Tuesday, August 07, 2012

Quantum correspondence

I've been corresponding with a German theoretical physicist ("R") recently about quantum mechanics and thought I would share some of it here.

[R] Dear Prof.Hsu: I enjoyed reading your recent, very clearly written paper On the origin of probability in quantum mechanics very much. I discussed its subject matter oftentimes with Hans-Dieter Zeh ... We both think that many worlds is an idea that is probably true in some sense.
[ME] I have corresponded with Dieter over the years and read most (all?) of his work in this area. I would say we do not really disagree about anything.

To me many worlds (MW)  is very appealing and should really be considered the "minimal" interpretation of QM since I do not know of any other logically complete interpretations.

However, anyone who endorses MW should think very carefully about the origin of probability. Since MW is really a deterministic theory (at least from the viewpoint of a "global" observer not subject to decoherence), the only kind of probabilities it allows are subjective ones.

It is disturbing to me that most versions of me in the multiverse do not believe in the Born Rule (and probably then don't believe in QM!). MW proponents (e.g., Deutsch) would like to argue that, subjectively, I should not be "surprised" to be one of the few versions of me that see experimental verification of the Born Rule, but I am still uncomfortable about this. (The use of "most" above implies adopting a measure, and that is the root of all problems here.)

I hope this helps -- all I've done in the above paragraphs is recapitulate the paper you already read!
[ME] The "subjective" nature of probability is because the theory is actually deterministic. (Einstein would have liked it, except for the many branches in the wavefunction.)  
Let's suppose you live in a deterministic world and are about to flip a coin. You assign a probability to the outcome because you don't know what it will be. In secret, the outcome is already determined. To you, the process appears probabilistic, but really it is not. That is actually how MW works, but this is not widely appreciated. See esp. eqn 4 and figure in my paper.  
Copenhagen is not logically complete because it does not explain how QM applies to the particles in the observer (which is always treated classically). Collapse theories have different physical predictions than MW because collapse is not unitary.  
[R] Without going into the details, it seems absolutely clear to me that the main protagonists of Copenhagen, Heisenberg, Pauli, Bohr etc. did not believe that there is some explicit, QM-violating collapse mechanism. Do u agree? 
[ME] I can't read the minds of the ancients. The only clear formulation is that of von Neumann, and there a measurement outcome requires collapse = non-unitary projection. 
[R] A lack of free will is actually also the way out of Bell for Gerard (t'Hooft), and he convinced me that the idea is not so crazy at all. I don't know why this loophole got so little attention in Bell experiments. What is your take?

[ME] ... it is funny that everyone (physicists should know better) assumes a priori that we have free will. For example, the Free Will Theorem guys (admittedly, they are only mathematicians ;-) take it for granted.

