The book Making sense of quantum mechanics (2016) overviews de Broglie-Bohmian mechanics, and examines its broader implications for quantum mechanics as a whole. I found it a gripping read. The author, philosopher-physicist Jean Bricmont, makes clear and mostly-convincing arguments, refuting many misconceptions about the meaning of quantum mechanics. I was led to the book by the online Stanford Encyclopedia of Philosophy, which recommended it as “a very good discussion”.
The de Broglie-Bohm (dBB) theory uses the wavefunction determined by Schrödinger’s equation, as in ordinary quantum mechanics (QM). It also assumes particles have definite positions and velocities at all times. These trajectories follow the probability current determined from the wavefunction. This contrasts with the standard interpretation of QM, where particles have no definite properties until a measurement or observation is made (except for eigenstates). Both interpretations make identical predictions about the outcomes of experiments, hence there is no experimental test that can distinguish between them. However, the conceptual implications are very important.
In §7, Bricmont sets up a populist history of QM, where Einstein and Schrödinger are dismissed as out of touch, and von Neumann and John Bell prove `hidden variables’ theories cannot exist. Then a cheeky dismissal: “all of the above is historically wrong.” Rather, Einstein was more concerned with non-locality than indeterminism. The view that QM is not complete should not be dismissed, but is a respectable position. Also von Neumann’s proof is overstated, and the community didn’t check it (see Pinch 1977 for the “sorry history”). Yet Bell “saw the impossible done” in the dBB model, and became its strongest proponent. Hence he clearly didn’t think it contradicted his theorem: Bell’s theorem doesn’t rule out hidden variables, only local hidden variables, or something weirder (?).
The Heisenberg uncertainty principle only concerns measurement outcomes, hence does not conflict with dBB (§5.1.8). Bricmont points out “all measurements can in the end be reduced to position measurements.” For example, a Stern-Gerlach device measures spin by whether particles move up or down. Similarly, momentum can be measured by comparing the position at two different times (§5.1.4). Yet even in dBB, many properties including spin cannot have hidden variables (§5.3.4).
Challenges for the theory include uniqueness, locality, and relativity. Concerning uniqueness, there are stochastic theories with random trajectories, and also an infinite number of theories with deterministic trajectories. While all concur with experiment, dBB is claimed as the most natural (§5.4.1). Concerning locality, Bricmont states that since Bell showed “the world is nonlocal, then the nonlocality of the de Broglie–Bohm theory is a quality, not a defect.” (§7.8) “Moreover, the nonlocality is of the right type… to reproduce Bell’s results, but not more, where `more’ might be a nonlocal theory allowing the transmission of messages.” (§5.2.1) But non-locality is a problem for relativity. The “nonlocal causal connections proven by Bell” occur instantaneously in QM, but in relativity simultaneity is relative, so which instant should be used? However this is a problem for quantum physics generally, not just for dBB: (§5.2.2)
…the problem of a genuine Lorentz invariance… in the face of EPR–Bell experiments is probably the biggest problem that theoretical physics faces today…
It is “the deepest unrecognized problem”, at least (§5.4.1; c.f. §8.4). One attempt at a solution is to introduce a preferred foliation (§5.2.2). [I have an idea on this, but it is early days…] At least `delayed choice’ experiments are not an issue, because in dBB “there is no sense in which our present choices affect the past.” (§5.1.4) There do exist Bohmian quantum field theories, though uniqueness is a challenge (§5.2.2).
Bricmont provocatively claims dBB “is a theory, while ordinary quantum mechanics is not” (§5.1.9); it is “not a physical theory” since it only predicts measurement outcomes (§5.3.5). Apparently, many philosophers require a scientific theory to be explanatory as well as descriptive. This includes realists (§3.3). Hence Bricmont calls dBB “the missing theory behind the quantum algorithm.” (§5.3.5) The Copenhagen interpretation, which emphasises the outcome of experiments, is influenced by positivism. However a strong “version of `logical positivism’… is almost universally rejected by philosophers of science nowadays (in part, because of the imprecision of the word `observable’)…” (§7.8; c.f. §8.4). This was news to me. Personally, I put much effort into conceptual understanding, so it is affirming to learn that trends are at least not opposed to this. I appreciate that dBB offers an underlying mechanism behind QM. But this does not imply it is the only deep explanation of the principles of QM, most obviously if `reality’ does not in fact work this way. 🙂
The mere existence of dBB refutes some popular claims about QM, says Bricmont: that QM ends determinism, that observers are special, and that QM can’t be understood. Yet “its main virtue is to clarify our ideas.” (§5.4.2) Bell wrote:
Should it not be taught, not as the only way, but as an antidote to the prevailing complacency? To show us that vagueness, subjectivity, and indeterminism, are not forced on us by experimental facts, but by deliberate theoretical choice?
Personally, my biggest motivation for learning de Broglie-Bohm theory was its definite velocities. In relativity, physical measurements depend on the observer. An observer’s velocity determines how to split spacetime, along with any tensors on it, into separate space and time parts. However the quantum hydrodynamics formulation also involves velocities, and is closer to the mainstream interpretation of QM than dBB (§5.4.1 cites some references). I also wonder how gravity might couple to each approach. dBB naturally suggests a particle’s exact location might gravitate, whereas the hydrodynamics view might suggest the entire wavefunction gravitates. Then, the theories would predict different experimental outcomes after all. Either way, quantum mechanics is now feeling less mysterious and more accessible, so Bell and Bricmont would be pleased.