Quantum Diavlog

By Sean Carroll | August 8, 2008 4:29 pm

Remember when I asked for suggested topics for an upcoming Bloggingheads discussion with David Albert about quantum mechanics? The finished dialogue is up and available here:

I would estimate that we covered about, say, three percent of the suggested topics. Sorry about that. But perhaps it’s better to speak carefully about a small number of subject than to rush through a larger number.

And I think the dialogue came out pretty well, if I do say so myself. (And if not me, who?) We started out by laying out our respective definitions of what quantum mechanics “is,” in terms that should be accessible to non-experts. (One user-friendly answer to that question is here.) Happily, that didn’t take up the whole dialogue, and we had the chance to home in on the real sticky issue in the field: what really happens when we observe something? This is known as the “measurement problem” — it is unique to quantum mechanics, and there is no consensus as to what the right answer is.

In classical mechanics, there is no problem at all; you can observe anything you like, and if you are careful you can observe to any precision you wish. But in quantum mechanics there is no option of “being careful”; a physical system can exist in a state that you can never observe it to be in. The famous example is Schrodinger’s cat, trapped in a box with some quantum-mechanical killing device. (Someone must write a thesis on the ease with which scientists turn to bloodthirsty examples to illustrate their theories.) After a certain time has passed, the cat exists in a superposition of states: half alive, half dead. It’s not that we don’t know; it is really in a superposition of both possibilities at once. But when you open the box and take a look, you never see that superposition; you see the cat alive or dead. The wave function, we say, has collapsed.

This raises all sorts of questions, the most basic of which are: “What counts as `looking’ vs. `not looking’?” and “Do we really need a separate law of physics to describe the evolution of systems that are being looked at?”

In our dialogue, David does a good job at laying out the three major schools of thought. One, following Niels Bohr, says “Yes, you really do need a new law, the wave function really does collapse.” Another, following David Bohm, says “Actually, the wave function doesn’t tell the whole story; you need extra (`hidden’) variables.” And the final one, following Hugh Everett, says “You don’t need a new law, and in fact the wave function never really collapses; it just appears that way to you.” This last one is the “Many Worlds Interpretation.”

I want to actually talk about the pros and cons of the MWI, but reality intervenes, so hopefully some time soon. Enjoy the dialogue.

CATEGORIZED UNDER: Science
  • http://www.booberfish.com/blog/ GP

    I never really bought MWI, but every time I try to think about why not I confuse myself. I tend to think that even if both possibilities exist, observing one doesn’t necessitate a world where the other occurred, but it doesn’t have to do with a wave function “collapsing” (what does that even mean?!). The cat is alive or dead in that box whether you look at it or not. It state of being both alive and dead is just in the description. It’s the best description we can have before making the measurement but that doesn’t mean that’s what it actually is. It’s more about statistics—with one hundred cat-filled killing machines, half will come out dead and half alive. I guess that’s leaning towards a hidden variables interpretation, eh?

  • Mark

    What about Cramer’s “Transactional” interpretation of QM?

  • http://www.domenicdenicola.com/ Domenic Denicola

    @Mark: in my experience, if you use broad enough strokes everything falls into one of those three categories. E.g. the much-touted “relational” interpretation is more or less many worlds in disguise. As another example, mechanisms like GRW collapse or Penrose-esque collapse fall into the category of what Sean called Bohr’s school.

    With regards to the transactional interpretation specifically, Wikipedia leads me to believe it falls into the first category, providing as it does a mechanism for collapse. However, it’s worth noting that the quantum foundations guys I worked with last summer at the Perimeter Institute had a rather poor opinion of the transactional interpretation. At the risk of misquoting, I believe on of them said that it only worked with a single particle. It’s also notable that it is supported almost entirely by a single person.

  • Chris W.

    GP (comment 1):

    You don’t have to lean towards a hidden-variables interpretation. You can just say we don’t know, and we can’t know; the world has a fundamentally statistical structure. The question then becomes how to make this absolutely compelling. Does quantum mechanics leave the door open for a deep determinism or hidden causality?

    John Stachel has expressed the view[1] that Einstein’s real objection to quantum mechanics was that it asserted a kind of compromise between determinism and sheer chaos, but didn’t make clear the terms of the bargain. If the evolution of the universe isn’t fully determined, then why should it have any structure at all?

    [Sean: Maybe you should try exploring this with Stachel sometime.]

    ——————
    [1] This was in Stachel’s own contribution to Conceptual Problems of Quantum Gravity, 1991 (A. Ashtekar, J. Stachel, editors).

  • http://countiblis.blogspot.com Count Iblis

    GP, you have to admit that the superposition of the two states is different from either one of the other. E.g., as long as the contents of the box is in the superposition and it hasn’t decohered yet (i.e. the state of the rest of the universe is the same in both parts of the superposition), you still have access to the initial state (in principle).

    This is perhaps best illustrated by changing the thought experiment by replacing the cat by a person and administering a deadly poison that kills with 100% certainty within, say, 5 minutes. So, the wavefunction of the person would describe a dead person after 5 minutes and after opening the box, we would see a dead person.

    However, according to quantum mechanics, we can still (in principle) talk to the person after the 5 minutes have passed provided we make sure the wavefunction of the contents of the box doesn’t decohere (in practice this is an unrealistic assumption). This works as follows. The process of asking a question to a person and then recoding the answer is equivalent to applying a perturbation to the wavefunction of the person and then measuring some observable. But in this case we want to undo the effect of time evolution since the poison was adminstered. The wavefunction evolves in time according to:

    psi(t) = Exp(-i H/hbar t) psi(0)

    The effect of the perturbation on the wavefunction is some unitary operator P applied to the wavefunction. We want to apply this to psi(0) when given psi(t):

    P psi(0) = P Exp(i H/hbar t) psi(t)

    Suppose that the person was sure to give some definite answer to the question. Then P psi(0) is an eigenstate of the operator, A, that corresponds to measuring the answer (the eigenvalue lambda):

    A P Exp(i H/hbar t) psi(t) = lambda P Exp(i H/hbar t) psi(t)

    And it follows that:

    B psi(t) = lambda psi(t)

    where

    B = Exp(-i H/hbar t)P^(-1) A P Exp(i H/hbar t)

    So, measuring the observable B when the person is dead gives the same result as asking the question and recording the answer to the person when he was alive! You can then, of course, ask another question, so you can talk to the person as if he is alive and well.

    Of course, the operator B is extremely complicated and involves measuring all the molecules in the system. So, it cannot be done in practice. But because it can be done in principle, this means that the person as he was when he was still alive continues to exist in the box long after the poison has killed him.

  • slide2112

    So, an infinite number of “me’s” being created by a continuous series of events is a perfectly viable interpretation of QM.

    Yet the most obvious solution, that Consciousness causes the collapse, is silly because it allows new age folks to say mind can change personal reality.

    The idea that Consciousness is a fundamental aspect of reality is as well supported as any interpretation suggested here.

  • http://tyrannogenius.blogspot.com Neil B. ?

    One thing I don’t understand, and furthermore am suspicious of: some attempts at measurement in QM aren’t possible in ways that involve literal inconsistency in the sought knowledge, but others aren’t. Because of Fourier composition of waves, you really can’t localize a wave packet and have a precise momentum as well. But I can create a photon with linear polarization axis at 20

  • Mark Harrison

    @ slide 2112 #6

    One problem is what you mean by “perfectly viable interpretation.” At the moment, all QM interpretations are empirically indistinguishable. The last ten minutes of the discussion about the 2^1000000 Seans was pure speculation due to a lack of evidence. Prof. Albert was trying to get Prof. Carroll to see why the Many Worlds interpretation seems to undermine our understanding of QM in the area of probabilistic predictions. That has no bearing on whether it’s right or wrong, just that it’s odd.

    When physicists run the equations and accurately predict the results of experiments, no interpretation is used. Schrodinger’s equation is experimentally verified; Profs. Carroll and Albert were discussing what story we tell ourselves about what’s “really happening” in the universe described by QM.

    The other problem is the definition of “consciousness.” My objection would be the same as Prof. Albert’s when he said he didn’t believe in free will. The term is practically undefined and therefore useless as a “fundamental aspect of reality.” If Consciousness could be defined in terms of a hermitian operator in Hilbert space, that would be exciting news.

  • Sad

    So, which “school of thought” seems to be held by most physicists? Inquiring minds really need to know.

  • mathematician

    @ Mark Harrison

    If a physical theory does not accommodate consciousness, then it has been disproved by experiment, and it should be discarded.

  • Eric Habegger

    I find Bohm’s theory of hidden variables most compelling. If one accepts the premise of vacuum energy, however you describe it qualitatively or quantitatively, it could neatly fall into the suspect territory. I really don’t buy for a minute the idea that not knowing the quantum state of a particle until you measure it indicates it exists in every possible state previous to the measurement. Why would that be any different from the axiom that if a tree falls in the forrest and no one is there to hear it did it still fall? Of course it fell!!!

