final essence which isn’t also the appearance of something.”

Thank you for reading.