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Directing the strokes of Ockham's razor
From TBTF Log, 2001-05-27

Directing the strokes of Ockham's razor

Discuss On a private mailing list, someone posted a couple of links about recent progress towards the development of a quantum computer, with the comment: Quantum computers provide irresistible evidence that the multiverse is real. I replied to the list:

J.W.Burton will correct me if I'm wrong, I'm sure. Quantum computers do nothing of the kind. They provide yet another experimental proof (and exploitation of) complementarity and non-locality. Whether the nature of the universe that underlies these characteristics -- the quantum reality -- is as described by Bohr (the moon is really not there when no-one's looking at it) or by Bohm (a new universe branches from every quantum choice), or none of the above, is an open question.

The authority invoked in the first sentence is Joshua W. Burton, itinerant professional physicist and one of the more cogent voices on that list, or any other for that matter. Dr. Burton rose to my troll, as I had hoped he would, with the following essay. It's the most compelling summary that one could desire of the current state of thinking about quantum reality, and it is 100% guaranteed to make your head hurt.

This work, posted on the TBTF Log by permission, is Copyright © 2001
by Joshua W. Burton <jwb at post dot harvard dot edu>. I've added
a few links to Dr. Burton's essay, and if they point to nonsense then
the fault is mine.

At some level, this is an aesthetic question. Galileo and Kepler did not prove that the sun does not revolve around the earth -- indeed, since we now know that the Einstein equations (G = 8pi T, of course, not E_0 = m) have general covariance, we know that no such thing can ever be proved, and that we are free to believe earth, moon and sun are simultaneously stationary if we have some good reason to work in such twisted coordinates.

I agree that quantum computers offer nothing new beyond a cool exploit of Hilbert space projection.* Whether quantum computers offer lots of new computational light or just a handy flashlight for a few dark corners known classical algorithms have missed, they say nothing about quantum mechanics that we haven't known since Bell's inequality was proved in the early 1960s.

However, at some point aesthetic considerations in physics move beyond the realm of fashion and become compelling in the minds of most working physicists. I think the cited article is essentially correct in noting that quantum computers (along with inflationary cosmology) have been influential in convincing most practicing theoretical physicists that Everett sum-over-histories, or sometimes Cramer's so-called transactional interpretation, are more fruitful ways to look at QM than either Bohm's curious picture or the old Bohr / Heisenberg / Schroedinger mess usually called "the Copenhagen interpretation." (Once in England I saw a sign that said "railway closed due to labour action," and remember thinking, "No it's not, it's closed due to labor inaction." That's the sense in which Bohr had an interpretation of QM.)

For those who don't have mental images to go with the names, here is the best Hillel synopsis (or elevator story, as they now say in Dilbert land) I can supply:

(Note that I'm not claiming that any of these people actually said what I'm hanging on their names. It's just that these views are, as a sociological matter, so denoted by practicing physicists, who have a spotty record at best for historical accuracy in their myth-building.)

No one anywhere is arguing about the math, only about what it means. Sum-over-histories allows you to ask questions (like what boundary condition to put on the universe's wavefunction near the Big Bang, or on the infalling star's wavefunction inside a black hole) that the others can't even formulate; it's more powerful than Copenhagen in roughly the same way that Bayesian statistics are more powerful than classical, but when both can ask the same question, they (provably) get the same answer.

Anyway, quantum computing no more proves many-worlds than the phases of Venus prove heliocentrism. But in both cases the new facts eventually do direct the strokes of Ockham's razor.

* The Shor algorithm is a lot more specific than most people realize. Quantum computers happen to be able to achieve rapid prime factorization, but there is really no very strong reason to believe that prime factorization was hard, and you almost certainly can't leverage Shor to solve NP-hard problems. A few of my brightest friends suspect that P != NP may be proved within our lifetimes by showing that P <= QP << NP, simply because the class of problems that quantum computers can solve in polynomial time may be easier to constrain than classical P.

[ TBTF Log, 2001-05-27 ]


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