For those coming in and reading various Bohm sympathetic papers, they might be a little puzzled. What is the name of this theory? Are there multiple theories? What should it be called?

So here is my view on the matter. There are three good contenders for the name: pilot wave theory, deBroglie-Bohm theory, and Bohmian mechanics. They are all the same theory.

Pilot wave theory was the original name given by de Broglie. It is somewhat descriptive, but places an emphasis on the wave without informing on what are the beables of the theory. It also sounds weak to my ears.

deBroglie-Bohm theory was the choice given by Bell. It describes the two independent discoverers of this theory. But it seems non-descriptive to me. It tells someone nothing about the theory.

Bohmian mechanics is a middle ground. The mechanics is crucial. It suggests that this is a theory about particles. It also fits in nicely with its sibling theories of Newtonian mechanics, statistical mechanics, and quantum mechanics. All three of those theories have important links to Bohmian mechanics. It also gives credit to one of the inventors, albeit to the one who discovered it second. But more importantly, the name Bohm has been cemented with this theory. De Broglie’s name never was, as far as I know. He proposed it and then it disappeared into the dustbin of silence. Bohm’s theory did too in some ways, but it was Bohm’s work that inspired Bell and his results. For that, it is reasonable to be in Bohm’s honor.

I would also say that Bohmian mechanics has a nice ring to it. Names are not shorthand histories nor abstracts for a theory. It is nice if they are linked to history and descriptive, but more importantly it should be lasting. This is the name that does all of that.

Indeed, I would say its major problem is that many of those I talk to want to call it Bohemian mechanics. But that is hardly a reason to reject it.

I have heard arguments that Bohm disliked the name Bohmian mehcanics and that it is therefore disrespectful to use it for that reason. Unfortunately for some, the wishes of those who come up with the idea are rarely listened to. I remember a story about Zorn of Zorn’s lemma and how he was haunted his whole life by that being his claim to fame while he considered that work to be trivial and his later work to be more important. It is all in the name. Zorn had no hope to escape this fate given how nice it sounds. The same is true of Bohm. He just has a great name for theory naming.

Related to this concern is the belief that Bohmian mechanics is different from the theory that Bohm came up with in 1952. This is false. The presentation is different, but both theories have the same trajectories as outputs. That is, they are the same theories of particle motions. It is true that the approach taken here, and by Bell, and by de Broglie, emphasize the first-order nature of the theory while Bohm’s presentation had an air of being second-order, but that is in presentation only.

The emphasis on the probability current that is present throughout this site and the work of DGZ and Bell is different from Bohm’s emphasis. But even the role of the probability is present in his work.

So that is my two cents worth on the name. It sounds better than the alternatives and it seems roughly valid in description and history, if not perfect. Do not even get me started on Bohm’s later theory names of the causal interpretation and the ontological interpretation.

Dear Mr. Taylor!

Nice site!

I am sure that you know that Bohm himself preferred the names: hidden variables, causal interpretation (the quantum system of the particle plus the field is causally determined) and later ontological interpretation (the stochastic version of the causal interpretation) and you are right to say that both approaches have the same trajectories as outputs. But I think there is a minor difference between the both approaches: the origin of the quantum force, which influences the motion of the quantum particle, expressed by the quantum potential is highlighted in the second order ansatz. But this quantum potential has no analogue in classical mechanics (e.g. depending only on the form, doesn’t fall off with the distance…).

I think this was the reason, why Bohm didn’t like the name mechanics in Bohmian mechanics. The advantage of the second order nature is the link between Quantum world (if there is) and the Newton world, where e.g. it is possible to express the classical limit. But at the end it is a kind of flavor, which name you prefer.

Reference:

D. BOHM, B.J. HILEY, The Undivided Universe: An ontological interpretation of quantum theory, London: Routledge, ISBN 0-415-12185-X, 1993, Reprint 1995.

Best wishes from Germany!

Sincerely

K. v. B.

PS It would be very nice if there is space for the two approaches on your site.

Thank you for an interesting website.

Unfortunately the equations on the home page are not rendered as equations, but appear as something like TEX source code. I have tested the page under MacOSX 7.1, with current versions of Safari, Firefox and Chrome browsers.

Somehow the site got updated and wiped out the MathJax code. It should all work now. Thanks for posting this. And now I will get notified of comments.

@KVB, It is true that there is great value in the second-order view for the classical limit. It is how one derives it. But it is very misleading. One way out is what Bohm does which is to not call it a mechanics, to try make the distinction in the name. Our way is to emphasize the first-order nature of the particle motions with the equations. Discussion of the quantum potential is worthwhile and hopefully someday will be discussed here. The Hamilton-Jacobi equations are very useful in many instances for non-spin situations. In my thesis, I used them to find alternate explicit solutions to the harmonic oscillator. Unfortunately, my methods do not extend to spin and so I dropped that line of research.

The term mechanics to my ear means particles and not the kind of dynamics it is. I could easily be wrong about that, but that’s my viewpoint.

As for the other names, I dislike the term “interpretation” intensely. This is not an interpretation of quantum theory. This is a completion. The standard quantum mechanics is not a theory. It is vague about when collapse is to occur. Bohmian mechanics and many other “interpretations” are not. They are completions, actual theories, and they should be named as such.