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Blogger Ian Durham wrote on Jan. 8, 2014 @ 20:50 GMT
Scott Aaronson (in B&W because he's sophisticated)
We’re certainly kept rather busy at these FQXi conferences so I haven’t had a chance to sit down and write another blog post any sooner. At any rate, I’ll try to summarize a bit about yesterday’s talks and try to express any definitive conclusions or progress that has been made in the relevant areas.

The morning session was a bit of a grab bag of topics. Officially the title was "Measuring and manipulating information" but due to the dreadful weather in the US several speakers were heavily delayed and so Ray Laflamme, who was supposed to speak on Monday, actually swapped places with Andrew Briggs and spoke on Tuesday. Ray gave a general overview of his work on quantum error correction and talked a bit about some of the work he’s doing on the experimental foundations of quantum theory (again, I’ll defer the details to the conference videos which will be posted after appropriate post-processing). The other speakers were Scott Aaronson and Caslav Brukner. Caslav spoke about his work on indefinite causal structures. Scott’s talk was typically provocative in that he likened objections to the Church-Turing thesis to people who keep claiming to have invented perpetual motion machines that violate the Second Law of Thermodynamics (photo, above left).

I think it is safe to say that everyone agrees that, at the most fundamental level, the universe is stochastic in some sense, whether that be quantum or classical which ultimately means probabilistic in some fashioned (note that this does not necessarily mean it is completely random, just that it is governed by the laws of probability, e.g. think of a weighted coin versus a so-called "fair" coin). That being said, one of the interesting things that was pointed out by Steve Weinstein was that probabilistic theories don’t have any sense of dimensionality and yet they can lead to quantum mechanics (indeed, there has been some suggestion that quantum mechanics is merely a special class of a more generalized probabilistic theory). Quantum mechanics fundamentally includes the notion of dimension so the question is where does it come from?

At any rate, we could go even deeper than that as Gregory Chaitin has done (as someone pointed out) by asking where the intrinsic stochasticity, i.e. randomness (or near randomness) ultimately comes from. Chaitin’s claim is that it arises from mathematics which puts him firmly in Max’s camp. On this point--whether the universe is really purely mathematical or not--there is still definite disagreement.

Sean Carroll
The afternoon session dealt directly with information and cosmology and featured talks by Sean Carroll (photo, left), Anthony Aguirre, and Yasunori Nomura. Sean’s talk was predicated on an intriguing question (yes, I’m actually reporting that I agree with at least part of something Sean Carroll said--but only part!). In again looking at this intrinsic randomness in the universe that I mentioned before, he began by asking the question: what is the difference between a standard thermal fluctuation, i.e. the translational, vibrational and rotational modes of particles, and a quantum fluctuation? He addressed this from the standpoint of an Everettian interpretation (many-worlds) but noted that ultimately it is independent of the interpretation. He claimed, much to the dismay of most of the quantum people in the room (such as myself) that in quantum mechanics thermal states are static while they are not in classical mechanics. He says that making them non-static requires an observation, i.e. he says that they don’t exist if the system is in an energy eigenstate.

Personally, what I think Sean is doing is conflating certain pure states with static states. So, for instance, an entangled state is a pure state. But a pure state need not be static. I think what he’s trying to say is that the fluctuation requires repeated observation. So, for example (though this is not a thermal state example, but it works as an illustration), consider the phenomenon of neutral particle oscillations (sometimes called flavor oscillations) in which some neutral particle can turn into its anti-particle and then turn back into itself again. The only way to actually determine that such an oscillation is occurring in a system is to repeatedly make measurements on the system. Each measurement gives either the particle or its anti-particle, never both. The general "state" of the system is represented as some superposition or mixture of the particle and anti-particle states. In this sense, the "state" itself is fixed until acted on by an operator (i.e. observed). But his mistake is that such a state is not an energy eigenstate. In fact the energy eigenstate arises from the act of observation. He then extrapolates this to a de Sitter space which has no observers and thus concludes that such a space has no quantum fluctuations and thus no randomness at its core. The group seemed to be split along disciplinary lines in whether or not they would agree with this, as I mentioned. But I really think that he’s mixing his quantum mechanical metaphors here (not to mention the fact that I have to wonder a bit what this had to do with information).

Alan Guth also spoke and, in particular, discussed the fact (which I made to several people independently at dinner one night) that time-reversal is really a full CPT reversal (there’s a bit more to it than that, but I’ll leave it there for now). At any rate, his key idea is that if the maximum entropy is infinite, then any realistic entropy is low. This relates to some of the discussions from the last conference two-and-a-half years ago: the "problem" (which some of us don’t think is actually a problem) of the low entropy early universe. But if the universe is forever expanding, then the maximum entropy might be infinite in which case any initial entropy would appear to be low. Of course Alan also pointed out that infinity is not necessarily the limit of finiteness but that’s a discussion for another time.

Anyway, I said I wasn’t going to summarize all the talks individually and I just violated my rule a bit. The only thing I’ll say about Yasunori Nomura’s talk is that he reinforced the prevailing view (agreed to by nearly everyone) that quantum mechanics is of fundamental importance in any of these discussions.