... Strangely, not many people understand how MWI evades Bell without non-locality. There are a couple of papers on this but they are not well appreciated. Actually the result is kind of trivial. 
... MW has no problem with Bell's inequality because MW reproduces [see footnote #] the experimental predictions of the CI (Conventional or Copenhagen or Collapse Interpretation). An experimenter in a MW universe will not observe violation of Bell's inequality, or of the GHZ prediction, etc.  
Does this mean that MW avoids non-locality? That depends on what you mean by non-locality (I imagine this is relevant to your H-D anecdote). On the one hand the Hamiltonian is local and the evolution of Psi is deterministic, so from that perspective there is obviously nothing non-local going on:  Psi(x,t) only affects Psi(x',t') if (x',t') is in the forward lightcone of (x,t). From other perspectives one can speak of "non-local correlations" or influences, but I find this to be simply creating mystery where there is none.  
More succinctly, in a deterministic theory with a local evolution equation (Schrodinger equation with local Hamiltonian), there cannot be any non-locality. Just think about the wave equation.  
# The exception is macroscopic interference experiments as proposed by Deutsch that can tell the difference between reversible (unitary) and irreversible (collapse) theories. But these experiments are not yet technically feasible.  
[R] No sorry, I must think beyond "just the wave equation". I must think about "result of a measurement" when facing the Bell trouble.  
[ME] The great beauty of decoherence and MW is that it takes the mystery out of "measurement" and shows it to simply result from the unitary evolution of the wavefunction. There is no mystery and, indeed, everything is governed by a causal wave-like equation (Schrodinger equation). 
Rather than belabor this further I will refer you to more detailed treatments like the ones below:  
The EPR paradox, Bell’s inequality, and the question of locality, Am. J. Phys. 78 1 , January 2010.
[Reference 36] Our explanation of the many-worlds interpretation branching in the text follows similar descriptions by Don N. Page, “The Einstein–Podolsky–Rosen physical reality is completely described by quantum mechanics,” Phys. Lett. A 91, 57–60 (1982), [Inspec] [ISI] Michael Clive Price, “The Everett FAQ,” www.hedweb.com/manworld.htm, and C. Hewitt-Horsman and V. Vedral, “Entanglement without nonlocality,” Phys. Rev. A 76, 062319-1–8 (2007).
... As I said, "non-locality" must be defined carefully. Even standard QFT can appear "non-local" to the foolish (positrons go backwards in time!). Recall that MW is the most "realistic" of all QM interpretations -- Psi contains all information (including about what is happening in a given mind, the process of measurement, etc.), and Psi evolves entirely causally in spacetime. So any mystery about this is manufactured. In the papers linked to above you can track exactly what happens in an EPR/Bell experiment in MW and see that everything is local; but the result is trivial from the beginning if you grasp the points I made above.


Brett Olsen said...

So if you're concerned about wavefunction collapse in the Copenhagen framework, and think that the many worlds theory is a way to resolve that issue, what do you think about the Bohmian pilot wave models?

steve hsu said...

I'm not an expert on Bohmian models, but IIRC they have problems with relativity and fermions. But in other ways (determinism) they may be similar to MW.

Cliff said...

Hey Steve, nice post.

I have a question: I see you've referred to problems about "adopting a measure" as "the root of all problems here". Im wondering if you could say in a few words why this is the case, because I hear this a lot and I have never been able to figure out what the problem is. It seems to me that there are only two measures that matter in QM and there is absolutely no ambiguity why they are the essential ones: There is the measure corresponding to probabilities, which can easily be specified because probabilities correspond to something conserved with this choice and not any other choice, and then there is also the measure corresponding to amplitudes which you can easily specify as the unique one where linearity is satisfied.

So I do not understand what people are talking about when they say there is some measure ambiguity, because as far as I can tell there is only one choice that makes any sense. Am I missing something?

steve hsu said...

The slides labeled "Born Rule" at the link might help: http://duende.uoregon.edu/~hsu/talks/benasque_2010.pdf

Carson Chow said...

I don't see why just a single branch of the MW wave function as the only thing existing is not an equally if not more minimal interpretation of QM.

steve hsu said...

Just an aesthetic choice -- do you prefer that Psi is real, or do you hate the existence of the other branches? But there are testable consequences (see Deutsch experiment; if you choose the one branch option at some point there are some macro superpositions you will not allow).


Kyrilluk said...

In Bohmian pilot wave, you get determinism without having to postulate the existence of billions of different Universes. Particles, positions and trajectories have an ontological interpretation. Bell's inequality and Aspect experiments have proven that the quantum world is non-local therefore any theories that don't predict the same phenomena is just wrong. Regarding Aesthetic, if we take the two slits experiment, we have either the choice of thinking that the "thing" (don't call it a particle because according to copenhagen, it is not) pass through both slit before "collapsing" and becoming a particle on a screen, or that a new Universe get born every time that a particle goes through one of the slits (MW) or that the particle just goes through one slit while being guided by a "real wave" (Psi).

If you want a QM theory that is devoided of mystery and weirdness, may I respectfully suggest that you consider Bohm Mechanics?

Regarding the issue with relativity, the issue is the same as for Copenhagen's QM.

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