Thoreau at Unqualified Offerings gets credit for inspiring two posts today with his proposed Murphy's Law experiment and this one, about an unrelated issue in quantum measurement. This is an analogy suggested by a colleague a couple of years ago, comparing the projection of a quantum wavefunction in the measurement process to the lottery.
The classic example of this problem is something like the double slit experiment with single particles. You have some position-sensitive detector that we can imagine as being made up of a large number of pixels, each having some probability of detecting a particle in the next little interval of time. When one of these detectors registers a particle, the probability of detection at any of the other detectors instantly drops to zero (either because there's been some real collapse of the wavefunction, or because decoherence has separated all the branches corresponding to detections by the various pixels into their own "universes"-- it doesn't really matter which). This strikes a lot of people as being problematic when they first hear it. After all, if you have enough detectors, this would seem to run afoul of relativity-- if the particle is detected in one corner, the probability of finding it in the opposite corner goes to zero faster than a light-speed signal could travel from one corner to the other. This seems to involve some "spooky action at a distance" (to slightly misappropriate a great phrase from Einstein).
My colleague, Jon Marr, suggests the lottery as an example of a classical analogue to this situation.
In the analogy, the role of the individual pixels is played by the many lottery tickets in circulation. Prior to the drawing of the number, each ticket has an equal probability of winning, but at the instant the drawing is completed, one ticket is selected as the winner, and all the rest are instantaneously projected into the "loser" state. This projection happens immediately, even though it may be some time before the holders of the tickets find out what happened.
This fits best with an information-oriented approach to quantum mechanics, I think. The "instantaneous" change, as in the pixel case, is a change in something you don't measure directly, and you don't end up with complete information about the situation until some time has passed-- if you imagine individual observers monitoring each pixel, they may know that their own pixel has not recorded a particle instantaneously (assuming they know the expected arrival time of the particle well enough), but they won't know which pixel did detect the particle until enough time has passed to get a message from the "winning" pixel. This is one of the factors that keeps you from being able to violate causality using quantum measurement.
When Jon first suggested this, I thought there was some problem with the analogy, beyond the fact that I didn't think of it first. I didn't use it in the book because dogs don't buy lottery tickets, but I can no longer remember what my other problem with it was. In keeping with Furr's Law, though, posting it here will generate a nearly instantaneous complaint in comments that will remind me what the problem was, or point out some other flaw. Pending that, though, I kind of like this.
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I'd say the main problem is that you can't apply Bell's theorem to lottery tickets. I think there are hidden variables involved!
I like this example for a different reason. It demonstrates that the "spooky action at a distance" rhetoric has nothing to do with quantum mechanics, it is all about pre-established correlations, and such correlations can exist with or without quantum mechanics.
Well, the weakness I can is that the analogy is somewhat misleading in that nothing really propagates instantaneously in the lottery case. The only real change happens in the human brain where the categorization of the ticket changes. We like to imagine the ticket status changing instantaneously but it's just a mental shortcut.
In case of entanglement an objective property of reality does change instantaneously, although we cannot know it until we use slower then light communication for comparison.
So the problem with the analogy is that it implies that entanglement isn't real, that it's only something in our description of reality changing instantaneously and not something about the reality itself.
The analogy is OK, but not quite as good as it could be. The problem is that you have a disconnected external agent, i.e. the lottery number drawing machine, deciding randomly which is the winning ticket and this agent might be located arbitrarily far from the lottery entrants. If you are saying that lottery entrants are analogous to locations where a particle might be detected then there is a problem because one would have thought that whether a detector clicks should be determined by a local interaction between the system and the detector. To mix analogies slightly, the particle doesn't "know" where it should be detected until it "knows" which location has the winning ticket.
Now, this objection only holds if you believe that the lottery drawing event is "objectively random", or at least if you believe that it depends on complicated deterministic events that are independent of the state of the particle. It is possible, on the other hand, that the particle contains a record of the same randomness that is used to draw the winning ticket, in which case the explanation is viable and is just a local hidden variable theory. Of course, this falls afoul of Bell's theorem, but then there is no shame in pointing out that a lot of non-Bell's theorem experiments that are thought to show "quantum weirdness" do in fact have fairly sensible classical analogs.
If you want to know sensible analogs of many quantum phenomena along these lines then you need to read:
http://arxiv.org/abs/quant-ph/0401052
As a non-physicist, I really like this analogy.
The only problem I can see, is that in the lottery, there are times when all tickets are losers (this happens often in Powerball and MegaMillions lotteries where there are too many options that a winning combination of numbers of numbers may never be picked or generated on a ticket). This would correspond to a series of detectors where there is a zero probability everywhere which I don't know if that can happen in physics.
I agree that this is essentially a hidden variable theory, and as such is not going to correctly describe entanglement phenomena per Bell's theorem. It's an attempt at an analogy for a simpler situation-- the problem of projective measurement (or "wavefunction collapse" if you want to use a loaded term).
That may actually have been the weakness I was thinking of, but I'm trying for something more limited here.