"Information and Cosmology" panel
In the panel session, led by Anthony Aguirre, Anthony attempted to be provocative by asking if information and entropy were really the same thing (photo, left). Personally, I don’t think he’s being provocative at all. We play fast and loose with the language too often and it isn’t that clear that they really are the same thing (see my previous blog post from the conference). Actually, to be fair, his claim really was that there is only indexical information (something Alex Vilenkin spoke about briefly). This is a fascinating idea and relates to some pure mathematics work done by a colleague of mine, Steve Shea. It’s a bit lengthy to explain in this post, but I’ll add a post about it a bit later. At any rate, Anthony also (provocatively) claimed that an infinite universe and a really, really, really big (but finite) universe might not be observationally distinguishable (and, believe it or not, the two provocative claims actually are related!).

Additional discussions during the panels session served to further accentuate the fact that the cosmologists and the quantum folks really speak vastly different languages. In particular, the cosmologists make numerous claims about probability theory that no quantum person (particularly anyone who has read E.T. Jaynes) would ever make. But then the discussion devolved into one about the quantum measurement problem.

So, if there was a single, consistent thing everyone from yesterday could agree on, I would say that it was the fact that quantum mechanics is of fundamental importance to any discussion of the nature of information, how it is processed in the universe, and, frankly, to anything else in physics, for that matter.

--

Ian Durham is a quantum physicist and FQXi member based at Saint Anselm College, New Hampshire. You can visit his blog here.

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Peter Warwick Morgan wrote on Jan. 8, 2014 @ 21:28 GMT
"what is the difference between a standard thermal fluctuation, i.e. the translational, vibrational and rotational modes of particles, and a quantum fluctuation?" An answer to Sean Carroll's question, at least for free quantum fields, is that thermal fluctuations are translational and 3-dimensional Euclidean invariant, whereas quantum fluctuations are Poincaré invariant. From a free quantum field perspective, there is no other difference. See my Physics Letters A 338 (2005) 8-12, arXiv:quant-ph/0411156v2, with the overlong title "A succinct presentation of the quantized Klein-Gordon field, and a similar quantum presentation of the classical Klein-Gordon random field". Of course one cannot be certain that this carries over nicely to interacting fields.

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Akinbo Ojo wrote on Jan. 9, 2014 @ 10:13 GMT
Concerning, Ian Durham's post today: "At any rate, Anthony also (provocatively) claimed that an infinite universe and a really, really, really big (but finite) universe might not be observationally distinguishable (and, believe it or not, the two provocative claims actually are related!)"

Observationally indistinguishable, probably right. But IF the starting premise for the two is same, i.e. if both observers are agreed that there was a beginning ,which by definition is not an infinite state, then at what time was the infinity attained? Can infinity even be attained by definition, or is it not more correct to say "tends to infinity"? Can zero change to infinity without passing through the number line? On this premise, logically and in a mathematical universe, really, really, really big (but finite) must carry the day, unless there is no beginning.

Akinbo

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Thomas Howard Ray wrote on Jan. 9, 2014 @ 13:44 GMT
Aaronson's thesis fails the completeness criterion. That perpetual motion (continuous measurement functions) is forbidden by local methods of computation does not imply that it is forbidden by global physical principles of conservation.

Probabilism itself, in fact, is the most "absurdly constricted physical principle."

For if all physical quantities are conserved (see Emmy Noether), effective computation is not identical to continuous functions in nature. The local-global distinction created by information processing, whether the processor be a brain-mind or an engineered computing machine, is an arbitrarily effective boundary and cannot be otherwise.

Consider that Chaitin's Omega (halting probability of a universal Turing machine) is algorithmically incompressible and algorithmically random. That there is, therefore, no effectively calculable probability on the interval [0,1] strongly suggests that nature's "programming without a programmer" in Chaitin's words, is complete even while our own programming cannot be.

Tom

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Thomas Howard Ray wrote on Jan. 9, 2014 @ 15:24 GMT
" ... the cosmologists make numerous claims about probability theory that no quantum person (particularly anyone who has read E.T. Jaynes) would ever make."

I think with good reason, Ian. Cosmology necessarily assumes an undivided universe.

Which is why I think you are misreading Sean Carroll's point about the universe in an energy eigenstate being non-static when observation is introduced.

Quantum persons who object to many-worlds think quantum fluctuations are physically real and subject to a probabilistic interpretation. However:

Were this true, there would be no sufficient reason for the universe to exist at all. The probability for global decoherence would quickly approach unity. So long as we have a comprehensible universe with observers in it, I think we can reasonably say that thermal fluctuations are a real physical result of a non-static universe -- the participatory kind of universe of which Wheeler spoke and always manifestly local, constrained at the boundary of many-worlds bifurcation. ("The boundary of a boundary is zero.")

The static quantum fluctuations of many-worlds preserve the non-probabilistic universe against collapse of the wave function and the assumption of nonlocality. The logic of computability is not always the logic of science, particularly at the cosmological limit.

All best from Mars,

Tom

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