    I just don’t understand how otherwise bright individuals could fall for that logic. Both the copenhagen interpretation and the many worlds interpretation fall into what I would call an “egocentric view” of the world. This view holds that unless an intelligent observer is there to observe a quantum event it doesn’t really happen. I think this view came about because the act of observing involves the exchange, sometimes in a complicated fashion, of photons between the observer and the observed. So you really do pin down while at the same time alter the quantum system in which the observed particle exists. The smaller and less massive the particle is that is observed the more this photon exchange will impact the state of the particle. But energy is always exchanged in the act of observation. But if I look at the moon and receive its photons it probably won’t affect the moon too much. Why would I ever “not” think the exact same thing is happening when observing particles in the quantum realm except that there the particles are so light the photon exhange actually does affect their state observably.

    I would call the MWs believers even more egocentric than the Copenhagen interpretation believers. They actually believe that by pinning down a quantum state they are creating a new entire universe that they inhabit that is different from all other universes where other potential observations might have been made.

    Information exchange is what makes the world go round and the information is finite but ever on the move. Energy is always conserved in the universe when information is exchanged. The observers and the observed are just the players in the drama.

  • slide2112

    #8, #10

    I am not signing up to go as far as mathematician does on this but…

    The key word here is interpretation. When interpreting the results of this hugely successful theory (theory does not seem to do QM justice) dismissing interpretations that include consciousness seems dishonest.

    It is one thing to say consciousness is too ill-defined (not undefined) to allow progress in a physical theory. It is another to ignore experimental results, dismiss the role of consciousness as one would a religion, and then come up with multi-verse like ideas. Where is the evidence for that?

  • Jason Dick

    I would call the MWs believers even more egocentric than the Copenhagen interpretation believers. They actually believe that by pinning down a quantum state they are creating a new entire universe that they inhabit that is different from all other universes where other potential observations might have been made.

    Incorrect. The MWI interpretation merely states that there are interactions occurring all the time that prevent different components of wave functions from interfering with one another. And this isn’t even a controversial statement: it’s a simple conclusion from observing the dynamics of interactions within quantum mechanics. Quantum decoherence is a real phenomenon that has been directly observed.

    It seems more absurd to me that you would accept a theory that is not only more complex than quantum mechanics, but also discards locality.

  • Eric Habegger

    Jason,
    I don’t think you are representing the many worlds theory as it is currently formulated. The individuals you represent actually believe any possibility that is represented by a wave function must exist simultaneously. And their theory is that once that wave function is identified by measurement the other possibilities must exist simultaneously, presumably in another universe.

    You tell me: is it more complicated to believe in conservation of energy and information or that there is infinitely more universes than the one we exist in, universes that have no potential for experimental contact. I prefer to believe in conservation of energy through the transferral of information. You are incorrect in your view.

  • adamk87

    Hey all, I just finished watching the excellent diavlog between carrol and albert over at bloggingheads and clicked on the link to this blog, and after reading the comments section thought Id ask what will probably be a stupid question.

    The extent of my knowledge on quantum mechanics is pretty much the aforementioned carrol/albert diavlog (deemed trustworthy), scenes from what the bleep do we know (suspiciously crackpot), and reading a few wiki submissions on the more famous aspects of the field.

    The most famous or the place you usually start when talking about quantum mech seems to be the double slit experiment, which wasn’t directly mentioned in the diavlog, but it sort of lurked in the background.

    Anyways my question, which has probably been addressed or pondered by someone, is the following: When the second slit is open wouldn’t we expect the variability or probability to change simply because as photons go through the slit they could presumably make contact with the disk and thus move it ever so slightly, which would make the photons that do “bump” but go through change, from just a single slit.

    My assumption is that my understanding of the slit experiment is wrong, but from what I understand (thankfully in this field ignorance is praised as knowledge) it seems like a plausible explanation for the different outcomes of the two experiments.

    Anyways Im interested to hear how you respond. Laymen terms, metaphors, etc. are much appreciated.

    Thanks.

  • adamk87

    edit: by “ignorance is praised as knowledge” I meant to say “humility is deemed wise”.

  • Jason Dick

    Eric Habegger,

    I don

  • Eric Habegger

    You are asking the central question of what reality is. I have my own views but they are obviously controversial and I certainly wouldn’t want to spoil the fun of letting someone just beginning from having their own journey. If you are approaching it from the beginning I can think of no better start than reading the appropriate section in Richard Feynman’s famous physics lecture trilogy. After reading it, then sleep on it for about five years. I’m only partly kidding – the concept is an enigma- and (just my own view) let it seep up from your subconscious over time. Don’t let any “experts” of whatever stripe overly influence you in the journey, yours truly included.

  • Eric Habegger

    That last comment was (obviously) addressed to Adam. Haven’t thought about Jason’s reply yet.

  • Jason Dick

    adamk87,

    I’ll describe the 2-slit experiment from the perspective of the many worlds interpretation (because I’m very much convinced that it’s accurate). Here’s the basic idea:

    First, you have a wavefunction of the particle. This wavefunction first passes through the two slits. After it has passed through the two slits, the part of it that has passed through one of the slits interferes with the part of it that has passed through the other. This interference depends upon the two components of the wave function having a coherent phase, which they do since both parts were once one part, and they haven’t yet interacted with anything that would mess up this phase. So, this wavefunction travels forward, oscillating as it goes, until it hits the screen.

    Now something interesting happens: an interaction that mucks up the phase. Basically, the part of the wavefunction that hits the screen at X gets its phase screwed up by the interaction with the screen such that it can’t oscillate any longer with the part that hits the screen at Y. These two parts both exist, but because their phases have been mucked up, there simply is no way for the part that says, “I hit the screen at X,” to talk with, “I hit the screen at Y.” And when we observe the experiment, we similarly end up with different parts of our wave function that can’t see one another, so we only observe one singular result.

    If we now change the experiment, so that we set up an apparatus to observe which slit the particle went through, the loss of coherence happens there, and we only observe one outcome once again.

    Did that help?

  • Jason Dick

    Oops, that talk I quoted from was last year, not last month.

  • Eric Habegger

    Jason,
    I certainly prefer a “decoherence” within a single universe better than the creation of multiverses. But it seems odd that I have never heard of it interpreted that way – maybe my own fault. I’m not sure I find the idea of decoherence satisfying as it seems a bit too abstract for my visually oriented mind. How does one characterize this decoherence iwthin a description that isn’t wholly mathematical in nature?

    My own inclination is that if we can eventually view quantum mechanics in the correct way it will transcend a strictly mathematical interpretation and be somewhat intuitive – in a way GR is. While this view of the many worlds interpretation is new to me I’m not sure it improves, at least for me, on some of the lack of intuition talked about in Feymann’s lectures. Would the lack of a discover of the Higg’s affect your view? People seem to fall into two groups regarding the primordial field – Higgs and ZPF. I’m afraid I fall into the latter.

  • Jason Dick

    Eric,

    Let me first say that I always thought that the Many Worlds Interpretation was nonsense until I learned of it in the decoherence context. I think proposing the MWI in the language of multiply diverging universes is entirely backwards: that’s a conclusion of what the wavefunction appears to do to observers within it. It’s not the foundation of the interpretation, which is simply that what we have is a wavefunction that just evolves. The claim, then, is that this can account for all observer effects, though I’ll admit that the work isn’t done yet to demonstrate that this is actually the case. Still, the work done so far seems quite promising.

    How does one characterize this decoherence iwthin a description that isn

  • MWI adherent

    [various anti-MWI comments]

    Ahem.

  • paul valletta

    So is there a chance,(no pun int!), that observing something, or not observing something, provides one with a greater or lesser knowledge of measure?

    For instance, if I do not observe something, can this be classed as actually increasing my knowledge about it’s whereabouts, being that in QM if you observe something, you lose your measured based knowledge about its momentum or position, thus by not actually observing something, I should actually increase my known accuracy of one or the other?

  • Mark Harrison

    @ slide2112 & mathematician

    Consciousness isn’t required to collapse the wave function. Read up on the Stern-Gerlach experiments, especially the sequential versions.

    http://en.wikipedia.org/wiki/Stern%E2%80%93Gerlach_experiment

    The first experiment with two z-spin measurements show that the first measurement collapsed the wave function such that no spin-down electrons were detected by the second detector. An inhomogeneous magnetic field acts as the “observer” here, nothing conscious or even living required.

    ====

    “If a physical theory does not accommodate consciousness, …”

    I don’t know what this means.

