For example, if quantum chaos somehow causes decoherence (…) maybe quantum computers can never work.

Somewhat off-topic: Israeli mathematician Gil Kalai has been working for a few years on why quantum computers cannot work. Here are some slides from a talk he recently gave: Why Quantum Computers Cannot Work and How [pdf].

]]>Thanks for the links Eirik (and Jed). Quite a few people work in the “quantum chaos” field. I started my physics career working for Jim Bayfield, who was one of the first to observe signatures of chaos in microwave ionized 1-d hydrogen atoms (effectively, a quantum kicked rotor: not quite as pure as the one in Jed’s link though).

The Ford paradox is an idea which seems to have fallen through the cracks. Maybe with good reason, maybe not. Most folks don’t use plain old information theory. Since the Ford paradox always bothered me, and since I’m now qualified to check up on his information theory, I figured I’d write it up in hopes someone would tell me the answer.

Mantica is still at work on similar problems using the decoherence approach. I’m not sure it applies in general to very simple quantum systems. Usually, the mechanism for decoherence involves interaction with the environment, or with other parts of the system. I have a day job which has nothing to do with physics, so I haven’t fully digested those results, which are pretty technical. Professor Cvitanovic was kind enough to send me a paper which might be a way out of the paradox from the other direction, but again I haven’t fully digested it yet. More or less, it is the same argument that people use against simple mechanical devices solving NP-complete problems: there is always some noise, and in a chaotic system, it gets magnified to where it smears out the interesting new information. I think combining this idea with the idea of a quantum break time might put the issue to rest. The “quantum break time” being, effectively, how many eigenstates fit into a period of time, such that the wave function tracks the classical motion. My original dissertation topic was going to attempt to look for a break time, but someone at Rice (I think) scooped us on that. While I haven’t worked anything out yet (again, I got to eat: the taxman cometh, and I need a new consulting gig), this sort of analysis probably produces actual numbers one can apply to real world systems and interesting experiments.

Such ideas are, of course, important. For example, if quantum chaos somehow causes decoherence, as the abstract to the paper Jed linked implies (and I think the Zurek paper you linked, though I only have the abstract to go on), maybe quantum computers can never work. The SQUID paper, I dunno; he seems to just add in a decoherence term to get the right answer. That might in fact be the right answer, but it implies there should sometimes be a decoherence effect going on. Presumably that should be modeled somehow (aka, “what physical conditions justify adding this term?”), or at least brought into the formalism in a way which is motivated by experimental tests. I remember Bayfield mentioning SQUIDs as a neat place to look; I guess that is an example of why. The Kirilyuk papers are more radical; modifying the Schroedinger equation to make it fit the Gutzwiller trace formula! Dunno about that. Seems a waste of paper to change all them Schroedinger equations for aesthetic reasons. Still, I can relate; the first time I grasped the way the Gutzwiller trace formula works, my mind was blown as well.

]]>Thanks for the pointers. The following experiment seems quite relevant: http://arxiv.org/pdf/1207.5465v1.pdf The authors seem pretty focused on the experimental paradigm, avoid bombast and don’t draw large conclusions.

]]>http://arxiv.org/abs/chao-dyn/9510013, http://prl.aps.org/abstract/PRL/v80/i20/p4361_1) cite decoherence and interaction with the environment as the solution to the paradox, although I haven’t been able to explicitly connect what they’re saying with what Ford is saying yet.

As for experiments, I found this, which at least is an attempt: http://www.researchgate.net/publication/1903922_On_the_correspondence_principle_implications_from_a_study_of_the_chaotic_dynamics_of_a_macroscopic_quantum_device

The first author also had another paper with such a bombastic name that I thought it was one of those mock papers: http://arxiv.org/abs/physics/9806002

]]>Ah, OK. I do understand that the classical equations couldn’t be derived from the quantum ones if the classical systems have more information. Many computer models wouldn’t need n bits about the state at T_0 to derive the state at T_n, but if I understand you correctly now, then real world classical systems would, and so perhaps accurate computer models of them would as well.

]]>The information is there in the classical world where we can see it: why can’t quantum mechanics come up with the goods?

Obviously QM is a good theory. New physics only comes when we stretch theories to their breaking point. This could be one of these things. Or it could be a misunderstanding, which could lead to new understanding. Or maybe I’m just missing something.

Gravity is present in the quantized double pendulum. Anyway, you don’t need to use a double pendulum for this experiment: you could use a kicked rotor or a Bunimovich stadium or whatever you have lying around handy.

]]>It looks to me less of a paradox and more of a two finger salute to quantum mechanics, information which isnt there simply isnt there,so perhaps we should look in other places.

While quantum information theory is for all intents and purposes useless at the moment the tests of Bells theorem largely invalidating hidden variables pointed to something going on.

You can make the standard argument that entangled information is not information but I find that more of an exercise of semantics than good science,I don’t know if we can correctly model the informational content of a quantum system(as opposed to a single object) without a deeper understanding of this “information”.

A dumbshit digression is that while our individual quantum objects are producing non random effects their relative spacial displacement could be considered to be more random,while I know gravity is totally irrelevant at that scale but could we postulate that some kind of information exists as as a kind of variant geometric relation and gravity emerges from this at a macro scale due to weak convergence?

]]>You didn’t quite grasp what I said. To specify the state of the chaotic system at any time you need n bits of information about where it was at . That’s pretty much the definition of chaos in information theory terms. Quantum systems, you don’t need so much information. Quantum mechanics is compressible. Or at least it looks that way on paper. That doesn’t make any sense if you expect to derive the classical equations of motion from quantum mechanics; there isn’t enough *there* there.

Informally, you can imagine the classical analogue of a wavefunction as a generalized function – a distribution. It’s zero everywhere there are no particles, and the integral over a region containing the particle yields a finite answer. The classical analogue of a zero-sized particle in this scheme is a Dirac delta function, which is also the limit of a quantum wavefunction of one particle as its de Broglie wavelength goes to zero (or, equivalently, as Planck’s constant goes to zero). A delta function encodes a position in space with infinite precision. Hence they can encode an infinite amount of information and hence have aperiodic behavior.

Perhaps I’m misunderstanding the problem, but the Ford paper you linked is behind a paywall.

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