Interview on Static Limit

By Sean Carroll | December 12, 2010 9:53 pm

David Reffkin is a radio host at KUSF in San Francisco. His usual gig is classical music, but once a month he hosts a special called Static Limit where he delves into physics and cosmology. Here’s an interview he did with me a short while back. Right at the beginning we’re talking about this very blog, which I am now using to plug the interview, which is mostly about my book. This is what’s known as “synergy.”

(Those viewing in an RSS reader, you have to visit the page to click the audio link.)

David assumes the listeners have been following along previous shows, so we don’t spend too much time defining general relativity and the Big Bang; we go right for the cutting edge. But we also covered a lot of meta ground, about the process of doing physics. He also gave me the most comprehensive list of errata (mostly minor typos) for my book, so I know he read the whole thing!

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  • Mark

    Sean,

    The interviewer asks you about “many worlds.” But I disagree with your answer that eliminating the collapse time-evolution and sticking with only unitary time evolution requires that the universe literally spins out multiple, reified copies of the observer. Just because multiple formal copies of the observer exist in the mathematical formalism doesn’t mean that those copies literally exist in reality.

    Even for classically chaotic systems, we need to include an increasingly nontrivial probability distribution that involves many “copies” of our system, but only people who subscribe to “modal realism” (see, e.g., the Wikipedia entry) believe that classical probability distributions consist of multiple, literally real worlds. There’s little more reason to believe in many worlds for quantum mechanics than to believe in modal realism for classical mechanics.

    You can have a mathematical formalism that contains multiple copies of a system without that system literally existing in multiple worlds. For every quantum system you can compute its personal density matrix, so why not simply identify the eigenvalues of that density matrix as an ignorance probability distribution in which, under that probability distribution, the system only occupies one of the corresponding density-matrix eigenstates? Then you still only have unitary time evolution, but you don’t need to assume many worlds.

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  • http://www.sunclipse.org Blake Stacey

    The interviewer asks you about “many worlds.” But I disagree with your answer that eliminating the collapse time-evolution and sticking with only unitary time evolution requires that the universe literally spins out multiple, reified copies of the observer.

    This was one point at which I couldn’t make myself agree with From Eternity to Here. Constructing symmetric, informationally complete positive operator valued measures in arbitrary finite dimensions? Seems to me like a technical issue — a matter of manipulating Lie algebras with the proper ingenuity. Getting probability to make any sense at all in an Everettian world-view? That is a hard philosophical problem.

    (STANDARD ACADEMIC DISCLAIMER: Pointers into the literature are not to be construed as endorsements of all statements contained therein. No statement of formal affiliation with the Church of the Smaller Hilbert Space is intended or should be inferred. Offer void where prohibited.)

  • Ray

    “For every quantum system you can compute its personal density matrix, so why not simply identify the eigenvalues of that density matrix as an ignorance probability distribution in which, under that probability distribution, the system only occupies one of the corresponding density-matrix eigenstates? Then you still only have unitary time evolution, but you don’t need to assume many worlds.”

    Um. I don’t think this works. There’s no guarantee that the eigenstates of your density matrix will have a good classical approximation, and even if you can guarantee this at the start of your experiment, you can’t guarantee it later on (e.g. in the stern-gerlach experiment, maybe you don’t know the initial spin of your ions in the z direction before it’s measured, but you can follow that up by measuring the spin in the x direction.) Basically, you’ve just gotten back to the Schroedinger wavefunction formulation, not to a coherent semi-classical reality, which is what the world as we experience is like.

    Perhaps you think you can get around this with some extra cleverness. Bad news, if you want the apparently random behavior of quantum systems to be explained by ignorance of “hidden variables,” you either have to change quantum mechanics in a nontrivial way (this would be detectable at least in principle) or you have to abandon locality (e.g. bohmian mechanics.) See Bell’s theorem: http://en.wikipedia.org/wiki/Bell%27s_theorem

    So, in summary, you can get rid of some of the randomness associated with the density matrix by appealing to ignorance, but you can’t get rid of all of it. Thus we have three relatively unpalatable choices

    1) many worlds interpretation QM
    2) imposing the poorly defined concept of measurement and wave function collapse
    3) abandoning locality at the fundamental level (despite the fact that observers still can’t send information faster than the speed of light.)

    Of these, I like 1 the best, but tastes may vary. Admittedly, it’s a little hard to extract the Born rule from the many worlds interpretation, but it seems to be the only way of assigning probabilities that makes sense, and even without QM, probability is somewhat philosophically problematic.

  • Steve B.

    Ray–

    I don’t believe that your argument is correct. You write: “There’s no guarantee that the eigenstates of your density matrix will have a good classical approximation, and even if you can guarantee this at the start of your experiment, you can’t guarantee it later on (e.g. in the stern-gerlach experiment, maybe you don’t know the initial spin of your ions in the z direction before it’s measured, but you can follow that up by measuring the spin in the x direction.) Basically, you’ve just gotten back to the Schroedinger wavefunction formulation, not to a coherent semi-classical reality, which is what the world as we experience is like.”

    But we don’t need an ion to have a “good classical approximation.” We only need human beings (and other big objects) to have a good classical approximation. And decoherence is famously good at ensuring that big, warm, messy systems with lots of degrees of freedom and lots of environmental interactions (like people) tend to have density matrices that are diagonal in a nice, highly-classical eigenbasis. (Like the basis of coherent states that look like sharp gaussians in both position space and momentum space when hbar is negligible.)

    Decoherence singles out the required classical-looking basis for objects that we expect to look classical. All Mark’s approach seems to indicate is that we should take seriously the density matrices coming out of decoherence, giving them an ignorance interpretation, in which case the Born rule is quite natural.

