There is one question I get asked frequently as a quantum physicist. It’s to do with my preferences regarding the interpretations of quantum mechanics. I am a realist in the sense that I think there is a world out there independent of us. I also do not like the idea that observers play an important role (some would say crucial) in quantum physics. I don’t think observers are needed at all, and, moreover, I am convinced that the only consistent way to account for everything (at present) is by treating the whole universe as a quantum system.

Photo by Scott Webb: https://www.pexels.com/photo/two-gray-bullet-security-cameras-430208/

Interestingly enough, there is one interpretation that ticks all of the above requirements. This is why the question I referred to earlier happens to be: “Why are you not a Bohmian?” A Bohmian is a person who subscribes to the de Broglie-Bohm, or hidden variable, interpretation of quantum mechanics. The interpretation is certainly realistic as its ontology (i.e., what it considers to be real) is basically that of classical Newtonian physics: particles have well-defined positions and momenta at the same time. Hence, it has the alternative name (hidden variable interpretation) since in quantum physics proper, positions and momenta are subject to the uncertainty principle and their values cannot be specified at the same time. The de Broglie-Bohm interpretation also does not require us to postulate a special status for any observers. In fact, observers and everything else in the universe are subject to the very same universal ontology. So far so good.

To make things even more interesting, this interpretation agrees with all the results of the standard quantum mechanics (which is why we call it an interpretation, for otherwise it would be a different theory). So, we can safely say that it has been “confirmed” by all the experiments done so far (just like the standard quantum mechanics).

Given all this good stuff, what’s my problem with it? I have basically two issues with Bohmian mechanics. One is that it is non-local. In other words, it admits spooky action at a distance: you do something over here and instantaneously something over there changes. Bohm himself emphasised this issue and actually thought of it as a welcome feature rather than a bug. His book on this topic, co-authored with Basil Hiley, is titled “The Undivided Universe” and you can already see from the title that they regard non-locality as the key aspect of the universe. Everything is non-locally connected to everything else.

The non-locality is needed because all the properties in this interpretation are described by c-numbers (i.e., the ordinary real numbers). And, if you want to reproduce quantum results – entanglement in particular, you then need action at a distance to correlate these c-numbers in such a way that they behave like quantum numbers (i.e., like matrices). After all, as John Bell told us, you have to give up either c-number-based reality or locality if you want to account for the correlations between quantum entangled states. I choose to give up the c-number-based reality, but Bohm chose to give up locality because he believed that giving up the c-number-based reality is a price too high to pay. Note that Bohmian non-locality does not imply signalling, so that the Bohmian mechanics fully complies with relativity (as I said, it really is just another interpretation).

But, if all Bohmian properties are c-numbers, where do we get the uncertainty principle from? Well, we assume that there is a (classical) uncertainty in the initial position and momentum of the particles and, since Bohmian mechanics is basically Hamiltonian, it preserves this uncertainty in time. So every particle is basically an ensemble of randomly distributed particles. This is another reason why I don’t like this interpretation, because it postulates an unavoidable initial uncertainty which, unlike with q-numbers, has no explanation for it (yes, many papers have been written on this very topic and some creative ideas have been suggested, but still, there is nothing convincing to put forward here as to the origin of this uncertainty).

Now, for my main point of discomfort with the hidden variable interpretation. It is extremely inelegant and cumbersome to use when calculating anything. Take the standard single-qubit interference experiment. We first put a particle in a superposition of being in two locations at the same time (I am using the language I like here), and then we bring these two back together to the same location to interfere them. All quantum experiments are of this kind. But, because Bohm does not want to accept that a particle can be in two places at once, his interpretation says that the particle is only in one of the two places. So how does it then interfere at the end? The trick is done by the so-called pilot wave (de Broglie’s terminology). The particle is guided by the pilot wave to interfere just as if it was in a superposition of two places in the first place. So, this pilot wave is the entity that has to exist in those two locations at the same time, even though it only acts on the particle in the (single) position where the particle is. This is where the non-locality of the interpretation creeps in.

Ok, you might say, tomayto, tomahto. Either the particle is in two places or the pilot wave is, I don’t see the big difference.

The difference is that we’ve (Bohm has) bent over backwards to avoid using q-numbers and give a c-number account of quantum physics, but – in the end – we still need the pilot wave (aka the quantum wavefunction) to lead us to the same conclusions (that are supported by all experiments). This is because the pilot wave ultimately obeys the same Schrödinger equation as the quantum wavefunction.

So, to many practising physicists, the Bohmian interpretation sounds the same as the standard quantum mechanics, but with just an awful lot of extra unnecessary classical baggage (such as particles being localised and having a well defined classical momentum).

There is, of course, another interpretation that says that observers are not needed and that the wave function is real and applies to the whole universe, and it goes under the name of Many Worlds. This is why my colleague David Deutsch says that “Bohmians are Many Worlders in denial”. Funny, but it is certainly true that these two interpretations are the only two realist ones.

Finally, how do Bohmians view quantum fields? You might not be surprised to hear that there is no consensus here. Some supporters say (Bohm was of this opinion) that the fields are classical but non-local and there are therefore no particles corresponding to them (so photons do not exist as excitations of the quantum electromagnetic field in Bohmian mechanics). Others believe that only particles should exist, even when it comes to fields (in other words, there are no fields according to this version of Bohmian mechanics). Each approach has advantages and disadvantages.

I find the Bohmian account of quantum fields interesting because, as some of my readers may know, I firmly believe that gravity will also turn out to be quantum mechanical. The experiments I have in mind to test this, however, won’t tell us if gravity is classical and non-local in the Bohmian sense or really underpinned by q-numbered gravitational potentials (and local, as I’d like to believe). Maybe, just maybe, the Bohmian interpretation will thus always remain an interpretation, and therefore choosing it over another interpretation will only be a matter of taste. I personally don’t like it, but I also don’t like Marmite, though I cannot give you any rational reasons for that…