The Quantum Pontiff

Everything and Nothing

Over at Uncertain Principles, the uncertainty father has a couple of posts up about parallel universes the many-worlds interpretation of quantum theory. Which reminded me of a rant I’ve been needing to write (sorry a bit of technical jargon to follow.)

History adds that before or after dying he found himself in the presence of God and told Him: ‘I who have been so many men in vain want to be one and myself.’ The voice of the Lord answered from a whirlwind: ‘Neither am I anyone; I have dreamt the world as you dreamt your work, my Shakespeare, and among the forms in my dream are you, who like myself are many and no one.’ “Everything and Nothing” by Jorge Luis Borges.

In the many-worlds interpretation of quantum theory one attempts to treat measurement in a way that doesn’t require an extra “measurement postulate” of quantum theory. One simply notes that if you measure a quantum system, you become entangled with this quantum system, and then any future behavior of you and the system you measure will be as if have done the measurement. Thus one could imagine that there is only unitary evolution of the wave function, and, since there is no reason to demote any of the universes in which your measurements come out different, one might as well think that these parallel branches of the wave function are equally valid realitys. Or something like that.

Interestingly upon reading a description of the many-worlds interpretation this is often followed by thoughts along the lines of “everything that can happen, does happen.” For example, here is the writer for a PBS special on Hugh Everett, the original proponent behind the many-worlds interpretation:

Byrne: …Actually, it’s very much in use in physics today. However, it has consequences to it that people were and remain uneasy with, which basically is that everything that is possible happens

But is this correct? Does the many-worlds interpretation mean that there is some probability that everything that can occur will occur?

Actually, as far as I can tell, it tells you nothing of the sort. In fact it tells you that there is a hell of a lot (to be defined technically below) which won’t occur. In fact in all quantum theories for systems of a minimal size quantum theory tells you that there exist an infinite number of worlds which won’t exist.

Suppose you have a quantum state of some large quantum system. This quantum state lives in a Hilbert space of some dimension. Now a projective nondegenerate measurement is given by a basis for this Hilbert space. In the many-worlds interpretation this is modeled by attaching a measuring system, unitarily evolving, and becoming entangled with the system being measured. But that really doesn’t matter much for our discussion. The important point is that every such basis corresponds to a particular measurement and in particular every such choice of basis corresponds to a different post measurement world. Now notice that if you make a measurement in which one of the basis elements points along the dimension of your quantum state then any measurement basis you chose all of the other measurement outcomes will never occur. And even if you chose to measure along a basis which doesn’t point exactly along your state, but such that some number of your basis states are orthogonal to you state, you will never observe these universes. In other words in quantum theory in any measurement setup (irrespective of the many worlds hypothesis) a quantum state can tell you that an infinite number of worlds do not exist after the measurement. But this all depends on the measurement basis choice, which, even in the many-worlds interpretation, is picked out by some physical interaction. Do we really expect all measurements outcomes to generically occur via any one of our basis choices? Not as far as I can tell.

I’m not sure were this meme that many-worlds implies all universes that can happen do happen came from, but I just don’t see how that could be true. Am I missing something here?

(And by the way, the above Borges story I link to is definitely worth reading and was such a favorite that I committed it to memory.)

Comments

  1. #1 Tristan
    November 20, 2008

    It sounds to me like you got it. The first half of your post seems correct about Everett’s many-worlds interpretation. After you make your measurement you are entangled. You see the coin as tails. But a second observer isolated from you doesn’t know if you saw heads or tails. To me, you are in a superposition of [coin is tails, you saw tails] + [coin is heads, you saw heads]. You’ve split. Then I can look. I too become entangled. In some external-to-observers sense, the coin landed heads and tails, and two realities of the universe continued on.

    I’m not an expert, but I think this stuff is very cool and very under appreciated, even by physicists.

  2. #2 Stephen
    November 20, 2008

    The “many-worlds implies all universes that can happen do” meme is a chronic source of annoyance for me too.

  3. #3 Blake Stacey
    November 20, 2008

    To my mind, the most appropriate Borges short story to memorize would be “Funes the Memorious”, a.k.a. “Funes, His Memory”.