    You don’t need _all_ systems (e.g., including tiny systems like electrons) to look classical, or have density matrices that are diagonal in a classical-looking basis (such as a basis of coherent states). You only need systems like people, cars, computers, measurement devices, etc., to look classical. The fact that electrons and ions tend not to have classical eigenbases is a feature, not a bug!

    As for Bell’s theorem, all that it implies is that quantum mechanics is weirder and more correlated than would be expected classically, and that some _non-signaling_ (i.e., information-free) influences can travel superluminally. (It’s the quantum no-signaling theorem that guarantees that no actual information is ever transmitted superluminally.) But phase velocities of EM waves can travel superluminally (without violating the constraints on information signaling from special relativity), as can lots and lots of other non-signaling phenomena. So who cares?

  • Ray

    “Decoherence singles out the required classical-looking basis for objects that we expect to look classical. ”

    Yes, but only at T0. At a later time, all bets are off. The point of the stern gerlach experiment is to take a system where a system that differs from the classical microscopically and evolve it into a system where there is a macroscopic difference from the classical.

    Sorry. Sean is absolutely right that we have a hard choice in interpreting QM.

    If you need an argument from authority to be goaded into paying closer attention, I can point to authorities from Bohr to Schroedinger to David Deutsch who saw the same thing.

  • Steve B.

    Ray–

    What do you mean “but only at T0”? The point of decoherence is that even if the big system doesn’t start in a highly classical state at the initial time T0 (although we generally safely assume that it does), it quickly evolves to such a state and stays in a basis of classical states for long periods. That’s one of the key reasons why people are so excited about decoherence!

    Classical states (coherent states being the paradigmatic example) are highly robust to environmental perturbations. Once the density matrix of a big system with many degrees of freedom with lots of interactions with a larger environment becomes diagonal in a set of highly classical states, it stays diagonal in that basis over long periods of time, at least as long as the environment keeps interacting with the system. Providing a heuristic argument to that fact is actually pretty easy; just look at the work of people like Zurek.

    Do you have an actual reference to support your contrary claim? If you’re going to attack the ability of decoherence to do its very raison d’etre, then you’d better have some more evidence to support your position.

    You write: “The point of the stern gerlach experiment is to take a system where a system that differs from the classical microscopically and evolve it into a system where there is a macroscopic difference from the classical.”

    I think maybe you’re misunderstanding the punchline of the Stern-Gerlach experiment. It’s true that the point of the experiment is to amplify quantum-mechanical effects into macroscopic observables. But that has nothing to do with any of the claims about decoherence and interpretations given above by me (and Mark, if I understand his points correctly). The apparatus sees quantum-mechanical behavior of the ions, but the apparatus itself doesn’t stop looking or behaving highly classical. The reading on the dial records a result that doesn’t agree with classical predictions about the behavior of the ions, but the dial itself always remains nice and classical, as required; the dial never looks like it’s in a superposition itself! And that’s all we need; we don’t need electrons or ions to look classical, just that macroscopic dials (and people) should look classical!

    There’s no contradiction with decoherence here; quite the contrary, because explaining why the Stern-Gerlach apparatus amplifies quantum effects to the macro-scale is precisely what decoherence is intended to do! If you’re going to claim that decoherence doesn’t do what is it’s whole purpose in life, then you’ve got a bigger argument than just with me.

    The remaining point of contention isn’t whether decoherence produces the correct density matrices, but how one supposed to interpret the density matrices that it produces. I’m of the perspective (and seemingly so is Mark up above) that we can just employ an ignorance interpretation to those density matrices, which is certainly less extravagant than many-worlds (and has none of the troubles with understanding the meaning of probabilities that one finds in many-worlds).

  • Ray

    ok Steve B.
    Here’s the mistake

    So decoherence says that it doesn’t take long for your system to evolve into a state that is diagonal in a space of semiclassical states. However, this says nothing about the eigenvalues. Note that if we take the ignorance interpretation seriously, then there is a unique density matrix representing reality as fully as possible. If it looks classical at macroscopic scales, then all of it’s eigenvalues are zero, except for a single eignevalue, which is 1. Evolving that forward necessarily leads to a density matrix that is diagonal in some set of semiclassical states, but it does not necessarily lead to such a state where the sole nonzero eignevalue is 1.

    To rephrase this in terms of the most famous example, schroedinger’s cat, decoherence says that the phase associated with the live cat will quickly randomize in comparison to the phase associated with the dead cat, but it does not imply that either of the associated amplitudes will decay to zero. Furthermore, you can modify the schroedinger’s cat experiment to include 2 cats where the first cat’s life depends upon the spin z component of a silver ion, while the second cat’s life depends upon a subsequent measurement of the same ion’s spin x component. There is no interpretation of quantum mechanics that doesn’t appeal to a nonunitary process like wavefunction collapse, in which the amplitudes associated with both cats’ lives have absolute value zero or 1.

    This is why decoherence is usually used in conjunction with the MWI, not as an alternative.

  • Steve B.

    Ray–

    You write: “However, this says nothing about the eigenvalues. Note that _if_ we take the ignorance interpretation seriously, _then_ there is a unique density matrix representing reality as fully as possible. If it looks classical at macroscopic scales, then all of it’s [sic] eigenvalues are zero, except for a single eignevalue [sic], which is 1.” (My emphasis.)

    Your if-then statement seems to indicate a confusion about the role and meaning of density matrices. There is absolutely nothing about classical mechanics that requires the eigenvalue distribution of a big system’s density matrix to be trivial, with only a single nonzero eigenvalue; where did you get that idea? Even in classical mechanics, a classical system whose effective classical dynamics is nonlinear will generally exhibit chaotic behavior and so will inevitably develop a nontrivial probability distribution, corresponding to a density matrix diagonal in a classical-ish basis with a nontrivial distribution of eigenvalues. That’s perfectly consistent with classical mechanics.