  • collin237

    Eric wrote:

    Why would that be any different from the axiom that if a tree falls in the forrest and no one is there to hear it did it still fall?

    The ground hears it. That is, the ground vibrates from absorbing the impact. That’s all “hearing” would mean in the context of physics.

    The egoism is caused by a reluctance to include speculation in a formal essay. A physicist trying to explain measurement using math would be seen by his peers as un-scientific. But trying to explain it in ordinary language can be excused as just dealing with the public. Once a physicist puts himself in this low-falutin mode of speech, he is vulnerable to all sorts of temptations in forming his thesis.

    Explicit collapse theories are a long way from being provable, but they are a responsible endeavor into a type of rational thinking that is unfortunately not very popular anymore.

  • Rebel Dreams

    Just a thought, and I hope that the real theorists here will correct me if I am wrong…

    The interpretation of Schroedinger’s Cat usually given in ‘pop’ physics books and programs tends to give rise to the suggestion, as stated above by slide2112, that ‘consioucsness’ becomes some quantum mechanism of determinancy. I, too, have a problem with that idea, for the same reasons he states. BUUUUTTT…

    What if, instead of ‘consciousness’, one substitutes the concept of ‘consequence’; i.e. the conscious observation of the cat’s state leads to a consequence of some kind, and thus the waveform collapse only occurs (and can only occur) when the collapse in one direction or another has a consequence on some aspect of the local space.

    That removes (IMHO) the troublesome idea of QM being predicated in some manner upon conscious observation, since that observation is only then, in this formulation, a specific flavor of consequence.

    Does this make sense, or am I rambling here? :D

  • mathematician

    @ Mark Harrison

    The fact that straw-men don’t have consciousness, doesn’t mean it doesn’t exist.

  • ST

    Many worlds is just the most literal reading of quantum mechanics. If Bryce De Witt had not given the name “many worlds”, this would probably not even be a controversy. Environmental decoherence + many worlds interpretation is all you need to understand that quantum measurement is just quantum evolution.

  • Sili

    And who, pray tell, is Neils Bohr?

  • http://eskesthai.blogspot.com/2008/07/sound-of-billiard-balls.html Plato

    I did not know there would be a series.

    A fundamental(foundational point of view) question to me is whether the content of one, can be based on the philosophical point of view(Science Saturday: Time

  • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

    Typo fixed.

    Jason, thanks for answering adamk87′s question. There’s no big deal about “bumping into” the apparatus; we can always make the slits and the detector big and massive enough so that they are unaffected by the photons. The fundamental issue is that the behavior of the photons is different if we watch which slit they go through vs. when we don’t.

  • http://countiblis.blogspot.com Count Iblis

    The fact that the interference pattern produced by interferometers involving mirrors is not affected by the mirrors recoiling, is actually explained by the fact that the mirrors themselves are described by quantum mechanics and have to obey the uncertainty principle.

    If you want to detect the “which path information” using the recoil of the mirror, the mirror’s wavefunction in momentum space would have to be sufficiently sharp. But then the wavefunction as a function of position would be broader than the photon’s wavelength, therefore you cannot have an interference pattern.

    More techically, the strength of the interference patern is proportional to the overlap of the wavefunction of the mirror (more generally, the wavefunction of the rest of the universe) when the photon recoils and when it doesn’t. The interference pattern will thus vanish when the overlap is zero, i.e. when the two wavefunctions are orthogonal. That in turn implies that there exists an observable such that the two wavefunctions are eigenfunctions with different eigenvalues. These eigenstates then correspond to the two paths the photon can take.

    In this article some less trivial cases of which path information are considered. You can
    produce entangled photons such that the “which path information” for one photon is present in another photon. Then you don’t get an inyterference pattern (you do get it when you measure certain correleations between the two photons). Unlike in the case of the recoiling mirror, the absense of the correlation cannot be explained classically.

  • Eric Habegger

    I still think there is a problem with the decoherence idea in that it treats the decoherence mainly via measurement interference with the wave function – as if the wave function is the final reality. But the wave function is just a statistical measure of potential. This is how it is described mathematically but it gives no fundamental insight on the nature of quantum reality from a non-statistical viewpoint.

    It has been shown that a pattern will build up on the target gradually of interference via the double slit experiments even if electrons are released one a time. This occurs as long as you don’t observe the path of the electrons. Obviously you can describe observing the path as creating a decoherence. But it tells you nothing fundamentally new.

    Doesn’t it seem much simpler, and also elegant, to just assume a memory effect is occuring in the vacuum from each individual electron passing through. The wave equation sensibility is just describing the build up of interference of each new electron being effected by the path of the previous electron going back ad infinitum to the first electron. The vacuum remembers!! And the decoherence effect that stops the interference and makes each electron act like a particle and not a wave is caused by randomizing the vacuum energy by shining a light on that path. Remember, the experiment always takes place in the dark for the interference effect to occur at the target and not along the path.

  • adamk87

    Hey Jason, thanks for elaborating on the experiment for me, but there are still some things that remain unclear. I think Ill just have to get some books on it.

    My question was in essence have all factors relating to the equipment used in the experiment been set up or examined such that what we observe is a reality and not just the equipment messing up the data. My guess is that when the experiment was first done the first thing that was questioned was the apparatus. I mean I don’t know much about physics or this experiment, but I was just wondering if either the ‘flash’ that is used to record the points or the disk that the electrons/photons are shot through could influence the data in such a way as to produce the results we observe.

  • Jason Dick

    Eric,

    The main point to be made is that what is “real” is largely an open question. Now, we know from measurements confirming quantum mechanics that “something” that behaves like the Schroedinger equation in the non-relativistic case actually exists. There is no question about this, and every interpretation of quantum mechanics that is in any way serious affirms this.

    The next question is, how much more do we need to describe observation? Decoherence provides the simplest answer: nothing else. All other interpretations assume the existence of other hypothetical entities in addition to the wavefunction that follows Schroedinger’s equation. The work done in decoherence theory seems to indicate that none of this is necessary, and since for the most part there are no observational effects from any of the added hypothetical entities from the other interpretations, they offer no new explanatory power and are simply culled out by Occam’s Razor.

    Attempting to claim that there is as yet reason to believe any other interpretation of quantum mechanics is rather akin to taking a set of data points that lies on a line, and claiming that we need to use a quadratic form to properly describe those data points. There is no need: the line works just fine. Therefore, unless we find some definitive evidence that the MWI is wrong, as weird as it is, it’s the only reasonable default position we should have with quantum mechanics.

    P.S. I’m sorry, but I don’t understand your statements about the vacuum.

  • Eric Habegger

    Jason,
    I think at this point we will have to agree to disagree as we both have our opinions. I will say this: If an interference occurs at the target in the two slit experiment even if electrons are released one at a time one can only conclude that the wave equation is being built up on a “memory” of the path of the last electron. There is no other way to put it.

    The problem I think you are encountering is not in understanding what I’m saying but in accepting that my explanation may be simpler to understand than yours. You have to accept that the quantum vacuum is a real physical entity and not just a useful mathematical abstraction. It seems to be an intermediary in all particle interactions. Not everything is just math – the math in physics actually represents something physical.

  • Jason Dick

    Eric,

    Errr, no memory of the paths of previous electrons is required. The probability distribution of where the first electron hits is completely independent of the probability distribution of where the second electron hits (assuming the first electron doesn’t change the apparatus, of course). In fact, simple memory tells you nothing whatsoever about the interference pattern. What is instead seen is that the behavior of the electron between the two slits and the screen is precisely as described by Schroedinger’s Equation. Somehow, until the electron hits the screen, it acts like a wavefunction. So why should I accept any explanation that claims that something different is happening at the screen, when one is available that assumes no such thing?

    And I have no problem with the idea that the vacuum is a real physical entity. I just have a problem with the claim that it is needed to describe what’s going on here.

  • Mark Harrison

    Eric & Jason,

    A way to settle this vacuum memory claim is to set up an ensemble of thousands of double-slit experiments and only send one electron through each. This way, the memory of the vacuum will not affect any other electrons, since there is only one electron per experiment. Then, tally up the positions in each of the experiments and note the pattern.

    If Eric is right, the distribution of the positions of the electrons should be uniform, instead of the standard double-slit fringes, since there will be no memory effect.

    All I need are thousands of electron guns, slits, film and labs. Where’s my grant money?

  • slide2112

    #26 Mark Harrison

    No, the measurement problem is there, read up on von Neumann measurement. The role of consciousness is either dismissed, or drop in favor of other interpretation. It is never shown to be wrong

  • Gary Mason
  • adamk87

    There

  • onymous

    The notion of “wavefunction collapse” is completely ridiculous, and it pains me that it is still taught to thousands of gullible youths.