  4. #4 John Sidles
    November 20, 2008

    Great post! The same dream-equals-reality theme is explicit in Mark Twain’s short story The Mysterious Stranger.

    Maimonides’ maxim “The gates of interpretation stand open” surely applies to quantum measurement. Despite efforts, I have never yet found a (nonlinear? nonalgebraic? coordinate-free?) generalization of Choi’s Theorem that adequately expresses this idea.

    Very plausibly, the longed-for clarifying idea is already in the mathematical literature … somewhere … if we could only recognize it … Kafka’s ultra-short story An Imperial Message expresses this longing.

  5. #5 Matt Leifer
    November 20, 2008

    I think you are correct and this confusion is indeed annoying. Apparently, some people have a problem distinguishing “more than one possibility is realized” from “everything is realized”.

    However, I suppose the real question that people are interested in is whether every possible history that they would deem relevant is realized. People don’t care so much about the exact direction that their spins are pointing in, but they do care about whether there are universes in which they are not a complete loser, e.g. universes in which they are a rock star or the president of the USA. This would depend on the way that these different possibilities are determined by the underlying quantum dynamics, which we are unlikely to have a decent theory of in the near future. Therefore it could still be the case that MWI implies that every relevant possibility is realized.

  6. #6 Kirk
    November 20, 2008

    The Many Worlds theory has been discredited for a number of reasons because some, like Roger Penrose, think it merely pushes the decoherence problem off to another place. Suddenly Many Worlds has come to life again, evidently to counter a new interest among Theists in the Anthropic Principle. That’s the way it looks to me by reading comments they themselves make, such as found in SA, etc. I don’t understand this attitude, I mean who cares what another group of people think? Did you read Feynman’s What Do You Care What Other People Think? I think it was in Waldrop’s Complexity: The Emerging Science… that Gell-Mann is quoted as directing a group “Just give me something to stop those Creationists!”. Good grief, is that anyway to run Science? A business that determines to destroy the competition is doomed. Everyone knows that. Successful businesses focus on satisfying customers and not on the competition.
    Most scorn comes from non-creative scientists, as Everett discovered for himself. And it’s no accident so many great thinkers (extremely smart AND creative) were associated with Wheeler. Someone should make a movie about him. Then again, maybe no one would watch it.
    There are a number of succinct explanations for what is essentially wrong with MW, I can recommend some. But it does not propose that everything that can happen, does, in one of an infinite number of divergent universes. Worse, other tenets which are even more interesting rarely receive any discussion at all.

  7. #7 Dave Bacon
    November 20, 2008

    Kirk, please do post the succinct explanations. I have my own interpretation of quantum theory, but it’s too short to fit in the comment section of a blog.

  8. #8 John Sidles
    November 20, 2008

    Hmmmm … let’s try to say something definite and positive.

    It’s clear that the now-dominant orthodoxy of quantum mechanics that centers upon decoherence and entanglement—as summarized in, e.g., Chs 2 and 8 of Mike and Ike—has been terrific for mathematics, science, and engineering.

    A paradise for mathematicians has been created by the axioms of the new quantum orthodoxy. Showing that these axioms describe nature has created a paradise for physicists. And a paradise for engineers is being created by new quantum-limited technologies and (more important) new global-scale enterprises based on these technologies.

    The philosophers have not yet entered a new paradise … but if a door were miraculously opened to philosophers, would they wish to enter? :)

  9. #9 Alex Besogonov
    November 20, 2008

    Kirk:

    Currently, no quantum mechanics interpretation tells us _why_ decoherence happens. All interpretations focus on _how_ it happens.

    Classic Copenhagen interpretation dodges this question altogether. Transactional interpretation (http://en.wikipedia.org/wiki/Transactional interpretation) is a little better because it gives us a plausible mechanism for this. Many-worlds also dodges this question, but differently.

    MW is internally consistent, there’s no _physical_ problems with it. There might be philosophical or ethical problems with MW, but they DO NOT affect validity of MW.

  10. #10 Dave Bacon
    November 20, 2008

    “People don’t care so much about the exact direction that their spins are pointing in, but they do care about whether there are universes in which they are not a complete loser, e.g. universes in which they are a rock star or the president of the USA”

    Matt you made my morning.