    Indeed, that’s precisely what we expect should happen in the classical limit of a quantum system; when deriving the classical limit, quantum effects manifest themselves as effectively nonlinear interactions, and so the quantum uncertainty gets transmuted into a nontrivial classical probability distribution for the density matrices of macroscopic objects like the apparatus, or human beings, all while those macroscopic entities remain diagonal in a highly classical basis. The classical limit of quantum mechanics is therefore seen to be semi-classical statistical mechanics.

    Your description of the Schrodinger-cat experiment in terms of decoherence is not correct; you’re using the language of state vectors, saying that the two live-dead components of the final state vector have random relative phases, but that neither amplitude is zero. That’s all well and good, but that’s not the full story of decoherence. What happens in any realistic scenario with a physical, macroscopic cat (whose cares about unrealistic scenarios?) is that the environment quickly couples to the system, and the density matrix of the cat quickly (and, given the number of degrees of freedom involved, irreversibly) diagonalizes to the expected classical basis, with a 1/2 eigenvalue associated to the classical alive-cat state and a 1/2 eigenvalue associatd to the classical dead-cat state. So in this one-world interpretation of quantum mechanics, we can safely say that the cat is alive or dead, with probability 1/2 for each possibility.

    The scenario of two cats works out the same way; it’s just a more complicated version of the argument above. The final state of the two cats is described by a combined density matrix with four states (alive alive, alive dead, dead alive, dead dead), each with probability eigenvalue 1/4. There’s nothing fancy going on here at all.

    Now, the natural objection is that there’s some sufficiently large system whose density matrix is still pure; what if we consider the whole galaxy, for example? Well, fine. But a cat is not a galaxy. If you want to know a specific system’s situation, you need to compute its own density matrix, and the results are precisely what one would expect from the usual understanding the classical limit.

  • Mark

    hey guys,

    I think Ray, you’re getting confused by thinking in terms of wave functions instead of density matrices. You speak with a certain level of authority about decoherence, but I’m not sure you fully understand the point or what’s going on with it, or are carefully following it all the way through to the end.

    At the end of the day, when you’re confused about what quantum mechanics is telling you about a certain system, try to carefully take into account all its interactions with other systems, like the environment, and then compute its personal density matrix to see what’s going on with it, and push through to really follow all the details; you’ll see that if you work at it, you’ll find that everything actually works out okay without any observable paradoxes.

    In principle, every system has a density matrix, even if it doesn’t always have a specific wave function because of entanglements to other systems. Trying to phrase everything in terms of wave functions can get very confusing, because you can’t even assign a wave function to a system that’s entangled to other systems, so you’re stuck with the wave function of the whole enclosing super-system; then you’re not even talking about the original system you were interested in the start with! You have to phrase questions carefully; if you want to ask what a particular system is doing, you need to look at its own density matrix, not the density matrix or wave function of any other system.

    Sure, at the end of the cat experiment, after the larger environment has gotten involved, there may be some huge, huge super-system that’s still not decohered to a classical-looking density matrix. But the definition of that super-system is growing in size at essentially the speed of light, as more and more of the universe gets irreversibly entangled with the outwardly-radiating thermal photons. The moment any part of the universe hears the news of the cat, it decoheres as well. So no big system ever experiences an observable contradiction to its own classical behavior.

    You have to really push your way through the decoherence story; if you stop halfway conceptually, it doesn’t always make complete sense. And if you want it to fail, maybe because you really secretly prefer another interpretation of quantum mechanics, then it’s always easy to find a superficial reason why it seems to fail and give a paradox. But if you really follow all the details to their logical conclusions, it really does work out pretty nicely. And decoherence safely allows you to give density matrices an ignorance interpretation, consistent with big systems really looking observably classical.

  • Ray

    “What happens in any realistic scenario with a physical, macroscopic cat (whose cares about unrealistic scenarios?) is that the environment quickly couples to the system, and the density matrix of the cat quickly (and, given the number of degrees of freedom involved, irreversibly) diagonalizes to the expected classical basis, with a 1/2 eigenvalue associated to the classical alive-cat state and a 1/2 eigenvalue associatd to the classical dead-cat state. So in this one-world interpretation of quantum mechanics, we can safely say that the cat is alive or dead, with probability 1/2 for each possibility.”

    exactly. And you can do this as many times as you want, making the eigenvalues shrink to 2^-whatever. In a classical system there is uncertainty due to ignorance, but the amount of ignorance doesn’t increase. Now, you could just say there’s an infinite amount of information you don’t know about pretty much any system. But then you’re proposing hidden variables all over again. Just because your using density matrices instead of wavefunctions doesn’t make the problem go away. Your hidden variables still need to be nonlocal. Now if you don’t have a problem with defining reality in such a way that real but unobservable interactions aren’t local, be my guest. Interpretation of QM is all semantics anyway.

    Now I get that I’m outnumbered on this particular comment thread, so you guys are probably going to go on thinking you’re right. But if you are right, you should be able to answer the following. In my two cats scenario, what exactly are the two bits of information the observer is ignorant of at the beginning of the experiment?

  • Ray

    Also, if you like wikipedia better than me, see the following.

    “Decoherence does not generate actual wave function collapse. It only provides an explanation for the appearance of wavefunction collapse. The quantum nature of the system is simply “leaked” into the environment. A total superposition of the universal wavefunction still occurs, but its ultimate fate remains an interpretational issue. Specifically, decoherence does not attempt to explain the problem of measurement. Rather, decoherence provides an explanation for the transition of the system to a mixture of states that seem to correspond to those states we perceive as determinate. Moreover, our observation tells us that this mixture looks like a proper quantum ensemble in a measurement situation, as we observe that measurements lead to the “realization” of precisely one state in the “ensemble”. But within the framework of the interpretation of quantum mechanics, decoherence cannot explain this crucial step from an apparent mixture to the existence and/or perception of single outcomes.”

    from http://en.wikipedia.org/wiki/Quantum_decoherence

    it cites http://arxiv.org/abs/quant-ph/0312059

  • Steve B.