  • onymous

    I would no longer think wavefunction collapse is so ridiculous if someone could present me with a theory of when it happens. If you believe in wavefunction collapse, what are the real laws under which wavefunctions evolve (which are now nonunitary), when does the collapse happen, how is the theory covariant (or why does it appear so to such high precision in experiment), and how do you experimentally detect the lack of unitarity?

    I think there’s a reason interpretational issues are usually discussed in the context of QM and not of QFT — in the latter context, it’s even harder to swallow the concept of wavefunction collapse.

  • ST

    There is no real collapse of the wavefunction. This is where decoherence is your friend. The whole point is that ONLY unitary evolution is there, and the “collapse” is an artifact of system-apparatus interaction.

    The system is in a superposition of many eigenstates initially. The eigenbasis for doing the expansion depends on the measuring apparatus. (i.e., you can expand a generic spin state as spin up-down or spin left-right or spin back-front, but “measurement” gives rise to a specific final state based on which of these three the apparatus is measuring). A measuring apparatus is precisely such a device that has states which couple to specific eigenstates of the system and evolve together. Because of the large number of states of the apparatus, the combined evolution is such that the overlap between one such (coupled) eigenstate of the system+apparatus, with another, is almost zero. A little bit of math shows that when this happens, one effectively ends up with probabilities instead of amplitudes. This is all there is to collapse.

    You still need many worlds here. Why? Because the eigenstates could have decohered away from each other because of coupling to apparatus-states, but still that does not tell us which branch we are in. This choice is where many worlds comes in. But this is no more an issue for (the mythical) “collapse” as it was for unitary evolution.

    There are some interesting questions you can certainly ask here, but I don’t see why people take pride still in saying that they don’t “understand” quantum mechanics. Decoherence + many worlds has solved the interpretational confusions of measurement. Whats funny is that I have even heard arguments against the landscape of string theory using arguments against the many worlds of QM. Of course, the arguments that one often hears against the landscape are also mostly based on gut feelings – either against (pereceived) speculation, or based on the (premature claim of) lack of predictivity. So maybe it is not that bad.

  • http://marcofrasca.wordpress.com/ Marco Frasca

    I think that Albert did not give properly Bohr’s view. All you need for the wavefunction collapse (or reality forming if you prefer) is to give an exact boundary between quantum and classical so that you have a sharp separation between these worlds and a measurement apparatus is a well-defined object whose interaction with a quantum system provokes collapse of the wavefunction.

    Marco

  • Jason Dick

    One other dumb question I had concerns the uncertainty principle. Is the consensus view that particles have a probability of placement vs a set space considered an inherent fact about particles or is there also a view that says we cannot specify where a particle will be because whenever we attempt to

  • ST

    “I think that Albert did not give properly Bohr

  • James Robson

    I had always intuitively rejected the “many worlds” interpretation as inelegant and a bit too star trek for my tastes. However, some of this discussion seems to have recast it as simply “decoherence” produced by the regular unitary evolution of QM when a microscopic system gets coupled to a macroscopic measuring device. This sounds more promising when expressed in words, but where can I find an (accessible) exposition of the maths behind it?

  • http://marcofrasca.wordpress.com/ Marco Frasca

    Dear ST,

    when you know what is classical and what is not and you know how both interacts you are done. You should try with thermodynamic limit, i.e. putting this limit to infinity. No need for a strange and useless universe proliferation (fairly good for science fiction writers) and some external entity to help you to come out of weirdness.

    Marco

  • Jason Dick

    Marco,

    It seems to me that you are presuming there exists anything that is truly classical. But if this were true, these classical systems would allow us to get around the uncertainty principle, which would make quantum mechanics inconsistent.

  • http://marcofrasca.wordpress.com/ Marco Frasca

    Dear Jason,

    I am just assuming that uncertainties are depending on the number of particles much in the same way as happens in statistical mechanics (t->-ibeta) so that, if the number of particles is large enough, you are in a pure classical realm. I mean something like Delta x = O(1/sqrt(N)) and Delta p = O(1/sqrt(N)). Then this object is classical. Rather I just note that a simple mathematical fact, that is the equivalence in quantum mechanics between thermodynamic limit and semiclassical approximation, is generally missed by well trained physicists.

    Marco

  • Lawrence B. Crowell

    The real question is whether quantum interpretations pertain to what is happening with nature, or whether they are what happen in the mind of a physicist.

    They have some utility in certain problems, but I doubt whether quantum interpretations have anything existential about them. Quantum interpretations probably should not be taken that seriously.

    Lawrence B. Crowell

  • http://marcofrasca.wordpress.com/ Marco Frasca

    Sorry, I meant

    Delta x/ and Delta p/ = O(1/sqrt(N))

    being and average values.

    Marco

  • Jason Dick

    Marco,

    But it’s still not a pure classical realm, only approximately so. It may be a very good approximation as far as any of our observations are concerned, but it’s still an approximation.

    And you don’t get away from the many worlds that are a consequence of decoherence theory by simply referencing the classical realm. To get rid of them, you have to explicitly exclude them by adding some new dynamics to the theory.

  • http://marcofrasca.wordpress.com/ Marco Frasca

    Dear Jason,

    For all practical purposes as claimed by environmental decoherence people supporting multiverse. I can say that also Dirac distribution cannot be realized in Nature but just fairly well approximated until my head does not hit a wall and I can understand what an approximation means…

    Marco

  • John Merryman

    ST,

    All the nonsense about Schrodinger

  • MWI adherent

    James Robson on Aug 10th, 2008 at 9:16 am:

    “I had always intuitively rejected the “many worlds” interpretation as inelegant and a bit too star trek for my tastes. ..where can I find an (accessible) exposition of the maths behind it?”

    Here.

  • Elliot

    I still like Jerome Rothstein’s information theoretic interpretation.

    All I can say in defense of this view, is it allowed me to sleep at night no longer wondering what quantum mechanics “really means”.

    Delusional? Perhaps. But a good night’s sleep is a good night’s sleep.

    e.

  • mathematician

    MWI adherent’s site: “And the Winner is… Many-Worlds! (the many-worlds interpretations wins outright given the current state of evidence)”

    It looks like MWI proponents are starting to act like string theorists.

  • MWI adherent

    “mathematician”:

    What a brilliant insight! Thanks for clearing things up for me. Previously I was deluded by all that lengthy evidence and argument; but it took someone of your caliber to point out to me that, clearly, MWI can’t be right, because, after all, its proponents think it’s right, and it’s obviously impossible to think you’re right while simultaneously being right! I mean, look at string theorists: they think they’re right, and everybody knows they’re a bunch of morons. Q.E.D.! Why didn’t I see it before?

    (/sarcasm)

  • ST

    James: “I had always intuitively rejected the “many worlds” interpretation as inelegant and a bit too star trek for my tastes. However, some of this discussion… ”

    I think ultimately it boils down to whether you are too chicken to *really* believe in the wave-function or not. I don’t mean you as in you, James Robson, but the universal You.

    Theoretical physics is about believing your theories until they blow up in your face. It is not enough that they merely make you uncomfortable.

    mathematician: “It looks like MWI proponents are starting to act like string theorists.”

    Being a string theorist, I have to say that string theory is in a far weaker place than many worlds. :) The wave function is simply the most fantastically tested object perhaps in the history of physics, and the many worlders merely want to attribute reality to it.

    As I have said repeatedly, many worlds is only about taking the wave function literally. This point is perhaps even moot from a scientific perspective, as long as we don’t come up with an experimental way of distinguishing between various interpretations. I cannot think of a way to test between Copenhagen and many worlds (I am no expert and have never really read/thought about either). Naively, it seems to me that anything that many worlds would call apparatus can be accommodated into Copnhagen by expanding the definition of the system. (Again, the wave function of the universe might be one place where this might not be true, so perhaps there is some extraordinary way in which cosmology can pick out the right interpretation. But let me stop speculating.)

    So this entire discussion, while fun, is only about us, and not about science. I personally like many worlds because despite the popular feeling that it is too extravagant (because of, well, the many worlds), I think it involves far less conceptual baggage than Copenhagen. In particular, I prefer a fully quantum mechanical world without any ad-hoc classical fixtures.

  • mathematician

    QED

  • Jason Dick

    ST,

    I think you can potentially verify the many worlds interpretation by looking at the boundary between collapse and no collapse, particularly if the interaction that generates collapse of the wavefunction in question is not used to perform any measurement. Doing so forces any theory of wavefunction collapse to explain how the collapse occurs in terms of physical processes, instead of whether or not a system was measured. The Copenhagen interpretation simply fails to do this, so any observation of collapse without measurement, and especially some physical mechanism providing gradual turn-on of collapse, completely destroys the Copenhagen picture.

