Welcome to this week’s installment of the From Eternity to Here book club. Part Three of the book concludes with Chapter Eleven, “Quantum Time.”
Excerpt:
This distinction between “incomplete knowledge” and “intrinsic quantum indeterminacy” is worth dwelling on. If the wave function tells us there is a 75 percent chance of observing the cat under the table and a 25 percent chance of observing her on the sofa, that does not mean there is a 75 percent chance that the cat is under the table and a 25 percent chance that she is on the sofa. There is no such thing as “where the cat is.” Her quantum state is described by a superposition of the two distinct possibilities we would have in classical mechanics. It’s not even that “they are both true at once”; it’s that there is no “true” place where the cat is. The wave function is the best description we have of the reality of the cat.
It’s clear why this is hard to accept at first blush. To put it bluntly, the world doesn’t look anything like that. We see cats and planets and even electrons in particular positions when we look at them, not in superpositions of different possibilities described by wave functions. But that’s the true magic of quantum mechanics: What we see is not what there is. The wave function really exists, but we don’t see it when we look; we see things as if they were in particular ordinary classical configurations.
Title notwithstanding, the point of the chapter is not that there’s some “quantum” version of time that we have to understand. Some people labor under the impression that the transition from classical mechanics to quantum mechanics ends up “quantizing” everything, and turning continuous parameters into discrete ones, perhaps even including time. It doesn’t work that way; the conventional formalism of quantum mechanics (such as the Schrödinger equation) implies that time should be a continuous parameter. Things could conceivably change when we eventually understand quantum gravity, but they just as conceivably might not. In fact, I’d argue that the smart money is on time remaining continuous once all is said and done. (As a small piece of evidence, the context in which we understand quantum gravity the best is probably the AdS/CFT correspondence, where the Schrödinger equation is completely conventional and time is perfectly continuous.)
However, we still need to talk about quantum mechanics for the purposes of this book, for one very good reason: we’ve been making a big deal about how the fundamental laws of physics are reversible, but wave function collapse (under the textbook Copenhagen interpretation) is an apparent counterexample. Whether it’s a real counterexample, or simply an artifact of an inadequate interpretation of quantum mechanics, is a matter of much debate. I personally come down on the side that believes that there’s no fundamental irreversibility, only apparent irreversibility, in quantum mechanics. That’s basically the many-worlds interpretation, so I felt the book needed a chapter on what that was all about.
Along the way, I get to give my own perspective on what quantum mechanics really means. Unlike certain parts of the book, I’m pretty happy with how this one came out — feel free to correct me if you don’t completely agree. Quantum mechanics can certainly be tricky to understand, for the basic reason that what we see isn’t the same as what there is. I’m firmly convinced that most expositions of the subject make it seem even more difficult than it should be, by speaking as if “what we see” really does reflect “what there is,” even if we should know better.
So I present a number of colorful examples of two-state systems involving cats and dogs. Experts will recognize very standard treatments of the two-slit experiment and the EPR experiment, but in very different words. Things that seem very forbidding when phrased in terms of interference fringes and electron spins hopefully become a bit more accessible when we’re asking whether the cat is on the sofa or under the table. I did have to treat complicated macroscopic objects with many moving parts as if they could be described as very simple systems, but I judged that to be a worthwhile compromise in the interests of pedagogy. And no animals were harmed in the writing of this chapter! Let me know how you think the strategy worked.
Although hardly an expert, I did recognize your cat analogy to the two-slit experiment. That’s too much of a classic to be unfamiliar even to duffers.
I am especially grateful to this chapter for putting me at ease with the “Many Worlds” interpretation. I was up until now completely put off by its name and the extravagance it implies. The decoherence concept feels much better to me as an explanation of what happens upon “observation”. “Collapse” now seems like the more vague concept.
If it makes even one person more comfortable with the Many-Worlds interpretation, the whole book-writing thing was worth it.
What was the difference you intended between saying ‘observing the cat on the sofa’ and ‘the cat is on the sofa’. In particular what difficulty in the interpretation of quantum mechanics were you trying to elucidate?
