Tuesday, May 12, 2009

The Inadequacy of Everettian Accounts of Evolution, Probability, and Scientific Confirmation

This is certainly a provocative title. The manuscript, which is a chapter in an upcoming book, I would guess, directly questions whether Everette's "Many-World" model for quantum theory is in fact adequate, or whether it has actually failed.

Abstract: There is a compelling intellectual case for exploring whether purely unitary quantum theory defines a sensible and scientifically adequate theory, as Everett originally proposed. Many different and incompatible attempts to define a coherent Everettian quantum theory have been made over the past fifty years. However, no known version of the theory (unadorned by extra ad hoc postulates) can account for the appearance of probabilities and explain why the theory it was meant to replace, Copenhagen quantum theory, appears to be confirmed, or more generally why our evolutionary history appears to be Born-rule typical. This article reviews some ingenious and interesting recent attempts in this direction by Wallace, Greaves, Myrvold and others, and explains why they don't work. An account of one-world randomness, which appears scientifically satisfactory, and has no many-worlds analogue, is proposed. A fundamental obstacle to confirming many-worlds theories is illustrated by considering some toy many-worlds models. These models show that branch weights can exist without having any role in either rational decision-making or theory confirmation, and also that the latter two roles are logically separate. Wallace's proposed decision theoretic axioms for rational agents in a multiverse and claimed derivation of the Born rule are examined. It is argued that Wallace's strategy of axiomatizing a mathematically precise decision theory within a fuzzy Everettian quasiclassical ontology is incoherent. Moreover, Wallace's axioms are not constitutive of rationality either in Everettian quantum theory or in theories in which branchings and branch weights are precisely defined. In both cases, there exist coherent rational strategies that violate some of the axioms.

It's 26 pages long, and at this point, I haven't had the chance to read it yet. But you might have time, so I'm not going to deprive you of the pleasure (torture?) of reading it. :)



Matt said...

I skimmed it, and I must say that it's an incomprehensibly poor article.

How can modern-day article on interpreting quantum mechanics not discuss density matrices, partial traces, or decoherence? Go and do a search in the PDF for these terms!

There's no mystery to quantum theory anymore, and all this endless debate is just a waste of time.

The basic object in quantum mechanics is information--which, by definition, consists of probability schemes--encoded as the eigenvalues of density matrices.

That's the only postulate you need. Just one postulate. State vectors are now known not to be the fundamental objects anymore.

And the density matrix for a subsystem is obtained by the partial trace prescription, which is the unique prescription that is universal, self-consistent under composition, and independent of the degrees of freedom of the environment. From the partial trace prescription, we automatically get decoherence, the Born formula, and a resolution to the measurement problem. All of this has been done, and it all works perfectly.

What else is there? Where are the remaining mysteries?

Anonymous said...

A couple of points.

First, if it is indeed just a chapter from a forthcoming book, then the author may in fact end up discussing those other topics.

Second, all of what you say, Matt, only elucidates the mathematical structure of quantum theory. It doesn't provide physical insight. I don't agree that the mathematics is the theory.

I truly believe that the question that should always be at the back of a physicist's mind is: 'What does all this tell us about nature?'

Whatever the convoluted formalism, whatever the specific mathematical structure, answering this question as directly as possible should be the key objective for physicists.

Therefore, for me, the most illuminating notions I've heard on quantum theory involve field theory, where the fundamental concept is the field, particles being mere quanta/bundles of these. IMO, that's a more palatable, physical explanation, since it tells us what nature is doing.

Matt said...


Yes, but the fact is that now all of the actual, practical "paradoxes" of quantum mechanics have been resolved. There are no more gaps in the mathematics when one goes from experimental set-up to measurement. There's no more ad hoc, non-unitary "collapse" or anything like that. The mathematics of quantum mechanics is now smooth, and is both fully self-consistent and self-contained. We don't have to put things in by hand anymore to make the observable results come out correctly.

So the only remaining issue is human prejudice. Some people are "uncomfortable" with quantum mechanics as it is. Perhaps they think it's too mathematical, or abstract, or that it doesn't give them enough "physical insight" into totally unobservable phenomena.

Well, too bad. Unless the mathematics has holes in it, or there's some contradiction with any kind of conceivable experiment, or some violation of observation, then that's just the breaks. Mother Nature didn't consult with human beings before deciding how the world would work.