    Ray–

    You write: “In a classical system there is uncertainty due to ignorance, but the amount of ignorance doesn’t increase.” But that’s abjectly incorrect. Indeed, in the presence of nonlinear interactions, classical systems are generally chaotic and effectively exhibit information loss with time. You seem to think that classical=deterministic, but that’s simply not generally the case. In particular, when you go to the classical limit of quantum system, quantum effects generally manifest themselves as nonlinearities; the quantum indeterminism appears as classical chaos, which is perfectly consistent with the fact that the density matrix eigenvalues of the cat or apparatus or person gets more nontrivial with time, even though the basis in which that density matrix is diagonal stays nice and fairly classical.

    This is actually a hugely important point, because quantum-mechanical time evolution is, in principle, linear, and therefore non-chaotic. The question of how classical chaos is possible depends crucially on the argument above.

    Then you say “Now, you could just say there’s an infinite amount of information you don’t know about pretty much any system.” Well, that’s not quite true; the amount of information about a truly classical system is infinite, but quantum-mechanically you know that the maximum entropy of a bounded system is generally finite. And, of course, at a much deeper level, the holographic bound indicates that the total amount of information associated to any finite region of flat space is bounded from above by A/4G.

    Then you say “But then you’re proposing hidden variables all over again. Just because your using density matrices instead of wavefunctions doesn’t make the problem go away. Your hidden variables still need to be nonlocal. Now if you don’t have a problem with defining reality in such a way that real but unobservable interactions aren’t local, be my guest. Interpretation of QM is all semantics anyway.”

    Well, sure. There are nonlocal ingredients here. Of course, branches in many worlds are also nonlocal entities, stretching across the universe. The difference is that no influences propagate faster than light in many worlds, whereas for the density matrix approach to work you do need non-signaling influences to propagate faster than light. But the no-communication/no-signaling theorem shows that those influences don’t carry information, and so they don’t violate the causality of special relativity, provided that the Hamiltonian is physically local, as it is in well-behaved QFTs. And there are lots of influences even in classical mechanics that propagate faster than light without carrying information, so what’s the big deal?

    And those nonlocal ingredients are obviously hidden. When I say that there’s a density matrix diagonal in a classical basis for a big system, and that the eigenvalues are a nontrivial probability distribution, then obviously the true state of the system is hidden behind that density matrix. (In many worlds, the alternative is to say that all those states are equally real, but then you run into massive trouble trying to understand what probability means at all.) So its state is a hidden variable in that sense.

    But unlike what one does in other interpretations, like Bohmian mechanics, one does not say that for all systems, there’s one set of hidden variables that’s singled out. In Bohmian mechanics, one says that the position basis is always the hidden variables. But decoherence says that the special basis varies from system to system according to the dynamics, although for big, macorscopic systems the basis of classical-looking states is nearly always singled out by decoherence, just as we need.

    And as for it all being semantics, well, to the extent that the various interpretations are essentially just interpreting the same mathematics in different ways, that’s somewhat true. But you’re still left with the trouble of saying what probability means in many worlds if all the possibilities all literally occur. The same objections attached to classical modal realism, which I think was mentioned earlier in this thread. If you say that not all the possibilities occur, so that probability has its usual meaning of ignorance and uncertainty, well, then there’s only “one world,” and that world is going to be a hidden variable. But so what?

    You say “But if you are right, you should be able to answer the following. In my two cats scenario, what exactly are the two bits of information the observer is ignorant of at the beginning of the experiment?”

    That’s not the right question. The correct question is, What is the consequence of the observer doing the measurement on a superposed quantum state? Afterwards the density matrices are nontrivial according to far-away secondary observers, reflecting the fact that those far-away observers don’t know how the measurement turned out yet. But the fact that the observer and system’s density matrices both become nontrivial is perfectly consistent with the mathematics of quantum mechanics.

    And, again, the same is true even of classical mechanics, when the systems are chaotic. Suppose we start with a classical system at time t0 in an exactly known state, but the dynamics is chaotic. At some later time, an observer measures the state of the system. According to a far-away secondary observer, both their two probability distributions are now nontrivial. So, “What exactly are the two bits of information the observer is ignorant of at the beginning of the experiment?” The ignorance emerges from the indeterministic behavior of the system, and that basic statement (that ignorance can sometimes emerge in this way) is true whether we’re talking about classical or quantum mechanics.

    Then you cite Wikipedia, which says that “But within the framework of the interpretation of quantum mechanics, decoherence cannot explain this crucial step from an apparent mixture to the existence and/or perception of single outcomes.” This is a poor paraphrasing of the paper you cite at the end of your last message. Read the conclusion of the paper! It explains the Wikipedia remark.

    What the author is really saying in the paper (and in the conclusion) is that decoherence alone, without any interpretation, is inadequate. Well, of course; it’s just abstract mathematics until you provide an interpretation, i.e., a connection to physical reality. But the author points out very clearly and deliberately that if you take a stand and pick an interpretation of what the density matrix means, as I’ve been doing here, then you can be okay. (For example, saying, as I am, that the density matrix is hiding a specific, one-world state is something that smells similar to the modal interpretation, although there are some differences between these two interpretations.)

    There is clearly debate among people who study quantum foundations about these issues. But the view I’ve presented here is one of the views people take seriously. It’s not the only view, and people who disagree speak with great definitiveness about why they disagree. But simply citing certain people who disagree doesn’t settle the argument, anymore than citing certain people who deny the existence of climate change settles that argument either.

    And the whole point is not that this is the only interpretation of quantum mechanics that will ever work; the point is that this interpretation exists, and is consistent with the mathematics of quantum mechanics and with unitary time evolution and doesn’t require a separate collapse postulate or a measurement paradox, and without needing the extravagance of many worlds and worrying about the meaning of probability when, in many worlds, all possibilities are literally realized.