    This test, it turns out, has been performed:
    http://prola.aps.org/abstract/PRL/v77/i24/p4887_1

  • collin237

    John,

    The concept of energy flowing through time and actualizing potential events is not analogous to quantum observation. Classically, energy impinges dynamically on a system and causes it to undergo some specific process. Classically, the cat dying is a dramatic event.

    In the quantum case, the observation of the cat dead is a direct transition to the already accomplished state. Presumably an energy transfer had occurred while the box was closed, without producing information. Then, when the box was opened, information appeared without an energy transfer. This is in stark contrast to the everyday world in which energy and information change at the same time.

  • Lawrence B. Crowell

    How can you take the wave function realistically? It is complex valued! :-) or for the Dirac field quaternionic valued. The problem is that we really don’t know what it means to take a quantum wave function in any realistic way. We might opt for MWI, or other might prefer Bohm, but these are really mathematical constructions which can’t be easily set in some sort of “quanta are real” certaintude.

    Lawrence B. Crowell

  • Jason Dick

    Lawrence,

    Why does the fact that the wavefunction is complex valued have anything to do with whether or not we should take it realistically?

  • Lawrence B. Crowell

    Anything which we regard as real is something which makes a detector “click,” make a CCD pixel activate, register a voltage or add a bit to a computer register. In other words what is real are things like particles, or as Johnson put it “I kick it and it kicks back.” Even general is a theory involving the relationships between particles — it is really not a theory primarily focused on spaces or points in space. Things such as wave functions, fields, and spaces or spacetimes are really our mathematical constructions.

    Lawrence B. Crowell

  • Jason Dick

    Except the complex phase invariance of these particles leads to conservation of electric charge. Is electric charge not a directly-measurable property?

    Furthermore, one can measure differences in complex phase by observing interference patterns from particles that take different paths of different lengths.

    So I don’t honestly see how your objection has any merit.

  • http://tyrannogenius.blogspot.com Neil B. ?

    I see decoherence coming up again, it seems the elephant in the quantum container. There was a good discussion of decoherence in the thread linked at http://blogs.discovermagazine.com/cosmicvariance/2008/07/07/everything-you-every-wanted-to-know-about-quantum-mechanics-but-were-afraid-to-ask/#comments. One of the “justifications” for what I call “art deco” because I don’t think it’s a genuinely viable concept, was that the wave function can be thought of as comprised of a bunch of other components, such as the innumerable positions a particle could have etc. (But so could a classical wave be so imagined by mathematical decomposition, with no particular consequences ….Why don’t the waves just remain interacting like classical waves, which have no basis for splitting up into versions of localized interaction?)

    Then, under “decoherence” each of these position components gets entangled with a version of the target/observer (in my rather sloppy rephrasing of the general idea) and ends up in its own little world and so on (but why there should be separate worlds for the different ways to hash out instead of the whole mess just staying superposed together, escapes me along with the rest of the hat trick.) However, note that in QM each of those “components” like the portion of the wave going down one path and the portion going down another, have amplitudes (well, amplitude over volume) less than one. IOW, they are the partial amplitudes for the particle appearing in each particular possible place (simplistically put in an example that we can construct at least.)

    But when a given “observation” makes the particle “appear at the observed location” the amplitude of the locally condensed-down wave concentrates back into amplitude “one”. That isn’t the same as each little Fourier subwave being led off into it’s own little dream world, where each would keep its own lesser amplitude. See, the whole wave has to pile back into that one little space, and if we multiply the outcomes then we have to increase the *total* amplitude of all the “worlds” combined – they have to borrow from each other in effect. I don’t think that works, because you can’t just get it out of the waves and their interactions (either the total amplitude should concentrate into *one* unique spot and take away from the other places – and thus no multiple outcomes, or the dividing up of the wave must leave each version in an attenuated state (with who knows what type of possible outcome.)

    And there are ironies, such as the attempt to say both that quantum interpretations don’t or can’t matter since all we have is the outcome and predictive schemes, but that nevertheless decoherence is the way to explain what happens! And note ST claiming that measuring instruments have some way of interacting with the wave functions of particles that somehow results in a localized detection, well does that make them special after all? Is a simple screen waiting for an electron to hit “somewhere” such a thing and how does it really concentrate the entire wave into one spot, and yet somehow also concentrate the whole wave into some other spot elsewhere (elsewhere on the screen *and* elsewhere in a sense we don’t even understand.) If art deco can explain the waves ending up in the way we finally observe them, why does it still need to split up all the possible results?

    Like I have said, IMHO art deco is a trick based on circular reasoning and hidden assumpit0ons, as well as sidestepping the issue of apportioning amplitude. Look at comment # 161, from a person who apparently would like to support deco but appreciates the problematical nature of the idea.

  • James Robson

    Hi Lawrence B. Crowel,

    It would seem from #54, and to some extent #69, that you adopt a rather solipsistic attitude to any attempt to “understand” the Universe. It all occurs in the “Physicist

  • Lawrence B. Crowell

    Look at it this way. You can consider a point in spacetime x, which under different coordinate conditions define a metric g_{ab}(x) and g’_{ab)(x), which are of course coincident. Yet in ADM relativity you then find in the subsequent time slice that the two metrics have pushed x to different points, say y and z. So for all we work hard to learn geometry and the rest, general relativity is not really about spaces — it is about the relationship between particles. The goedesic deviation equation tells us how two particles will move relative to each other. All the geometry stuff is really mathematical modelling.

    Feynman in many ways made a point of this. He worked to illustrate what happened with particles. He did not get caught up in lots of wave function talk or about the mysteries of QM waves. I tend to hold much the same viewpoint, in particular when it comes to quantum interpretations.

    Our models are descriptions of nature, and they have some value in that sense in informing us how nature functions. Yet by admitting what we work on are model systems we can avoid getting caught in intellectual traps — such as people in the early 18th century who worried about the reality of gravitational lines of force.

    Lawrence B. Crowell

  • collin237

    I don’t get why people think MWI completes QM. It claims that the observer, as he knows himself, is only a small region within an expanding state space of his “actual” existence, but it doesn’t explain what makes him occupy one region rather than another.

    Perhaps he chose it? That is a clever cop-out. Since there is no known way to model consciousness in a physical theory, you sweep the mystery of decoherence under the rug of conscious choice. Not only is there still a mystery; there is now the second mystery of why this choice should have precisely the same statistics as Copenhagen randomness.

    The only thing MWI completes is the equation journals of the pencil-pushers at the laboratories. That is not what physics is supposed to be about.

  • Jason Dick

    Neil B.,

    But when a given “observation” makes the particle “appear at the observed location” the amplitude of the locally condensed-down wave concentrates back into amplitude “one”. That isn

  • Jason Dick

    Lawrence,

    Yet by admitting what we work on are model systems we can avoid getting caught in intellectual traps — such as people in the early 18th century who worried about the reality of gravitational lines of force.

    Then why is it that gravitational waves exist, if gravity is just about relationships between particles?

  • ST

    Jason #65: A belated thanks for the link – I saw your message only now. Anyway … If you are saying that the experiment you pointed to verifies that decoherence is real, I fully agree. But I do not consider that to be an experimental test of many worlds vs. Copenhagen.

    Many worlds is an “explanation” why we are in one of the decohered branches (as opposed to another) with some probability. But a true adherent of Copenhagen can still get away with the claim that this is some kind of staggered collapse. Afterall, the time-line for collapse is not really fundamental to the whole Copenhagen interpretation (even though, perhaps, Bohr himself might have believed that the collapse was instantaneous).Of course, it becomes increasingly contrived to differentiate what is classical and what is quantum in the Copenhagen interpretation in light of such macroscopic deoherence experiments, but then again, there has never been a precise difference between the two to begin with! The only real way to tell what is quantum in Copenhagen is to do an experiment like the above!!

    As I said in a previous post, as long as we are willing to be fuzzy about what is classical and what is quantum (and that is the fundamental reason why I prefer many worlds), we can always expand the definition of the system.

    Mathematician: Love, I mean LOVE, your pithy one-liners. :)

  • ST

    “As I said in a previous post, as long as we are willing to be fuzzy about what is classical and what is quantum (and that is the fundamental reason why I prefer many worlds), we can always expand the definition of the system.”

    Just in case anybody is still reading this: I meant that the distinction between classical (observer) and quantum (observed) is not a priori well-defined in the Copenhagen view. And that is why many worlds is appealing to some of us.

  • mathematician

    Physics doesn’t need “MWI adherents”, “Copenhagen adherents”, etc..

    “Adherents” generally don’t have a good track record of getting things right.

    The last “adherents” in physics to have gotten it right were the “gluon adherents”.

  • Jason Dick

    ST,

    I think the problem that experiments like that pose for the Copenhagen interpretation is that it forces the interpretation to become more specific in what is meant by “measurement”. The basic Copenhagen interpretation simply fails to explain what’s going on here, and it needs to be buttressed with some new machinery to more accurately describe the collapse, making the Occam’s Razor case for the MWI even stronger.

