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January 20, 2004
Bohmian Mechanics
More than anything else, I dislike philosophy in my physics. Mainly because physicists are not any good at philosophy. The two fields need to be kept separate. So I present Bohmian mechanics: Quantum mechanics without the philosophy. And that is it, really. Those two equations – Schrödinger's equation and an evolution equation – predict all the results of orthodox quantum mechanics. No observers, no waveparticle duality, no wavefunction collapse, no playing dice with the universe (although the nonstochastic nature of the theory is not its main motivation). What I like best about Bohmian mechanics is its simple mathematical specification. Once you have the two basic equations, all the rest of quantum theory falls out in the math. Here is a slightly more indepth explanation by Sheldon Goldstein. I could put it more simply, but I do not love you all enough to create my own gifs for the equations. Bohmian mechanics (or the de BroglieBohm theory) is the minimal completion of Schrödinger's equation, for a nonrelativistic system of particles, to a theory describing a genuine motion of particles. For Bohmian mechanics the state of the system is described by its wave function together with the configuration Q defined by the positions of its particles. The theory is then defined by two evolution equations: Schrödinger's equation for and a firstorder evolution equation And here is an a very readable dialogue prepared by Roderich Tumulka which covers some obvious objections one might have to the theory. This is Sheldon's Goldstein's homepage, where you can find a large number of his published papers on Bohmian mechanics as well as the latest preprints. Like Quantum mechanics, Bohmian mechanics can be extended to include the creation and annihilation of particles. It is straightforward enough to create Bohmian Field Theories from Quantum Field Theories. The most serious objection to Bohmian mechanics is that it is nonlocal. This creates serious problems for Lorentz invariance. Because Bohmian mechanics has exactly the same predictions as Quantum mechanics, it predicts the correct result for the EinsteinPoldalskyRosen Experiment. (Bohmian mechanics actually has some close historical ties with EPR. It is the same Bohm and Bell for both.) Bohmian mechanics cannot get around the implied nonlocality in the way that QFT does because BM claims that the particles involved are all real, and that what you see is what you get. You can find one paper on Goldstein's website, published in Classical and Quantum Gravity, that shows one method of dealing with this: Opposite Arrows of Time Can Reconcile Relativity and Nonlocality. However, I do not find the approach suggested to be at all fruitful. It is an interesting thoughtexperiment, but not much more. I am not actually too bothered by the nonlocality of Bohmian mechanics. To me, it is already a substantial departure from relativity to claim that Lorentz invariance says nothing about particles and such, but rather certain mathematical constructs which are what is really real. A modification of Lorentz invariance based on the idea that particles and all that are real seems an equivalent way of dealing with the consequences of EPR to me. In fact, the Bohmian way of dealing with this puts the problem in a much clearer light. Either way, Bohmian mechanics is Quantum mechanics if Quantum mechanics were just another boring old theory with none of the philosophic romance. I happen to like it a lot more that way.
Posted by Thrasymachus at
11:12 AM