    So you can have your cake and eat it too, without having to subscribe to many-worlds. You don’t have to subscribe to this particular interpretation, but it’s there, and it’s axiomatically simple, and people outside the foundations community should be aware of it, instead of saying, as Sean does in his interview, that getting rid of an explicit collapse postulate inevitably requires many-worlds.

    By the way, isn’t this fun? I appreciate your taking the time to discuss all this! When do people ever do this in a serious way on a popular-science blog?

  • Ray

    “The difference is that no influences propagate faster than light in many worlds, whereas for the density matrix approach to work you do need non-signaling influences to propagate faster than light.”

    This is the crux of the issue. I find the superluminal propagation of influences (signaling or no) more problematic, you find the difficulties with defining probabilities in the MWI more problematic. Thus you like nonlocal hidden variables (without choosing a specific set like the ones in Bohmian mechanics) and I like the Everett interpretation. Decoherence demonstrates that it doesn’t make a lick of difference as far as experimental predictions go, and that’s the beauty of the thing.

    “And there are lots of influences even in classical mechanics that propagate faster than light without carrying information, so what’s the big deal?”

    only nonrelativistic classical mechanics. Both General Relativity and Maxwell’s equations have local realist interpretations.

    “By the way, isn’t this fun?”

    Absolutely. I appreciate your taking the time as well.

  • Steve B.

    Ray–

    Chiming in again!

    So we’re now essentially in full agreement about the broad issues of the discussion, and we fully understand each other’s perspectives. (Let’s see if everyone else on this thread feels the same way.) And you’re correct about my use of hidden variables that are not a specific set, in contrast to the Bohmian interpretation; that’s precisely the idea. The variables depend on the system in question and the dynamics, and can be quite bizarre for tiny systems; but they tend to be highly classical variables for big systems, as would be expected.

    You’re correct that decoherence demonstrates that it’s just a question of interpretation. I agree. And you’re correct that I find trouble with defining probabilities in many-worlds (and with the idea that there really are infinitely many worlds), and that you find trouble with non-signaling superluminal influences.

    I suppose my argument is that we have no evidence from any other branch of science of the existence of many worlds, which are a very bizarre idea (doesn’t make the idea wrong, of course!), whereas we do have lots of examples of non-signaling superluminal influences in many branches of physics.

    You write that there are superluminal influences in “only nonrelativistic classical mechanics. Both General Relativity and Maxwell’s equations have local realist interpretations.” I think you may be misunderstanding me. In nonrelativistic physics, there’s no speed of light anywhere, so _signaling_ phenomena can travel at arbitrary speeds. You could imagine using Newtonian gravity to transmit a message at any speed you like!

    Relativity, of course, precludes doing so, because it would lead to a violation of causality; a sufficiently fast-moving Lorentz observer would see the signal go backward in time! So Coulomb’s law and Newtonian gravity are replaced by Maxwell’s equations and General Relativity, which do not transmit signals faster than the speed of light.

    But what about _non-signaling phenomena_? Those do indeed occur even in relativistic theories, including Maxwell and General Relativity. Phase velocities (as opposed to group velocities) are a famous example; indeed, there are numerous experiments that send phase velocities far faster than the speed of light. There’s the famous “ant’s shadow” thought experiment, in which an ant crawls across a giant spotlight projected on a wall light years away, and that shadow appears to move superluminally. The tachyons that arise ahead of spontaneous symmetry breaking in quantum field theories are superluminal as well. There are loads of other examples; try asking a group of people all to raise their hands at once—that’s a “superluminal wave.” Heck, you can even do it with the fingers on your hands!

    What all these superluminal propagating influences have in common is that they don’t transmit information from one side to the other—they’re non-signaling—so nothing forbids their existence. We know that they exist, so saying that they can also exist in quantum mechanics is far less bizarre or shocking than many worlds, at least to me, and, again, avoids having to deal with the meaning of probability when all possibilities simultaneously occur (as is the case in many worlds). So why worry about superluminal phenomena that don’t carry signals? What’s the big deal?

    I know I’m giving you a bit of a hard time here; sorry about that. I totally understand if you prefer Everett; heck, I’m a fan of his, too! To each his/her own. My only point in all this was that if you want to avoid an explicit collapse postulate, and you don’t want to add lots of other ingredients like pilot waves, then you aren’t just stuck with Everett. You just take density matrices seriously, and accept the consequences like some hidden variables and some new non-signaling superluminal influences.

    And I appreciate your time as well! The question is whether anywhere else is appreciating our time. :)

  • Ray

    Good. It seems we are agreed that we are agreed that the choice is between many worlds and nonlocal influences. I was kind of thinking you might bring up superluminal phase velocities (tachyons are also in this category.) Where nonlocal hidden variables differ from the above phenomena is that nonlocal hidden variable theories require information to travel faster than light (Bell’s theorem) — it just happens to be unobservable information. OTOH you can recover the phenomena in the classical examples by using a formalism like retarded potentials where it is clear that the value of the relevant field only depends on influences within the past light cone. Likewise, in Everettian QM, no information, observable or otherwise travels faster than light.

    I do take your point that Sean could have been more comprehensive by saying that the choice is between Copenhagen, MWI, and nonlocal hidden variables, rather than just mentioning the first two. But, all three pose philosophical challenges, and the philosophical challenges associated with the first two are much easier to explain, so I don’t really fault him for the omission.

    “The question is whether anywhere else is appreciating our time.”
    Good question. My guess is everyone else has stopped reading.

  • Steve B.

    I would guess the same thing. :)

    As for your comment that “the philosophical challenges associated with the first two are much easier to explain,” well, I’m not sure whether I agree or not.

    Yes, it’s true that talking about an infinite number of universes, while bizarre, is pretty simple to explain, and kind of fun. And it might seem more complicated to explain in a radio program why nonlocal variables present a conceptual challenge to relativity and causality.