  • Lawrence B. Crowell

    Jason Dick: Then why is it that gravitational waves exist, if gravity is just about relationships between particles?

    —————

    Maybe with gravitons? Physical models and its mathematics are really similar to art in a way. They are representations of what we observe in the natural world. They are representations of the world, but the particular geometrical structures we appeal to are not necessarily how nature is organized. In our more modern world Newton’s lines of force have been replaced by spacetime curvatures. We are less inclined to see on a fundamental basis a gravity field according to a radial vector field — even though we can do all sorts of Gauss law calculations and predict planetary orbits. These representations are useful up to the limit they permit us to predict things about the world. Ultimately what is real in science is what makes a detector record a value. Physics is an empirical science after all.

    Lawrence B. Crowell

  • Eric Habegger

    At the risk of kicking a dead horse (darn horse just keeps getting up!) I must insist that the hidden variables view of Bohm has much more going for it than MWI – for one reason. You will find in Feynman’s illustration with electrons, and I think also with Young’s of photons in the 1800s, that the that the build up of interference at the target occurs even when there is space (in time) between individual particles being released.

    This is not my interpretation – this is not something that needs to be further tested to prove – it has already been shown in experiments that Feynman – to his discredit – made very little fuss about, if I remember right. But it is a big thing. In fact you could say that in a perfectly cold environment of 0 degrees K that state that exists in the path in the vacuum to the target between the two slits will exist indefinitely. At that temperature that path could exist for eons and be perfectly preserved. If one doesn’t describe the physical vacuum through which this path is carved a “hidden variable” then I say its only a matter of semantics. If one looks at it this way, and one is intellectually honest, one must describe it as something that acts like a hidden variable. It also shows that the evolution of “state” in the vacuum is directly related to the passage of energy and information and that this is what we are really describing when we discuss the passage of time.

  • http://tyrannogenius.blogspot.com Neil B. ?

    Jason, (anyone

  • Jason Dick

    Neil,

    But you didn

  • Eric Habegger

    “How can the Bohm interpretation account for the gradual turn-on of wavefunction collapse in carefully-designed experiments?”

    Jason,
    I actually find the use of “lines of force” visualization quite useful. The vacuum isn’t a unified whole as such but has some granularity which can be broken down to Planck length increments. One can represent each of these increments as possessing a random line of force whose orientation can be altered. The passage of a photon, or any particle for that matter, through this quantum foam will have an effect on the orientation of that force. If you pass a particle through this quantum foam there will be a meandering path created whose average value will be a vector formed from the initial velocity and energy of the particle at launch. To get the least meandering path one would want to irradiate the path before launch to target to completely randomize the “foam”.

    One this initial particle has arrived at the target, and assuming the system is completely isolated from outside energy, a fairly straight path will be created in the vacuum. As each following particle is launched the lines of force created by previous particles will create an interference. It really behaves no differently than what Faraday discovered 200 years ago but in a granular and discontinuous way. As long as particles are launched at a low enough angle to previous launch velocities a predictable interference will build up.

    But once you launch particles or radiation transverse to the path its like scattering billiard balls. Its very unpredictable what the final result will be. In essence the previous predictable interference path is destroyed. You have essentially randomized all these tiny lines of force and have started the process of re-initializing the experiment that we started at the beginning. But one doesn’t have to completely reinitialize in “one swell foop”. One can do it in small increments at various points on the path and divide it in time

  • Eric Habegger

    “To get the least meandering path one would want to irradiate the path before launch to target to completely randomize the “foam”.”

    I should have said that after randomizing the path you will get the least “deviation” from the initial trajectory along the entire path when subsequently shooting a photon or electron through it. “Meandering” probably isn’t too scientific a description. In effect the particle then acts like a particle and not a wave by randomizing information from previous particles.

  • Jason Dick

    Except particles don’t interfere with previous particles. They interfere with themselves.

  • Eric Habegger

    “Except particles don

  • James Robson

    Hi, again, Lawrence B. Crowell,

    Thanks for your reply to my comment.

    You seem to try to give an analogy to the QM interpretation issue using a GR equivalent. Your example uses the ADM formulation but I’m not sure why this particular formulation is need to make your point?

    Certainly, it would seem (from the tediously philosophised “hole argument” – if nothing else) that GR teaches that the geometry (i.e. the coordinitised set of spacetime points) is nothing more than a bookkeeping device (well this is not entirely true as the associated topology and dimension, for example, seem to be fairly relevant, at least classically).

    We are left without the props of any special coordinate systems constructed with measuring rods and clocks and so, unless the events in question occur at the same spacetime point, then the interpretation is up for grabs (ish…) and strange things can seem to happen. I agree this is odd, and I happen to think that relativity (even special) is, in the long run, harder to comprehend than QM. It just seems easier at first.

    However, even in GR things still happen at definite coordinate “points” with definite “momenta” (how measured – what meaning? Ok, granted…) But we seem easily able to ignore the new situation and retain the Newtonian clockwork comfort of our childhoods.

    Not so with QM.

    As for Feynman – I think one of his greatest legacies was pedagogical and he instilled real understanding in generations of students. I never had the pleasure of meeting him, but still I find it hard to believe that he would be satisfied with the ignorance that we currently have regarding the understanding of Qm. (As I said, I don’t really know so I shouldn’t speculate)

    Also – why did Einstein move us beyond the “people in the early 18th century who worried about the reality of gravitational lines of force.”?

    For purely practical, experimental reasons?

    -James.

  • Jason Dick

    Eric,

    Then how do you explain the Aharonov-Bohm effect?

  • Eric Habegger

    Maybe someone can reiterate what the Aharonov-Bohm effect actually is. Its been too long since I read about it.

  • Peter Shor

    About Mark’s question, I don’t believe the Transactional Interpretation is compatible with the quantum factoring algorithm. That is, the naive understanding of the Transactional Interpretation leads you to believe that factoring is in randomized polynomial time, which is generally not believed by computer scientists (and this would extend to any problem in BQP, which is much less believable). And I’ve looked for some description of the Transactional Interpretation that goes beyond this naive understanding, and was unable to find it. This is entirely consistent with Domenic Denicola’s comment that it is believed that the Transactional Interpretation only works with one particle.

    On a related topic, I have never been able to make sense of the factoring algorithm in Bohm’s interpretation (although at least you can see where the computational power is coming from in that interpretation). Can anybody help me here?

  • Jason Dick

    Eric,

    The Aharonov-Bohm effect is an effect where magnetic fields outside the path of the electron have an effect upon its phase. Basically, if you have a two-slit experiment, and place a solenoid between the slits, turning on the solenoid shifts the interference pattern. Note that the magnetic field never actually crosses the paths of the electrons.

    Of course, this effect is well-understood in terms of normal quantum mechanics, but it just reinforces the statement that it’s actually the phase of the individual particles that are interfering with one another. Since the various particles are often not produced with coherent phases, it makes no sense for the interference to be between particles.

  • mathematician

    Is there an up to date review of BQP and its relation to various classical computational complexity classes (and any other quantum ones as well)?

    (I don’t know what BQP is. I’m just going by the context.)

  • jim

    Thanks. That was a great Diavlog. I would like to see you do another one on QM with Anton Zeilinger, and I’d pay money to see one between Zeilinger and Albert. It reminded me that I don’t really get the MWI or why people like it.

    Tell if I’m wrong here: The MWI means that there are branches of the wavefunction where the most improbable series of events actually do occur. For example, there’s a branch of the wavefunction of the universe where every quantum experiment done on earth after this post results in the least probable of outcomes. Doesn’t the fact the we don’t ever see anomalous outcomes of quantum experiments (such as a quantum coin flip that keeps coming up tails for the rest of your life) mean that the MWI doesn’t work?

  • Christopher M

    I don’t quite get Albert’s obsession with the idea that taking the MWI seriously precludes someone’s being surprised at extremely unlikely quantum events. Sure, the theory predicts with probability one that such events will happen. So what? That just means that it predicts with probability one that someone (somewhere in Hilbert space) will find themselves in a position to be quite surprised.

    Albert seems to think that this surprise is somehow illegitimate because there’s no basis (within the theoretical resources of the MWI) for any background expectation of what “should” happen. That is, it was inevitable that there would be a person who sees a million z-spins in the same direction; I am that person; there’s no reason to think I “should” (even in a probabilistic sense) have been some other person. There are two things to say in response.

    1. Isn’t Albert’s objection resolved by the pretty weak assumption that one expects to experience macrostates (so to speak) that arise from a large number of different microstates, just because if all the microstates happen (as the MWI proposes) then there’s nothing to choose between them and most people will be in positions to observe one of these “likely” macrostates? But this is just thermodynamics and Albert wrote a good book on that so I imagine he knows what he’s talking about.

