Archive for April 2006

Realists on the counter attack

25th April 2006

Martin Daumer, Detlef Duerr, Sheldon Goldstein, Tim Maudlin, Roderich Tumulka and Nino Zanghi, a collection of scholars noted for their advocacy or realist interpretations of quantum mechanics, and Bohmian mechanics in particular, have posted an article on quant-ph that attacks the idea that quantum theory is “fundamentally about information”. The article is a response to a recent essay in Nature by Anton Zeilinger, and is mainly a criticism of his particular viewpoint.

Most of their argument is based on the fact that interpretations like Bohmian mechanics offer a clear counterexample to various claims, such as that QM shows nature is fundamentally indeterministic and that the Bell and Kochen-Specker no-go theorems rule out realism. I think this is all fair enough, and I agree that it is well worth taking the time to become familiar with the Bohm interpretation if one is at all interested in foundations. It is quite amazing how often it can be used as an example to clear up confusion and misunderstandings about what we can infer from QM. On the other hand, this is a far cry from saying that Bohmian mechanics should be taken seriously as a description of reality. There are several arguments against doing so, which would take too long to go into right now. Perhaps I will do so in another post when I have more free time.

In any case, Zeilinger’s Nature essay seems a rather easy target to me. It was a short article, and there was clearly not enough space for any detailed arguments. Whether or not you think that Zeilinger in fact has any compelling arguments, there are many other contemporary approaches that also claim QM is about “information” in some sense, and it would be good to see a more in depth response to all of these from the realist camp. Examples include the quantum Bayesianism of Caves, Fuchs and Schack; the axiomatic approach of Bub, Clifton and Halvorson; and Hardy’s axiomatics.

Those of you who are waiting for Rovellifest 2 – fear not, for it is coming within the next week or so. For now, I feel like I need to write something on a topic I feel positive about, to aviod this blog descending into a sea of negative criticisms.

Rovellifest 1

17th April 2006

Carlo Rovelli has recently put 3 papers on the arXiv, which have attracted some attention within the blogsphere (see here, here, here and here). The one that concerns us here at QQ is the paper about EPR in the relational approach to QM. I don't want to comment on the particular argument in that paper, which seems fine as far as it goes, but I do want to say a couple of things about Rovelli's approach in general, since it seems to be a popular topic at the moment. The main ideas of the approach can be found in Rovelli's original paper.

Here is an (admittedly cartoonish) summary:

1. We should shift attention from things like the measurement problem and instead try to derive QM from the idea that it is a theory of the information about one system that is available relative to other systems.

2. Quantum states are not absolute concepts and the state of a system is only defined relative to some other reference systems. Different reference systems do not have to agree on this state. If they do come to agreement it is only after the reference systems themselves interact with each other according to some Hamiltonian.

3. The question of whether a system has some particular property has no absolute meaning. However, some property of a system can be well-defined relative to some other system, provided the systems happen to have interacted in such a way that the second system records the appropriate information about the first system.

4. All the relational states just represent the subjective point of view that one system has about another. There is no absolute meaning to such states and no meaningful "wave-vector of the universe" can be constructed because there is no external system for it to enter into relations with.

5. This is all just a twist on the usual kind of relationalism that we have in other physical theories, e.g. special and general relativity.

In my opinion, there is a good deal wrong with relational QM as formulated by Rovelli, although I am not particularly opposed to relationalism in general. In this post, I'll make some comments about 4 and 5. A forthcoming "Rovellifest 2" post will point out a problem with 3, which I believe is more serious.

To address 5, it is worth noting a striking disanalogy between relational QM and other sorts of relational theories in physics. For example, in Newtonian mechanics we are very used to the idea that that there is no absolute meaning of the position of a particle A, but you can define its distance to a reference system B. This is generally different from the distance of A relative to another reference system C. Similarly, there is no absolute notion of when two events are simultaneous in special relativity, but this is well defined relative to any inertial reference frame.

However, in these cases it is always possible to find some transformation that relates the descriptions relative to different reference frames, provided you know the relations between the frames themselves, e.g. the Lorentz transformations in special relativity.

Now consider a quantum system composed of a subsystem A and two observers B and C. Suppose both B and C separately interact with A, possibly measuring different observables on A. Relative to B, A is supposed to have some definite property after this interaction and similarly for C. However, you generally can't convert between B and C's description of the situation if you only know the state of B relative to C. You can if they happened to measure the same observable, but that's a very special case.

In fact, the only way to relaibly convert between different observers relative states of the same system is to know the entire "wave-vector of the universe", something that is meaningless for Rovelli due to 4.

So, it seems we are left with two options:

1. Add in a "state of the universe" so that one can reliably transform between different descriptions of the same subsystem.

2. Abandon the classical notion that one can reliably transform between different descriptions of the same system.

Adopting 1 would essentially entail accepting an Everettian/many-worlds type scenario, something that Rovelli is keen to distance himself from. Therefore, I conclude that he must accept 2.

Abandoning reliable transformations is not a completely absurd thing to do, but it is important to note that this is a departure from what we usually mean by the term "relational". I am still not entirely convinced that it is consistent, although I haven't managed to think up a scenario where it would cause a problem yet. My suspicion is that it might be attacked by a "Wigner's Enemy" type of argument of the sort that was levelled against Chris Fuchs' Bayesian approach by Amit Hagar, which seems much more relevant to the relational approach than to its original target.

N.B. "Wigner's Enemy" is a new name I just thought up for the argument.  I figure he must be an enemy rather than a friend because friends don't usually try to erase your memory. 

The Church of the Smaller Hilbert Space

13th April 2006

This is supposed to be a balanced blog, but my nonexistent readership may wish to know exactly what I do believe about quantum mechanics. The document below explains everything.

WARNING: The document below contains geek humor that also parodies the style of a certain well-known religious text. If you don’t find jokes about density operators funny and/or you are a devout religious person then you may find its contents offensive. The document below does not necessarily represent the opinions of its author, or indeed any person, animal, alien or sentient artificial intelligence, living, dead or yet to be born.

Ten Commandments of the Church of the Smaller Hilbert Space

Update:  The link is now working.  Apologies for the delay.

The Free Will Theorem

13th April 2006

Michael Nielsen recently posted a comment by John Sidles about a preprint by Kochen and Conway that was posted on the quant-ph arXiv yesterday. It's called "The Free Will Theorem", which is certainly a provocative title. Here's my comment on the paper that I left on Mike's blog.

Hmm… I had a look at this paper. The title sounds a bit crackpot, but given the status of the authors I was willing to give it a chance.

First of all the name “Free Will Theorem” opens a whole can of worms, which we probably don’t want to get into. Suffice to say, what they actually prove is an “indeterminism theorem”, i.e. they use a Bell-type argument + a no-signalling requirement to prove that nature must be indeterministic. I have heard similar arguments before, in particular Y. Aharonov and D. Rohlich mention it in their book, although I’ve never seen it written down formally before.

To call this a “free will theorem” one has to get into the debates about whether free will is compatible with determinism and, if not, whether indeterminism even solves the problem. Most contemporary philosophers seem to answer yes and no respectively, so I don’t think this theorem has much to do with free will, although it would take a lot more space to go through the arguments for and against thoroughly.

However, what I did think was interesting about the paper was the “hexagon universe” toy-model that they introduced in the second half of the paper. Given the current interest in understanding aspects of QM via simpler toy theories, e.g. nonlocal boxes and Spekkens toy theory, this might be a useful addition to the canon. I haven’t managed to decipher all the details of this model yet, so I’ll have to defer judgement on that.


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