    But I think it would take two seconds to say, “Well, the alternative to an infinite number of universes, with questions of what probability even means in that context, is simply to allow certain influences between systems that can go faster than light, but in a way that can be shown never to carry signals.” Given the significant complexity of Sean’s conversation, I think that would have been a perfectly reasonable thing to say.

    I suppose I still disagree when you say “that nonlocal hidden variable theories require information to travel faster than light (Bell’s theorem) — it just happens to be unobservable information.” It all depends on what you mean by information. So now we’re back to semantics.

    If you define information according to information theory, then, no, the superluminal influences of this interpretation of quantum mechanics do not carry information in this sense, because if two systems are widely separated and the Hamiltonian is local, then their respective density matrices evolve totally independently of one another. In particular, the information content of each system, as measured by the Shannon entropy formula, indicates no exchange of information between the systems. That’s precisely the no-signaling theorem, which you can look up. The two density matrices can only affect each other if you bring the systems into local contact, or by exchanging some physical intermediary, like photons.

    But do the two systems affect each other “behind their density matrices” in some mystical, unobservable way, by exchanging some vague notion of information that doesn’t constant a signal? Well, I suppose, but, again who cares? Why is that so disturbing? It’s a small price to pay for getting to have just one universe, rather than an infinite number!

    And I’m sure the science-enthusiast part of the public would be happy to know that it’s possible to do quantum mechanics this way. It’s true that there are subtle differences between non-signaling superluminal influences in different branches of physics, but, come on, there’s nothing at all like many worlds anywhere else! Infinitely many universes represent a much bigger conceptual pill to swallow than some new non-signaling superluminal influences that merely add on to the list of other non-signaling superluminal influences that we already know about and that we’ve observed in the laboratory already.

  • Ray

    But do the two systems affect each other “behind their density matrices” in some mystical, unobservable way, by exchanging some vague notion of information that doesn’t constant a signal? Well, I suppose, but, again who cares? Why is that so disturbing?

    I’ll accept an infinity of unobservable worlds containing “more of the same” over anything “mystical.” Especially if that mystical thing violates a well established principle like the cosmic speed limit. The superluminal motions that are allowed by the MWI can be robustly called illusions. Nonlocal hidden variables OTOH are explicitly defined as capturing a reality that is not expressed in the density matricies. This is no small price. It is akin to the difference between performing a symbolic ritual of bread and wine, and accepting the literal miracle of the transubstantiation.

    It seems even we atheists have our theological commitments. :p

  • Steve B.

    The word mystical was supposed to be in quotation marks; I was being sarcastic. (Clearly some human emotions don’t translate so well over text protocols.)

    Your response appears indicative of habituation. If you’d heard for the very first time that the two non-collapse interpretations were the two that we have been discussing, I really don’t think you’d consider an infinitude of universes less mystical than some new forms of non-signaling superluminal propagation. (Although many-worlds is certainly a cooler idea, ripe with possibilities for fantasy-seeking.)

    The fact that the proliferation of pararallel worlds are all “more of the same” makes the very existence of that cornucopia of worlds no less mystical! That’s like saying that a horse made of atomic unicorns isn’t mystical, because it’s just a horse. If many-worlds seems less mystical, then that’s, again, indicative of your having grown accustomed to the frankly shocking idea.

    It’s also indicative of something else. Ever since Bell’s theorem, the term “hidden variables” has become so radioactive that people missed the simple fact that Bell’s inequality ruled out only local hidden variables. So there’s understandably a negative reaction whenever the term “hidden variables” arises, even when it’s the less exotic of the possibility interpretations and requires no new formalism.

    The simple fact is that quantum mechanics is weird, and the question is what weirdness we’re going to tolerate. You say an infinite supply of parallel universes for which the notion of probability itself becomes inscrutable, and I say yet one more form of non-signaling superluminal propagation. Who’s to say what’s the more unacceptable? No experiment could ever tell the difference, at least apart from a quantum suicide experiment. (No thanks!)

    And I have to find contention with your remark that the “thing violates a well established principle like the cosmic speed limit.” No, I’m sorry, but it does not.

    Special relativity puts a price on non-locality by linking it up with acausality. But acausality is manifestly only an issue when signaling is a possibility. And, as I’ve said before, provided that the Hamiltonian is local (as it is in all our QFTs), there’s no possibility of signaling acausally, thanks to the no-signaling theorem. (Hence the name!)

    The cosmic speed limit is a speed limit on _signals_, full stop. There is no speed limit on anything else, and no logical reason why there should be, apart from human prejudice. The statement “entity A satisfies rule R” implies nothing about whether another entity B satisfies rule R; to say otherwise is a simple logical fallacy.

    So a framework or interpretation of a physical theory that includes non-signaling influences that obey no speed limit is abssolutely not in conflict with relativity. Indeed, it’s a perfectly reasonable question why Nature should place any kind of speed limit of non-signaling phenomena; why should it? And in this interpretation of quantum mechanics, we say, sure! Bring it on! What isn’t forbidden by some law or logical contradiction is perfectly allowable.

    What’s fascinating is that you can actually ask whether quantum mechancis is the most non-local theory in this regard. Could one devise a theory that is even more non-local without violating causality? The answer is actually yes! In a series of interesting recent papers, quantum computing theorists have shown that quantum mechanics is not the maximally non-local causal theory that one could ever come up with. But the other, more-nonlocal theories don’t agree with experiment; they imply stronger correlations than in quantum mechanics, and those correlations are unsupported by experiments.

  • Mark

    Wait, I’m reading this stuff!

    Can I add a few things? I think it’s clear that you two are never going to agree on your favorite interpretation of quantum mechanics. Ray says that it’s a well-established principle that everything must obey the cosmic speed limit (even stuff that doesn’t move signals around), and Steve basically seems to think it’s a well-established principle that there’s only one reality (even though we wouldn’t be able to know otherwise).