    2. I’m not sure there’s a problem even without that assumption. Do you really need a background expectation of what should happen in order to be legitimately “surprised”? Isn’t it enough to say that this kind of surprise is legitimate when what one observes is an outlier among the set of things that could have happened? Who cares, looking backwards, what was likely or not? Even if it turned out that (given the initial conditions & dynamical principles of the universe) it was inevitable that all the electrons I’m looking at would have their z-spins up, I would still find that fact to be worthy of note, or if you prefer, “surprise.”

  • Christopher M

    (I suppose the Born probability rule prevents the analogy with thermodynamics from being very good. But isn’t that the problem one should be talking about, not this attempt to derive facts about how physics works from human notions of “surprise”?)

  • Jason Dick

    Christopher,

    His objection, as near as I could tell, was in the deriving of probabilities from the MWI. After all, if all outcomes occur, why should we be surprised by any outcome that has non-zero probability?

    Here’s how I look at it. Imagine that we are sitting here before conducting an experiment. The experiment in question is a quantum-mechanical version of flipping a coin many times: we’re going to perform a quantum mechanical measurement of a system that has two possible states. Before performing the experiment, I’m going to make a definitive statement about what I expect to see and what I don’t expect to see. For example, if we make 100 “flips”, I don’t expect to see all heads or all tails as outcomes. In fact, I expect to see that the number of flips will be approximately 7 flips away from 50 heads.

    Now, in the MWI, why am I justified in making this statement? Consider that immediately after the experiment, “I” will have split into 2^100 different worlds, and will observe every single outcome. There will be a “me” after the experiment who observes the 100 heads result. There will be a “me” after the experiment who observes the 100 tails result. But I can still be firmly justified in expecting to see around 7 flips away from 50 heads because nearly all of these 2^100 future me’s, each of whom has equal amplitude, will not see these outcomes. Therefore I might imagine that by making these choices, I’m choosing to attempt to say as much as I can about what will happen in the future as accurately as I can. I do this by maximizing the selves who are unsurprised by the outcome and minimizing the selves that are surprised. Because this game is completely isomorphic to just dealing with probabilities, we might as well consider it such.

  • Christopher M

    Jason,
    I may have misunderstood, but I thought that Albert’s objection (if that’s the right word — probably “puzzle” is better) had to do with how the post-experiment “you” who sees 100 heads should think about the probabilities. Why should that instance of you find the 100-heads result surprising? (After all, the objection goes, the MWI predicted with certainty that this version of “you” would exist.) I won’t repeat my answers to this objection. I’m not even sure they’re all that good, especially since it isn’t the case that all possibilities in configuration space occur with equal probability. (Unless perhaps that is the case, and the Born probability rule is more apparent than real — but I don’t know the physics or the math remotely well enough to have any wisdom on that question.)

  • Jason Dick

    It’s surprising because most of the observer amplitude finds very different results. For the typical observer to see one instance of 100 heads in a row, the experiment would need to be repeated around 10^30 times.

    To contrast this to a different system, think about winning the lottery. The probabilities are such that it is no surprise whatsoever that somebody wins the lottery quite frequently. But if, for example, I purchased one lottery ticket a week, I would be very, very surprised if that somebody turned out to be me. By analogy to the coin flip scenario, it makes sense to equate the observers in the 2^100 different worlds as being different observers that share the same past worldline. Because they each have equal amplitudes, and because so few of them experience events like 100 heads in a row, it only makes sense to be surprised when I find myself in that situation.

    Now, then, going back to looking at the experiment beforehand, the point remains that we have one observer that splits into many. If we were to consider adopting a strategy to ensure that the amplitude of this observer that is not surprised by the result is maximized, we’d find that the best strategy the observer can adopt is to make use of the Born formula and to consider the future possibilities as probabilities, despite the fact that they all occur.

  • Lawrence B. Crowell

    Peter Shor wrote: On a related topic, I have never been able to make sense of the factoring algorithm in Bohm

  • Jason Dick

    Huh? How’s that going to work for, say, the three-slit experiment?

  • Lawrence B. Crowell

    I had not thought of a 3-slit experiment. I suppose we could consider the Bohmian path as a set of three paths which are loops that pass through all possible pairs of loops. Maybe some sort of braid group or knot system can be formed from these loops.

    Lawrence B. Crowell

  • Jason Dick

    Sounds hopelessly contrived to me. And I suspect that the result will depend strongly upon the choice of path, and it seems questionable that it would coincide with the predictions of quantum mechanics.

  • collin237

    Jason wrote:

    It

  • Jason Dick

    It still works in this scenario if I and my brother are identical twins, though.

  • Lawrence B. Crowell

    Bohm’s interpretation is somewhat contrived as it is. There is this quantum potential

    $latex
    Q~=~-{hbar^2over{2m}}{{nabla^2 R}over R}
    $

    for R the polar amplitude, which is often computed by first finding solutions for a system by standard methods. So Bohm’s QM is weak or contrived to some degree. Also since it avoids Hilbert space and discrete states it also fails in the domain of relativistic QED where particles are produced. Yet, if one wanted to connect Bohm’s theory to quantum factorization what I suggest above might be one way of doing this.

    Bohm’s QM is not the most convenient approach to working with quantum information issues — to say the least.

    Lawrence B. Crowell

  • http://tyrannogenius.blogspot.com Neil B. ?

    Jason, this statement in #98:
    But I can still be firmly justified in expecting to see around 7 flips away from 50 heads because nearly all of these 2^100 future me

  • John Merryman

    collin237,

    Aug 11th, 2008 at 3:58 pm
    John,

    The concept of energy flowing through time and actualizing potential events is not analogous to quantum observation. Classically, energy impinges dynamically on a system and causes it to undergo some specific process. Classically, the cat dying is a dramatic event.

    In the quantum case, the observation of the cat dead is a direct transition to the already accomplished state. Presumably an energy transfer had occurred while the box was closed, without producing information. Then, when the box was opened, information appeared without an energy transfer. This is in stark contrast to the everyday world in which energy and information change at the same time.

    (Sorry for the delay, I was away.)

    I realize relationships at the quantum level are complex and inherently fuzzy, but in post 49 you asked a basic question; ” How does the universe knows which is the observing system and which is the observed?” To which I offered a simple answer.

    Whether they change at the same time, or not energy(the observer) goes from past events to future ones, while information(the observed) goes from future potential to past circumstance.

    Consider the light passing through the slits and striking the screen. The energy goes from one event, the slits, to the next, the screen. On the other hand, the information that is these events goes from potential to actual. So while the energy may be conserved and therefore not collapse, the information would seem to collapse, at least within the context of the observer’s particular world.

    It would be hard to argue another world is formed, as this would require a duplication of the energy, as it means a duplicate observation. If energy and information were analogous, then information would also move from past circumstance to future potential and many worlds would result, but only energy does. That’s why the physical energy of your brain moves into the future, but the information of your mind recedes into the past.

  • Jason Dick

    No, how can “I” be justified in expecting any particular outcome at all

    The point is that before the measurement, the observer is one person. After the measurement, the observer becomes many different persons. Consider the situation where we’re talking about gambling, and let’s say you want to bet in such a manner that you maximize your winnings afterwards.

    Now, in this situation, some of the observers after the experiment are guaranteed to win, while others are guaranteed to lose. But how do we maximize the overall win/loss ratio? It turns out that the way to do that is to understand the system as operating probabilistically under Born’s rule. Maximizing the probability of winning using the Born rule turns out to be the exact same thing as maximizing the winnings of the multiple selves after the experiment.

    BTW, I am proud to report that Google search for “quantum measurement paradox” brings up a post of mine in place #2

    That’s probably because the more common terminology is “quantum measurement problem”.

  • Jason Dick

    John Merryman,

    It would be hard to argue another world is formed, as this would require a duplication of the energy, as it means a duplicate observation.

    You’re misunderstanding what is going on in the many worlds interpretation. Energy is not duplicated. If the system splits into two after the observation, all that has happened is that the wavefunction of the system has been placed into a superposition of two states, and those two states are such that they don’t interfere strongly with one another. Because the observer is also quantum-mechanical, they exist in the same superposition of two states. But since the two states don’t interfere significantly, each component of the superposition isn’t capable of observing the other.

  • omh

    John Merryman –

    As jason has pointed out, there are not ‘two universes’. The MWI is simply a statement that the unitary evolution of the wave function is mathematically equivalent to ‘many worlds’. There is no problem regarding energy conservation. And even if you misunderstand the idea and think that it is literally saying that universes are being created or destroyed, there is no physical law regarding the conservation of energy across multiple universes. All that physicists know is that energy is conserved in the world we can see around us.