I suspect there is a nuance in your quote that I am failing to grasp.
Or something closely related to it, like the Rovelli relational interpretation.
Aaron– I’m not sure what you are asking that isn’t addressed in the quote in the original post (or in the book chapter). Quantum mechanics says that there is generically no such thing as “where the cat is.”
You alluded to some problems in recovering the probability formulas from the MWI. What exactly are those? I assume mathematically, the only place squares can come from is unitarity. Is the milder statement proven, that if a probability formula makes sense (i.e. obeys Bayes law etc.) it has to be the one from the copenhagen interpretation.
Sean,
An extremely lucid description of quantum mechanics. An enormous national savings in energy consumption could be claimed if we contented ourselves with the obvious description of nature that the formalism provides. Whatever “interpretation” problems remain are purely human. As experimenters entangle ever larger systems I don’t see any realistic alternative remains.
Thanks, Sean
Sean– Thanks! And good name.
Ray– I’m not an expert on the state of play, this is an area of current research. But the basic idea is simple — so the MWI explains how the wave function evolves into two non-interacting “worlds.” It’s clear what the coefficient of each branch is in the full wave function. But why are we supposed to interpret the squares of those coefficients as the “probability” that we’re going to observe that outcome? I personally think this is just a matter of getting some details right, but other people take it very seriously.
Are you trying to point out that the observable states depend on the measurement instruments? Or are you trying to caution readers away from thinking there are naturally preferred states.
Neither, really. I’m trying to nudge people away from identifying “what we observe” with “what is real.” Wave functions are real, but we don’t observe them directly.
I think this may well be my favorite chapter of the whole book. It was the most lucid explanation of quantum mechanics I’ve read so far, and for the first time, I feel like I can explain at least the basics concepts to my friends.
So thanks!
>I personally come down on the side that believes that there’s no fundamental irreversibility, >only apparent irreversibility… basically the many-worlds interpretation..
That’s probably where the bulk of the debate will lie.
George Ellis wrote ‘On the Flow of Time’ for the Foundational Questions essay contest. With your entry and his together, I think the case was almost made clear for non-reversibility. But there are subtle differences like these. He went a little further with the many worlds issue (in that essay), and though it was a brief treatment, I think he summarized the opposing view succinctly and with clarity.
Anyway, most people will not realize that this ‘quantum indeterminacy’ business is actually far easier to understand than the ‘regular’ probability theory, as applied today in assigning values of uncertainty to macroscopic events. No matter what formulation of probability is used (bayesian, frequentist..etc), the entire field, from what I experience every day, can be summarized as a ‘science of ignorance’. This basically describes both the formulation and the affliction, and it is hard to decide which is worse. That even mildly useful inferences can result from it, in any realistic setting, is incredible – and I say that as someone who has written accurate programs driven by the calculation of millions of probabilities per minute, with various underlying theories.
Every statistician should be made to read Feynman’s classical talk, “Simulating physics with Computers”. Esp. the questions he was asked at the end. It really hammers home how *real*, how non-problematic and beautiful quantum probability is, with the unfolding of time, in contrast to the ‘normal’ uncertainty people are supposedly comfortable with.
Hey, I really liked the new creative ways of expressing QM herein; but you lost me with decoherence. I hope you can take that as constructive criticism to hopefully improve that part of your explanations. Kudos!
I tend to stay away from etiological arguments in physics about what is real or not real. I’m of more of a what is observed is observed kind of guy myself.
As far as reversibility, consider the conjugate observables of momentum and position, the eigen states of each are superpositions of the other, so successive alternating observations of position and momentum will alternate between “collapsing” of the wave-function in each observable. In effect each alternate observation undoes the effect of the last. The only problem comes in when one restricts the definition of wave function to being a eigen state of a particular observable, rather than an arbitrary element of the space of all states. But that is a hard idea to express without resorting to Hilbert Spaces and Fourier Analysis.
