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A response to “Quick Impressions of Bohmian Mechanics”

This is written as a response to:

Quick Impressions of Bohmian Mechanics

—-Addressed to the author of that blog.

I applaud you for taking the time to read about Bohmian Mechanics. Just as a word of warning,  Shelly Goldstein was my PhD advisor and  I consider myself to be very lucky to have worked with him.

To be clear, his chip (and mine) is about realism and clarity of theories, not Bohmian mechanics. For example, he and his group have formulated realist theories of GRW [flashes or mass-densities on space-time] and many worlds [matter densities on space-time whose time evolution is needed to distinguish the different realities, like channel interference on TV]. See Many-Worlds and Schrödinger’s First Quantum Theory and The Quantum Formalism and the GRW Formalism

One of the key questions that we realists pursue is, what is the theory about and what in the theory corresponds to reality? For Bohmian mechanics, it is about particles with positions that change over time. The correspondence to reality is a simple mapping of positions of stuff.

When you look around you, what is the stuff you see in your story of the world? Is your dog a bunch of eigenvalues? a wave function on configuration space?  How is a dog represented in QM? In BM, a dog is a bunch of particles moving around according to some dynamical equations. Pretty simple-minded and it works. Nothing magical at that point. But in QM, the magic is generally at that point. There is something called collapse which somehow makes a dog. Though collapse to what (and when), I am not sure, perhaps a sharply peaked wave function whose substantial region of support gives the blurred region of dogness?

For a bit of suggested introspection, ask yourself whether you would enjoy talking about quantum mechanics as much if it was not so mysterious. If a particle always traveled through one slit, would it not be a little less fun to talk about quantum mechanics? I looked through your recently posted slides and it struck me that you enjoy the fact that the cat is both dead and alive until someone looks (“ridiculous but true”). To me, I want a story of physics that has what I see being as close to the theory’s description as possible. I only ever see a cat that is either dead or alive. So is it not the case that a theory, such as BM, that reflects that reality is better than one that has to explain away the discrepancy with collapse or splitting or magic? All other things being equal, of course.

And as to the chipness, imagine working with people who asserted that 4=1. And they did stuff, got correct answers, and were generally very happy that the magic 4=1 equation solved their problems. Now you come along and explain about modular arithmetic and this is a different number system and that 4=1 is nonsense in the usual arithmetic, but not in modular arithmetic. And their response is, “Bah! You don’t get the new stuff. Why should we care about that stuff when we have our computations.” Imagine your frustration. You state something simple and obvious and get nothing but insulted. And you see people still telling the public that, “Yeah, just take 4=1 when you need to and it works. It is ridiculous, but true.” Argh. Also pause to think about how modular arithmetic would be illuminating and allow further informed extensions while “4=1″ may be a misleading basis to start from that people have to blindly accept.

And the unholy union? Well, the measurement stuff is there to make contact with physics labs. Obviously the theory itself does not care about measurement situations. Stuff just evolves. It just happens that when analyzing physics experiments, one needs to take into account the actual details of the experiment. A measurement of the position observable need not give the position of the particle. It will only do so if the experiment is setup correctly.

I do not think the article claimed to explain spin, but rather to state that the mystery non-classical stuff of spin is handled just fine. But there is a derivation of sorts for spin using Bohmian notions. In my  thesis, chapter 3 ends with deriving Dirac spinors and the Dirac equation from a Bohmian pursuit of a mapping from the value space of wave functions to the velocities of the particles. Clifford algebras and the spin stuff are exactly what is needed to do so.

In general BM, gives explanatory power and allows for clear-minded extensions. For example, BM easily extends to manifolds and vector bundles while QM is less easy due to the loss of global position and/or momentum observables. BM can be used on these spaces to put QM with modified observable notions on them as a computational formalism.

By focusing on what needs to be evolved (particle positions), all else follows. Identical particles, for example, require the proper unlabeled configuration space and that immediately gives the choice of boson vs. fermion. Focusing on the configurations leads to that choice. In QM, one can do the same, but then someone might ask, why can we change the configuration space and, actually, configurations of what?

Check out the work of Roderich Tumulka One particular nice set of papers is his work relating to black holes where BM leads to some interesting findings:

Space-Time Singularities and BM, part 1

Space-Time Singularities and BM, part 2

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