The only problem I can see, is that in the lottery, there are times when all tickets are losers (this happens often in Powerball and MegaMillions lotteries where there are too many options that a winning combination of numbers of numbers may never be picked or generated on a ticket). This would correspond to a series of detectors where there is a zero probability everywhere which I don't know if that can happen in physics.
Sure. You just have detectors with limited efficiency. If all of your detectors are only 90% efficient, one time in ten they'll just fail to record a real particle, which means that a repeated single-particle experiment will include shots where nothing at all is detected.
So the problem with the analogy is that it implies that entanglement isn't real, that it's only something in our description of reality changing instantaneously and not something about the reality itself.
But the same is true in quantum mechanics: wavefunctions don't collapse in reality, we just pretend that they do in our description of reality because keeping track of the full decoherence process including the detailed state of entanglement of the system and its environment is too difficult. There's no actual instantaneous change in physics.
onymous: "But the same is true in quantum mechanics: wavefunctions don't collapse in reality,(...) There's no actual instantaneous change in physics."
Once you measure spin of one particle of an entangled pair all further measurements on both of them will give consistent results. This means that either they had such spins all along or that their spins are a byproduct of measurement.
The first option is hidden variables and is (mostly) excluded by Bell's tests where the directions of measurement are set randomly after pairs are produced so the only way pre-correlations could explain results is if you accept complete determinism and the possibility that an experimenter is programmed to set the right direction in his measurement device so that it aligns with the direction of the spin of particle which he is about to measure. Although possible it seems rather far fetched (not the determinism per se but the required amount of interlocking).
The other possibility which seems to be the usual interpretation is that the act of measurement determines the outcome but this means both spins have to be determined in the same instant. Experiments done showed that it happens faster then at the speed of light. So this interpretation does mean that a change in physical reality can propagate faster then light.
I suppose it's all a matter of semantics, but no, I don't think it's reasonable to say anything propagates faster than light. What happens is that the wavefunction is in an entangled state, it happily evolves in a unitary way dictated by a local Hamiltonian, and interactions entangle its state with that of its environment in such a way that the wavefunction can be approximated by a sum of nearly orthogonal pieces, which we pretend are different "universes" or "measurement outcomes" or whatever you might like to call them. Whatever apparent faster-than-light propagation happens is just a consequence of starting with a particular state that involved some correlations.
We probably agree on the physics, I'm just picky about the language because I think a lot of people get confused about the physics of quantum mechanics because they encounter poorly-chosen language like "action-at-a-distance".
This analogy works better with the pre-printed scratch off type of lottery, at least for illustrating what a hidden variable would be. The information about winning/losing is set when the tickets are printed, but this knowledge is decoupled from the spread of knowledge about whether the good prizes (or in fact, all prizes, as once in a while happens) have been claimed.
onymous nailed it in 9. So much public misunderstanding of science comes from misunderstood/ unrecognised analogy and poorly chosen language, we all should be more wary about how we say things.
Just to hammer the analogy to death: your detector inefficiency seems more to relate to what would be a lost winning ticket. In a Powerball-type lottery, the people running the game know there a winning ticket was sold, but it is never claimed. That's a detection problem.
If there is no winner, that seems to me like a spontaneous annihilation of the particle for no real good reason upon attempting to detect it.
Of course, this all assumes you're using a Powerball-type lottery and not something like a 50/50 raffle at a ballgame where there always is a winner (and only a single winner). The Powerball lottery always pops into my head as the generic lottery system.
I like Bells Bertlemann's socks analogy. Bertlemann always wears two different color socks. To make it easy, say he always wears red and blue socks. If you see one foot has red on, WITH THIS PRIOR INFO about Bertlemann you INSTANTLY know the other one is blue. Perfectly classical.
In QM, it would be like if socks had color, and say stripes/solid. And measuring the color of one sock IF WE HAVE PRIOR INFO ON STATE PREPARATION will instantly change the stripe/solid info. Not a perfect analogy for sure. But EPR/Entanglement is about TWO particle correlations with two different "physical" properties.
For a more physicsy classical analogy, blow up a shot put into two parts. If you measure the momentum of one piece, WITH PRIOR KNOWLEDGE that the CM was at rest initially, you know the momentum of the other piece INSTANTLY. Spooky action at a distance.....
Discussions about measurement "hits" don't effectively deal AFAICT with Renninger-style null measurements: If the object is not interacted with, then the output somewhere else is different than it would be (Elitzur-Vaidman interaction-free bomb detection, etc.) The WF does not "interact" with the target object, but is reallocated on account of it's being there.
In any case the model says a WF spreads out and ends up localized in one spot (say, of a giant enclosing sphere) and not any others, which has nothing to do with interference issues.
the lottery ticket is stateless. the (human) mind plays no part in material states.
analogies help us to understand, and can be ill fitting, or loose with language. that's fine, in fact we invite it, no analogy is perfect, if it were it would be identical to that of which it is being used to explain.
all the science in this posting is of a poor quality, out of date or misunderstood. that's fine too. at least we're talking.
it is certainly important that the public should get involved in science in this way, but it's not of any real use to the serious scientist to talk about these things so loosely, and inaccurately. instead, we concentrate on the detail of the real problems., and we develop the solutions (answers) that will free us all in the end.