  • mathematician

    Re Peter Shor #92

    Is there an up to date review of BQP and its relation to various classical computational complexity classes (and any other quantum ones as well)?

    (I don

  • ST

    Jason: “The basic Copenhagen interpretation simply fails to explain what

  • John Merryman

    St, Jason,

    So you want to constrain and condense the argument for an unconstrained and un-condensed view of reality?

    Maybe a bipolar argument is necessary to support a bipolar reality.

  • http://www.quebecregion.com/campagne_publicitaire/hiver_2007-2008/400/index-e.htm Q-CD

    @Jason & ohm

    Hi,

    I definitely think your last answer is correct according to MWI. I don’t understand, however, how one can consider it’s enough to solve the problem.

    Yes the energy is conserved overall, but that’s not the same as “each world in MWI must have the same energy content”.

    Energy conservation [I]as MWI predicts it[/I] corresponds to the former. Energy conservation [I]as we see it[/I] correspond to the latter. If it is a natural feature of MWI that both correspond… well then I just missed something, please let me know what.

    In fact, MWI would offer a natural explanation if energy would prove to be [I]not[/I] conserved in our (partial) world, as one might imagine from this http://fr.arxiv.org/abs/0804.2178

  • http://www.quebecregion.com/campagne_publicitaire/hiver_2007-2008/400/index-e.htm Q-CD

    PS: in my previous post please understand “each world in MWI must have the same energy content” as “in MWI each possible observer will experiment energy conservation”.

  • Jason Dick

    Q-CD,

    I don’t think we’ll get non-conservation of energy in any interpretation of quantum mechanics, let alone with MWI. The basic problem is all of the interactions in quantum mechanics conserve energy, and since any change in the energy levels will involve an entanglement between some other particle that carries off or supplies the energy of the state, it seems to me that the most you’ll be able to do is have energy reshuffled differently in the different worlds of the MWI.

    Here is, basically, what you would need for energy conservation to be violated:

    1. Start with a single, discrete energy state.
    2. Make a change to the system so that it is split into a two-level state with different energies, without transferring energy to/from the environment
    3. Make a measurement of the energy level of the system: some of the worlds will measure an energy increase, some an energy decrease.

    It’s the bolded point in step two that I don’t think is going to ever be possible.

    As for the heat bath theory paper you mentioned, I think it’d be interesting to compare the entropy transfer of that setup with the entropy required to perform the measurements. Somehow I suspect that we’ll find that the measurement itself requires an entropy increase that makes up for the decrease in entropy of the system. If not, then this will be a method to obtain free energy (that’s why I strongly doubt that it’s going to be the case).

  • John Merryman

    Jason,

    Wouldn’t the scale be tipped in favor of the direction/world that received the most energy and that determines whether the cat is dead or alive? Once the scale has tipped, with that original quantum break, it has a cascading effect to the macro level, so that while at the quantum level there is inherent fuzziness, this doesn’t carry to the macro level, since valid worlds built around both events would require sufficient energy to manifest them. ?

  • http://www.quebecregion.com/campagne_publicitaire/hiver_2007-2008/400/index-e.htm Q-CD

    >the most you

  • Peter Shor

    mathematician wrote on Aug 13th, 2008 at 4:56 am

    Is there an up to date review of BQP and its relation to various classical computational complexity classes (and any other quantum ones as well)?

    ===========

    I would suggest Lecture 10 in Scott Aaronson’s class (and maybe some previous lectures as well, depending on what your background is:

    http://www.scottaaronson.com/democritus/

  • mathematician

    Thanks! Looks good!

  • Jason Dick

    Q-CD:

    Those worlds are probabilistically-suppressed just as they are in any interpretation of quantum theory. We still don’t expect to see such violations because they’re going to be so rare.

    As for quantum suicide/immortality, I think it ignores something crucial: death isn’t instantaneous. If, for example, the “me” in the current world is going to die in ten seconds, but the “me” in a different world from which I have already decohered will not, it is of no help whatsoever as far as my future is concerned. It also ignores the fact that the elimination of consciousness is going to be a gradual process, such that death itself is an inherently classical phenomenon.

  • Q-CD

    @ Peter Shor: thanks for this interesting link

    @ Jason Dick: that’s definitely a good point. Thanks for this discussion ;)

  • Leigh

    The discussion was very interesting but seemed to reach somewhat of an impasse relating to an amoeba

  • TwisMinion

    It is perfectly fine for the amoeba to bet which side it will end up on.
    Say it guesses that it will end up on the left
    If you follow up with the amoeba on the left after the split, you will find that it was 100% correct.

  • http://www.twis.org/audio/2008/08/19/268/ TwisMinion

    I admit not understanding the many worlds theory, or the larger implications of wave collapses and would like to hear more…

    But i would also like to have the issue of sperm addressed… as in, if every sperm reaches the destination, then the many worlds are of every potential variation of every potential life that ever could have transpired?

    It isn

  • Jason Dick

    But i would also like to have the issue of sperm addressed… as in, if every sperm reaches the destination, then the many worlds are of every potential variation of every potential life that ever could have transpired?

    It doesn’t necessarily mean this. There is no reason to suspect that macroscopic probabilities due to ignorance of all of the relevant variables are the same thing as superpositions of quantum states. That is to say, sperm are quite large enough that they’re largely classical objects. So there is no reason to suspect that every one makes it in a different one of the many worlds.

    The proliferation of worlds within quantum mechanics means that every possible outcome occurs, but this doesn’t mean that every imaginable outcome occurs. And it further doesn’t mean that every outcome which, given our limited information, we think might occur will do so. Many outcomes that we think might occur may, given fuller information, prove to be impossible.

    As for the amount of information, well, the Hilbert space that describes quantum mechanics is an infinite-dimensional space. There is no limit to the amount of information.

  • http://www.twis.org/audio/2008/08/19/268/ TwisMinion

    -Thanks Jason…

    The many worlds theory only comes into play when an observation is made of a quantum state? Ok, that is a relief of sorts…

    That would mean only quantum physicists could be affected by this.

    Does the multi-verse re-enter a symmetry with the rest of us after the observation, or are we all experiencing a butterfly effect from the various different observations made by these quantum observers?

  • Jason Dick

    The many worlds theory only comes into play when an observation is made of a quantum state? Ok, that is a relief of sorts…

    That would mean only quantum physicists could be affected by this.

    Haha, well, it’s not quite that simple. Basically it’s just difficult to understand quite what the quantum mechanical effects on macroscopic, highly complex systems like our own bodies are. I mean, we understand quite well what the classical limit is, but we don’t really understand how this all translates back to quantum mechanics, so it’s not really worth worrying about (unless, of course, you’re interested in discovering those details).

    What’s basically happening with the many observers is that they’re continually dividing, each one only seeing one of the possible outcomes. Recovering some sort of symmetry would be effectively the same as a reducing entropy. We see the effect as, in essence, a loss of information to the environment. These other worlds are inaccessible to us. Basically, portions of the wavefunction of the universe which we can now interact with will become inaccessible to us later through decoherence: the information content of those portions of the wavefunction are effectively lost to us.

  • http://www.twis.org/audio/2008/08/19/268/ TwisMinion

    information loss? hmmm…

    ok, still, so i can envision the dividing observers… but what comes after?
    do they un-divide at some point or splinter off infinitum?

    If there are multiple observers there must be multiple universes to go along with them, right?

    i think the information loss aspect allows for the infinite splitting to go on without having to consider it… if it happens, it happens in a way that we can’t see and therefore doesn’t matter… ok…

    but if it’s supposed to only be a limited experience then there are issues… like, what to do with all these “you’s” that just saw different things but are supposed to react the same…

  • Jason Dick

    They splinter off ad infinitum until maximum entropy is achieved.

    And it’s not so much that they’re multiple universes, but that there are multiple, approximately classical, approximately non-interacting “worlds” of the infinite-dimensional Hilbert space.

    I personally think that “multiple universes” is just bad use of language, as “universe” means all that exists. So you can’t, by definition, have multiple universes. It’s just that different components of the wavefunction of the universe can’t interact with one another to any significant degree. These different components are viewed by observers within them as worlds unto themselves, because they can’t see what else is out there.

  • http://www.twis.org/audio/2008/08/19/268/ TwisMinion

    ok, so here’s where i try to play with this…

    each observer takes some note of the trailing digits of collected data…

    doesn’t matter what those digits are, but we know they are different to each observer…

    we then use these trailing digits to formulate a date and time and show up to our favorite restaurant at that date and time…

    now we have split the universe for more than just a few moments, for all our other observers are eating at different times, at different tables, and having different meals… further creating a butterfly effect on the macro scale on all the other people the observer encounters…

    quantum physics can become contagious it seems…

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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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