Does not the Sofa and Table have their own wavefunctions also?..and these should be equated therein?
Neat, if you ask where the cat is by giving co-ordinates (sofa and table are just co-ordinates), then the question is as meaningless as asking if single wavefunctions are “real” ?
best p.v.
It seems lots of theoretical physics is about inverse square laws and things that go at right angles to other things, much like real physical terms in classical physics, like electromagnetism that does. But look at this. I have always thought that the difference between maths and physics is that applied maths in physics, is mainly deduction sideways, whereas physics is deduction longways and side ways. I’ll explain.
The first deduction is sideways to get the coefficient – then the wave function that is (at right angles to) the coefficient squared to get probability, is longways. I suppose it’s like seeing around the quantum corner. There can be as many sideways ones as long ways ones but the longways ones are rare and meddle with the observer influence and the problem with classical time. In the collapse of the function, the deduction to form the coefficients are equally just as part of the system as the others, but we see them as part of the same whole, but hidden and assume it’s just any deductive method. The thing is to see the difference between the two methods and why we assume only one is about observer infuence. The maths deduction system as an intervention could also be observing our universe and we not know. This makes time it self quite appleaing to think about, let alone many worlds, whcih is just as interetsing of course.
Could time turn around corners?
I admit to some confusion. Decoherence loses information to the environment, so doesn’t that make it irreversible; i.e. make you unable to reconstruct previous coherent state?
@Metre: It basically means you’d have to act on the whole thing — the system and its environment — to reconstruct the previous state. But in practice a macroscopic environment has millions of billions of billions of particles, so that’s for all intents and purposes totally impossible. In technical terms, the evolution of System+Environment is “unitary” (reversible, basically) but actually reversing it is an impossibility. Whereas in the old-school “Copenhagen Interpretation” of Quantum Mechanics, the measurement process actually makes a non-unitary change (i.e., irreversible *even in principle*) . . . which raises all sorts of questions about why measurement doesn’t follow the same rules as everything else (since ordinary evolution of states *is* unitary).
Forgive me if this has been addressed, but in what way is this question linked to CP (or T) violation?
I have been looking forward to this chapter. Although I’ve read about the Copenhagen and “many worlds” interpretations before, the concepts were explained more clearly in this book.
To extend the idea of entangled systems, let’s take two entangled systems that are independent of one another, each with an observer. For the observer within each system, their own system appears decoherent, with one outcome assigned 100% probability. My question is this. Does one system appear coherent (uncollapsed) to an observer in the other system? I would think so. So if the cat/dog example applied to a particular house in the U.S. and also to a particular house in Australia, each with their own cat/dog system, an observation in the U.S. would not collapse the superposition state that exists in Australia. Is this correct? In effect, the cat/dog system only appears collapsed to its own observer, plus anything else entangled with that observer. The rest of the universe could continue to treat the cat/dog system as a coherence wave function.
Also, I was thinking through how you identified which of the “many worlds” the observer sees, by essentially naming which state is observed (sofa, yard). For the space of states described in previous chapters, such as a box with x number of gas particles, we assumed each value could be quantified. Each particle had a specific value for position, momentum, and time. With the uncertainty principle, it seems that we can never specify each value precisely so we are never able to assign a particular value 100% probability to any state and we are always in some way in a coherent state, no matter how macroscopic or entangled we are. Is that correct?
Corey, you lost me at “Let’s take two entangled systems that are independent of one another.” If they’re entangled, then surely they’re not independent, no?
Sean, you are the effing man. That is all.
There are several problems with MWI and the idea that we can handle quantum time in easy reversal. First, the “splitting” problem and separation of the “worlds”. Just aside from the basic issue of why the various alternatives would be effectively “separated” in any sense instead of being fully “superposed” in all effect – there are internal contradictions IMHO. Just take the question of where the paths must “part ways” in some sense. They can’t always be separated, since we need their mutual action to show interference effects (or else you’re really going out on a limb.) So the “split” has to take place at some further level, like where “detectors” are going to click on way or the other. This is fishy. The whole point is supposed to be (if you read up on MWI and its handmaiden, the decoherence interpretation of waving away (pardon the pun) the measurement problem), that “detectors” are not special.
