Tuesday, August 19, 2008

Bohmian Quantum Mechanics

From time to time a friend of mine keeps trying to get me interested in "Bohmian" quantum mechanics. In a nutshell, this is a theory that was developed to try and restore some classical physics to the quantum world and explain the random and "spooky" nature of the quantum theory.

It does this with a device known as the "quantum potential". Whats kind of interesting is that it doesn't dispense with quantum mechanics as you know it at all. It incorporates it into a larger, albeit much more complicated picture. So Schrodingers equation is still with us.

Even more interesting, Bohmian quantum mechanics gives the same experimental predictions as "standard" quantum mechanics. As far as I know nobody has been able to propose an experimental test to distinguish between the two.

Bohmian quantum mechanics isn't exactly fringe, and its not cook science, but its not mainstream either. There are a couple of reasons for this. I would take a guess at them as:

1) Standard quantum mechanics is driven down the throats of budding physics PhD's. They probably won't even hear much about Bohmian quantum mechanics, so why bother with it?
2) Its mathematically nasty. For me, classical mechanics is actually messier and more difficult from a calculational standpoint than quantum mechanics is. Ordinary quantum mechanics just involves some simple PDE's and linear algebra, but classical mechanics is actually a bit more hairy. Bohm brings some of that back and adds to it. So the mathematical machinery might make it distasteful for some to bother with.
3) Occam's razor. Given #2, and the fact that standard quantum mechanics agrees with experiment, why pick the more complicated theory?
4) Religious adherence. I do think that there is a religious fervor about quantum mechanics as its currently laid out. It can't be wrong, can it?

Quantum mechanics is so bizarre that I don't think we should be surprised if someday its found there is more to it. Maybe it is Bohmian quantum mechanics. Isn't it easier to believe that there is a quantum potential filling space-time that guides particles and makes them entangled and all that, instead of just believing by fiat that there is spooky action at a distance and things aren't real until you measure them? I tend to take this view, but think that Bohmian quantum mechanics is on the right track but not the right answer. What Bohmian quantum mechanics really does is restore causality, which was Einstein's point of view. But I don't think Einstein was much of a fan of what Bohm came up with.

Here are some books to read if you're interested in diving into the controversy. First lets start with popular level books by Bohm himself:

Wholeness and the Implicate Order

The Undivided Universe

If you have some mathematical background but aren't an expert, this book is a great intermediate between a popular book and a textbook. I highly recommend it. But I can hardly believe they are charging $80 for it! I bought it way back in 1992 for $20. It has an excellent historical review on the Einstein-Bohr debates, gets to the core of the spookiness of quantum mechanics and introduces some concepts from Bohm:

The Meaning of Quantum Theory

Finally, the only known textbook on Bohmian Quantum Mechanics, sure to give you lots of headaches:

The Quantum Theory of Motion

I encourage everyone to take a look at the Bohmian theory. I for one, know I am real when nobody else is looking.

1 comment:

Arjen Dijksman said...

Nice to read your positive post on Bohmian mechanics. There is plenty of room in Quantum Mechanics for underlying common sense interpretations. Every quantum entanglement or erasure experiment should be analysed also in the light of a Bohmian or Broglian interpretation. The weirdness of the result then disappears. Or to recall a quote of Bell's:
"While the founding fathers agonized over the question 'particle' or 'wave', de Broglie in 1925 proposed the obvious answer 'particle' and 'wave'. Is it not clear from the smallness of the scintillation on the screen that we have to do with a particle? And is it not clear, from the diffraction and interference patterns, that the motion of the particle is directed by a wave? De Broglie showed in detail how the motion of a particle, passing through just one of two holes in screen, could be influenced by waves propagating through both holes. And so influenced that the particle does not go where the waves cancel out, but is attracted to where they cooperate. This idea seems to me so natural and simple, to resolve the wave-particle dilemma in such a clear and ordinary way, that it is a great mystery to me that it was so generally ignored."