    I think it’s clear from my own comments earlier that I tend to side somewhat more with Steve, but I see where y’all are coming from. If Steve’s main point seems to be that there are non-many-worlds interpretations that are just as good as many-worlds at eliminating the measurement paradox and the collapse postulate, then it seems like he’s succeeded. If his main point is that his interpretation is the best one, well, I don’t think anyone can prove he’s right!

    Do you guys/gals suppose Prof. Carroll might be willing to read our little conversation and weigh in with his own point of view?

  • Ray

    Mark

    I think it’s clear that you two are never going to agree on your favorite interpretation of quantum mechanics.

    Word. Couldn’t have said it better myself

    Steve B

    Could one devise a theory that is even more non-local without violating causality? The answer is actually yes! In a series of interesting recent papers, quantum computing theorists have shown that quantum mechanics is not the maximally non-local causal theory that one could ever come up with.

    That sounds awesome. Link. Link.

  • Mark

    Whether there’s one world or many, isn’t the universe big enough for the two of your interpretations of quantum mechanics? :)

  • Steve B.

    I’d like to add one more thing about the interpretation I’ve been arguing for, acknowledging Mark’s sage advice that we’re never going to agree.

    The fact is that we already use density matrices to encode ingnorance probabilities and hidden states (in the prosaic sense of the term “hidden”) in quantum mechanics. So in the interpretation I’ve been boosting, we just take density matrices seriously; rather than adding on any new ingredients to quantum mechanics, we just allow the ingredients we already have (specifically, density matrices) to be what they want to be, to do what they’re meant to do; namely, we allow density to always describe ignorance probabilities and states hidden by that ignorance.

    There are no conceptually new ingredients to quantum mechancis in this picture, although some of the hidden ingredients are more hidden than before; there are no pilot waves, or parallel universes, or other conceptually new ingredients beyond those uncontroversial ingredients we already have (although some of those uncontroversial ingredients behave in slightly less conventional ways, but without truly violating any actual laws of physics).

    That’s the sense in which this approach to quantum mechanics is as minimal and conservative as possible, at least as conservative as allowed by the inevitable weirdness implied by Bell’s theorem that nobody can get rid of.

    Oh, and those papers I mentioned. Here are a few:

    “Causality and Nonlocality as Axioms for Quantum Mechanics”
    Sandu Popescu, Daniel Rohrlich
    http://arxiv.org/abs/quant-ph/9709026

    “Information Causality as a Physical Principle”
    M. Pawlowski, T. Paterek, D. Kaszlikowski, V. Scarani, A. Winter, M. Zukowski
    http://arxiv.org/abs/0905.2292

    See also these related blog entries:

    http://scienceblogs.com/pontiff/2009/05/information_causality.php
    http://www.technologyreview.com/blog/arxiv/23541/

  • Steve B.

    One reason I think the work in those papers is relevant to our discussion is that they imply that Nature could in principle have been instead described by a theory that has strongner nonlocal non-signaling propagation than quantum mechanics, but, unlike quantum mechanics, that does not admit a many-worlds-type interpretation.

    If Nature had been described by such a theory instead of quantum mechanics, then we really wouldn’t have much choice but accept the existence of non-signaling superluminal propagation—i.e., nonlocal hidden variables. It’s only because the correlations of quantum mechanics are slightly weaker than maximal that many-worlds is an alternative possibility.

    But had things been otherwise, there wouldn’t have been a causal violation; there doesn’t seem to be any fundamental reason why Nature should dislike superluminal propagation that doesn’t transmit signals.

    In other words, Ray, if we took your point of view and declared that any superluminal propagation was absolutely forbidden, even if no signaling were ever involved, then we would never have been able even to consider the possibility of these alternative theories. Why close ourselves off that way, when Nature gives us no fundamental, inviolable reason to do so?

  • Ray

    If Nature had been described by such a theory instead of quantum mechanics, then we really wouldn’t have much choice but accept the existence of non-signaling superluminal propagation—i.e., nonlocal hidden variables. It’s only because the correlations of quantum mechanics are slightly weaker than maximal that many-worlds is an alternative possibility.

    Ironically, I would take that as an argument in favor of MWI. My principle of local realism rules out all sorts of things that are logically possible but not observed, while your principle of no signaling does not. This means my principle has more predictive power.

    Also, I would point out that while there is some debate over how much MWI forces the Born rule on you, it certainly strongly suggests it — which is to say that for a wide range of measures (the ordinary L2 thing, world counting etc.), the total measure of worlds where there is a statistically significant deviation from the Born rule approaches zero as the period of observation approaches infinity. Of course, even in classical physics probability is a bit odd (Hume’s problem of induction comes to mind.) And of course there’s no fundamental principle which prevents you from choosing the values of nonlocal hidden variables, such that the one world of your interpretation grossly violates the Born rule’s prediction either.

    So I think the only philosophically consistent objections stem from raw revulsion at the idea that you have millions upon millions of near identical twins whom you will never get to meet.

    I would link papers to support my assertions in the second paragraph, but you can get pretty much the same papers by Googling “born rule derivation,” and I’m not sure you disagree with anything I said in that paragraph anyway.

  • Steve B.

    Ray–

    You write: “Ironically, I would take that as an argument in favor of MWI. My principle of local realism rules out all sorts of things that are logically possible but not observed, while your principle of no signaling does not. This means my principle has more predictive power.”

    That’s certainly untrue; you know full well that just as quantum mechanics is only one of many conceivable no-signaling theories, so it is likewise only one of many conceivable many-worlds theories. (Although I doubt that anybody’s been looking for them, since they’re much less interesting and falsifiable than new non-signaling theories.) Neither imposing no-signaling nor many-worlds uniquely defines quantum mechanics. That is, after all, part of the point of that information causality paper, to find some principle that actually does uniquely define quantum mechanics! (Although I would argue it’s not the only way; indeed, I don’t take no-signaling as the fundamental definition of quantum mechanics, even though it certainly satisfies that property.)