  11. #11 John Sidles
    November 20, 2008

    To purse Alex Besogonov’s fine post, decoherent quantum orthodoxy not only tells us how decoherence happens (namely, via dynamical entanglement), it also tells us why the resulting dynamics has a random element.

    Namely, orthodox quantum mechanics specifies a state-space that is so large (having exponentially many dimensions), that almost all quantum trajectories are necessarily algorithmically incompressible.

    So for example, when our QSE Lab purposefully entangles the MRFM cantilever state with 10^16 outgoing photons (as happens every second), there are so many possible experimental records resulting from photometric measurement of those photons (namely, 2^(10^16)), that almost all of those records are necessarily algorithmically incompressible, hence (Chaitin-Kolmogorov) random.

    This doesn’t bother us as engineers … heck, we simply low-pass filter the data stream. :)

    But it does transform the quasi-philosophical question “Why is quantum mechanics random?” to the (possibly better-formed?) quasi-philosophical question “Why does the state space of the universe seemingly have exponentially many dimensions?”

    The latter way of thinking about quantum mysteries seems (to us engineers) to be mathematically easier to come to grips with, via (e.g.) the Holographic Principle.

  12. #12 Ian Durham
    November 20, 2008

    Dave, et. al: it was my understanding that the “entanglement” isn’t really what we normally think of as entanglement (if we associate “entangled states” with non-factorable states) because it is not, mathematically, like a Bell state or a GHZ state – it’s actually some sort of additive state like |world1> + |world2>. So if you become entangled (or coupled) to one of the two, it’s not clear that a measurement on the one necessarily causes a collapse of the other. Of course, I have my own issues with MWI largely related to permutation invariance, though the only ideas written down are a tad out of date, but express a similar note of discontent.

    Matt: Lucky for you, you are constitutionally barred from being President of the good old US of A. In about a year or so, like nearly every President that preceded him, Obama will wish he was likewise barred from holding one of the least desirable jobs on the planet.

    Dave, John, et. al: My personal favorite Borges story is The Circular Ruins, in particular the passage

    After nine or ten nights, he comprehended with some bitterness that he could expect nothing of those students who passively accepted his doctrines, but that he could of those who, at times, would venture a reasonable contradiction.

    And if you like Borges and Garcia-Marquez, you should read some Shiva Naipaul and Haruki Murakami (whom Seth Lloyd knows personally).

  13. #13 Dave BAcon
    November 20, 2008

    “No one saw him disembark into the unanimous night,…”

    Dude I wrote my literature thesis as an undergraduate on Borges…

  14. #14 Ian Durham
    November 20, 2008

    Dude I wrote my literature thesis as an undergraduate on Borges…

    I know that. I think we had this conversation about two years ago (and you told me Charlie Bennett is also a Borges fan). ;)

  15. #15 John Sidles
    November 20, 2008

    Thank you, Ian, for the pointers to Shiva Naipaul and Haruki Murakami … I will surely look into their work!

    Constructing narratives being, of course, the second-foremost level of applied complexity theory … behind only raising a child.

  16. #16 Ian Durham
    November 20, 2008

    … behind only raising a child.

    That’s just flat-out chaos (my almost-eight-year-old lectured me last night on the difference between ‘international’ and ‘multi-national,’ a difference he says he figured out on his own – God help me).

    If you read Murakami, you have to read more than one to really get the feel.

    BTW, I listened to the QIBEC NIST podcast on MRFM from 2006 and was wondering if QSEPACK was the outcome of that work?

  17. #17 Eleanor Rieffel
    November 20, 2008

    Thank you, Dave!

    Yes, I’ve long been puzzled as to how this meme got so popular when much of what is startling about quantum mechanics is that it predicts that certain things classically expected to happen do not happen at all.

    My favorite example is the GHZ experiment in which the four outcomes classically expected do not occur at all (and the four outcomes not anticipated classically all occur), but the surprise of most of the canonical quantum mechanical experiments, from the double slit experiment to Bell, is at least in part that certain things do not happen. I had fun a few years ago writing a section called “The Fewer Worlds Theory of Quantum Mechanics” in a paper aimed, among other things, at correcting certain popular misconceptions about quantum mechanics and quantum computing (http://xxx.lanl.gov/abs/quant-ph/0702121). I’ve thought for some time that it might be fun to write a paper expanding on that theme. Perhaps now is the time?