1. OK. So let’s say I have a MZ interferometer with beamsplitter BS1 to “split” an incoming photon. Then we recombine the waves in another, BS2. We know we can arrange to get all hits in channel 1 at detector D1, etc, showing (to a realist) that some waves went through both paths in order to interfere. But there is still choice after BS2. We can do more splitting of the wave towards other detectors, or adjust path differences so it’s e.g. 70/30 chance for D1 v. D2 instead of 100%, or even just exactly where on D1’s counter does the photon “hit.” Only then does MWI imagine “splitting” of some sort. (Oh, people say evasive things like “the options don’t interfere anymore” but interference is just a way to get nice patterns instead of sloppy ones, it doesn’t change the basic point of *there being present* a superposition or not.)
But consider that if detectors aren’t special, then BS1 should have sent the waves into separate “worlds.” After all, by itself BS1 serves to instigate options, of either going one way or the other. Let’s have BS1 by itself and alternate detectors D1′ and D2′ outside BS1 instead of recombination later. Then we could say the “choice” and split consists of one world where the photon was sent through to D1′, and another world (or whatever the equivalent is) in which it reflected to D2′. So the big stinker here for MWI is: BS1 is already a quantum choice juncture. It should *already* split the wave into worlds (or whatever the hell they are) before they ever get to BS2. Hence, there should be no interference. We should be in either the world where the photon took the choice to go one path after BS1, or the other path, but not any world in which it took “both.”
2. Time-reversal: Yeah, Schroedinger equation per se is time reversible but that doesn’t lead to reasonable time reversal of events, even in QM. Consider a light-emitter in front of a screen. OK, the wave functions travel from the emitter to the screen, and somehow end up hitting at select spots. Maybe all the possible hits are represented “somewhere” and in proper proportions etc. But try to run it backwards: WFs proceed “from” the screen, and – why the hell should they converge on the emitter if there’s no real causal requirement? You could say the universe was just lucky to keep having backwards light converge on the same spot. But the irony is, if the prior “receiving” atoms are now “emitters” of equal standing, then the WF proceeding from them should be an expanding shell and not reconverging back to a lucky spot. Actually it’s easier in classical mechanics since you just imagine the particles all moving backwards – however absurd, it’s just as “doable” and will continue to work “right.” But the WFs are not inherently equivalent from emitter and absorber (?) In QM, you have to not only start the reversed world out “just right”, but it has to continue to be “lucky” after that …
To find more such arguments, Google for “decoherence” + “circular argument” as well as “quantum measurement paradox.”
I like the cat example. Is the litter tray in another part of the multiverse?
US,
I think you have a point in one case (1), that you get into trouble if you think about the wave function for the whole universe splitting up, which is how many worlds tends to be talked about (though also it seems to me that it isn’t fair to insist that the splitting happen at a clearly specified instant; we seem to be talking about an emergent property, it should be a little fuzzy in the same way as critical temperatures are for finite systems for example). I suspect that this is part of the motivation for Rovelli’s interpretation (which someone mentioned a ways back), and I also feel I ought to mention that it seems not to be a problem (at least a problem of the same significance) in Bohmian mechanics, which is also time reversible. Looking back, it seems like Corey’s question brings up the same issue.
On (2), I think you’re missing the point. Part of the premise of many worlds is that the wave function evolves deterministically according to Schrodinger’s equation alone (or some equivalent); there’s no need to be lucky. Of course you need to specify a lot more about the “initial” wave function than just “photons are emitted from these spots”, but that’s just because there is a lot more going on (more degrees of freedom, to be technical) than one might think at first. The thing is actually to take the complex conjugate of the complete final wave function describing the whole system (universe? multiverse?), which is (includes?) a very particular superposition of states in which photons are being emitted in different patterns.