    One of the deep problems with attempting to define probability in many-worlds (and there are many; Blake Stacy cited one paper that provides more examples) is that it relies on a version of frequentism, i.e., branch counting. But frequentism is circular: You need to perform a literally infinite sequence of measurements to get it to work, via the central limit theorem. Because if you perform only a finite (even if large) number of measurements, then you always have nonzero probabilities for all possibilities, and you have to assume they’re “unlikely” to make them go away. This is the one the key troubles with trying to “derive” probability from quantum mechanics, rather than employing an interpretation, like the one I’ve been advocating, that simple assumes Bayesian/ignorance probability from the beginning.

    And it bedevils all the papers that you mention, like the Farhi et al. argument, where they define frequency ratios for large numbers of identical experiments and show that Born-rule-violating outcomes have amplitudes that “go to zero” when the number of experiments “goes to infinity.” Well, great, but there are never an infinite number of identical experiments, so in truth the amplitudes of those bad branches are never actually zero, and thus they have to argue that their small amplitudes make them “unlikely,” which is again circular.

    And actually many-worlds is still worse than the usual troubles with frequentism, because the simple fact is that every branch is there; it exists! No branch “goes to zero.” If two branches separate with respective amplitudes sqrt(1/3) and sqrt(2/3), what is the meaning of the statement that one is “more likely” than the other?

    These are only a few of the many reasons why many-worlds and probability don’t work well together, even if at a purely mathematical level, where you can take limits, measure-theoretic probability theory seems to work. But see that paper mentioned earlier for more reasons for logical confusion. I’m not going to list all the logical issues here. But they are many, and they are unresolved. (And perhaps unresolvable.) It’s not merely a “raw revulsion at the idea that you have millions upon millions of near identical twins whom you will never get to meet.”

    Then you say “And of course theres no fundamental principle which prevents you from choosing the values of nonlocal hidden variables, such that the one world of your interpretation grossly violates the Born rules prediction either.” Well, sure. But that’s true of classical probability theory as well. There’s no fundamental principle that prevents a fair classical coin from (by chance) landing heads a million times in a row, and thereby “violating” the predictions of probability theory. That’s the reason why you can’t “derive” probability from deterministic assumptions; with only a finite number of measurements, there’s no hard and fast prediction that you can make that doesn’t cite circularly probability theory itself. (“The more experiments you perform, the unlikely outcomes become less likely.”) But the point is that you don’t have to accept anything more than we already accept when doing classical probability theory.

    In the approach I’ve been advocating, there’s a superficial and aesthetic downside because non-signaling phenomena can break the cosmic speed limit, but that presents no logical contradictions. That’s important: There are no fundamental logical contradictions. But many-worlds presents the same logical confusions as classical modal realism when it comes to probability theory itself, and that’s why I don’t prefer it. Probability theory needs a logical bed to sleep in, and many-worlds logically doesn’t provide one.

    And unless you’re advocating classical modal realism, then you’re furthermore admitting that there are two kinds of probability in Nature: classical ignorance probabilities, and quantum many-worlds probabilities. In my approach, they’re unified; there’s just one kind of probabilities, namely, ignorance probabilities. That’s one more sense in which the approach I advocate is more minimal and conservative than yours.

    But we’re clearly never going to agree; how could we ever know which one is ultimately correct? My point, again, was just that! Yours is not the only road. The universe really is big enough for both us. (Right, Mark?)

    So let’s call a truce, shall we? You take that side over there, and I’ll take this side over here, and we’ll have somebody else (Mark? Blake?) patrol the border. :)

    I gotta go. It’s been a great chat, but rather time-consuming, wouldn’t you say?

  • Mark

    Steve B,

    I think you got confused what Ray’s principle was; he meant local realism as his principle, not many worlds. Although I don’t think I can accept what he means by “local realism” if there are in fact many worlds. I simply don’t know what “realism” itself is when all possibilities are simultaneously real!

    And local realism itself isn’t a strong enough principle, either. Steve was wrong about confusing many worlds and local realism, but it’s similarly true that local realism alone isn’t strong enough either to get quantum mechanics as the unique theory.

    But I do agree with Steve’s point that just because you can slap down a probability measure on something at the level of abstract math doesn’t mean that thing is really probability. And I have a lot of trouble with the idea of probability and many worlds going together, too.

    And I suppose it’s just personal preference for me, but I find many worlds to be a bit too religious for me. It’s like an alternative gospel for science/atheist people, and people cling to it for a lot of the same reasons. (I know I wish there was another world out there in which I was more successful, or worlds in which I was immortal! :) ) That doesn’t mean it’s necessarily wrong, but it does explain why people seem so attached to it when there are other interpretations that solve the measurement paradox too.

    This really has been quite a conversation, hasn’t it? I hope everyone here had some fun, and nobody took this stuff too seriously! And everybody seems to have corrected some mistakes in their thinking along the way, and their misunderstandings of each other’s ideas.

    The real question is, if a few smart people have a deep and intense conversation/debate about the fundamental meaning and interpretation of quantum mechanics, and nobody else reads it, then did it have any significance at all? :)

    But I think I’d like to call it quits, too. Everybody’s made some good points, and I have a lot I’d like to chew on now. :) So long, and thanks for all the fish!

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Cosmic Variance

Random samplings from a universe of ideas.

About Sean Carroll

Sean Carroll is a Senior Research Associate in the Department of Physics at the California Institute of Technology. His research interests include theoretical aspects of cosmology, field theory, and gravitation. His most recent book is The Particle at the End of the Universe, about the Large Hadron Collider and the search for the Higgs boson. Here are some of his favorite blog posts, home page, and email: carroll [at] cosmicvariance.com .

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