  18. #18 John Sidles
    November 20, 2008

    Ian Durham asks: “BTW, I listened to the QIBEC NIST podcast on MRFM from 2006 and was wondering if QSEPACK was the outcome of that work?”

    Broadly speaking, yes. That work is driven wholly by a practical need to simulate (large, hot, noisy, interating) spin systems in quantum spin microscopy.

    Basically, QSEPACK is a pragmatic union of the algebraic axioms of (e.g.) “Mike and Ike” Chapter 2, the information theory of (e.g.) Mike and Ike” Chapter 8, the sparsity theory of (e.g.) Candes and Tao, and the Kahlerian differential geometry of (e.g.) Shing-Tung Yau (and a whole lot more folks). Hundreds of researchers and articles, really … it’s amazing how it all fits together.

    That’s why, for folks like me, the WWW is really all about algorithm-mining and theorem-mining, not data-mining.

  19. #19 Neil B ?
    November 20, 2008

    I have been trying to rebutt MW/decoherence over at UP (Chad says he was stimulated to write on it again since I keep dropping subtle hints.) I have a rather long comment there explaining why those ideas just don’t explain why we have a localization event, a “collapse.” I gave a brief version too, and here is a medium sized one:

    Talk of superposition or entanglement of detected/excites at A and not at B, with WFs correspondingly not at the other place, is premature because: Unless “collapse” was already a feature of reality, there wouldn’t be any such thing or meaning to “exciting one detector” (and not the other) in the first place. The photon WF would just excite both detectors simultaneously (if the WF has amplitudes those places) and that would literally be the story, period – forever and so on. It would be rather like a classical EM wave spreading out. The result wouldn’t depend on interference or not. Pure wave mechanics just keeps it all waves, all piled up upon each other in superposition regardless.

    Also, a point I didn’t’ make there: In true entanglement (as with *two* photon systems) the wave state of each photon is non-local: there literally isn’t a definite polarization or etc., for either one by itself. Only the combination has the traits. But in the pseudo-entanglement case given in typical apologetics such as Chad’s, the photon WF is definite (in principle) even though it might have been fiddled with by environmental factors.

    Really, the task of the apologist is to take wave equations and get something like “collapse” out of them, as they are. But if you *start* with that and don’t cheat by introducing the desired result in the back door first (making it a fallacious circular argument) then the waves just stay waves as in the original perplexity. (If WM would have led to collapse on its own, I can’t imagine the old QM hands all those decades wouldn’t have just worked it out – if it was a true explanation directly from Schrödinger evolution and not sophistry, which it is.)

    The amplitudes don’t even mean chance of “being there” in any concentrated sense just per wave behavior. Without collapse introduced by hand, you basically just have something akin to classical E&M, with interactions like induction and wiggling of distant charges, but never anything like a hit at one place and not anywhere else. Sorry folks, the art deco just doesn’t get off the ground.

    BTW check my blog out for a cute and perplexing twist on “quantum suicide.”

  20. #20 Neil B
    November 20, 2008

    “It sounds to me like you got it. The first half of your post seems correct about Everett’s many-worlds interpretation. After you make your measurement you are entangled. You see the coin as tails.”

    See, that just shows what the problem in this unfortunate post-modernist diversion. What do you mean, “after you make your measurement … You see the coin as tails.” Uh no, why do “you” see it as tails? What is, and why does a “measurement” act special if there’s just wave evolution? There should be just both results, together, like earlier candid thinkers knew would result unless something odd intervened.

    Sure, we know that isn’t what happens, but that’s what you’re trying to explain using something else. And if “I” see it as tails, who the hell sees it as heads? That would be literally someone else in another universe, sorry.

  21. #21 Ian Durham
    November 20, 2008

    John: I may e-mail you about QSEPACK at some point but don’t want to digress too much here.

  22. #22 Tristan
    November 21, 2008

    Neil – Good, valid points. I wasn’t contending that the interpretation explains why a measurement outcome has gone a certain way for someone. Nor that it explains some sort of collapse dynamics. The level of understanding of the interpretation that I was trying to convey seems a little too low for this discussion.

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