Scientific American recently had an article about this, and it led me to wonder about the following thought experiment:
Suppose you have two experimenters who are separated by a goodly distance- in spaceships a light-hour apart for example. Each has a particle that is entangled with the other. Now suppose the two expermenters are at zero relative velocity to each other. If I understand Special Relativity correctly, despite their distance from one another they share the same reference frame, and so can agree on an event being simultaneous (or DOES separation alone introduce a difference in reference frame?). By previous arrangement each will test their particle at the same time. One experimenter will measure the up/down spin of his particle and the other will measure the left/right spin of her particle. According to Quantum Mechanics, their measurements should produce a contradiction, and according to Special Relativity the measurements should take place before any signal could pass between them. What happens?
Again, it’s my understanding that something does change when we open the boxes. Before the first person opened his box, it was not determinate what information was in the box. There was no fact of the matter as to whether it said to meet at Betelgeuse or Sirius. Then the box was opened, and there was such a fact of the matter, and instantaneously, there came to be a fact of the matter on the other side of the transaction as well.
That’s the thing that puzzles me. But as I said in an edited in comment in a previous post, maybe the deal is that waveform collapse isn’t considered to involve a change in information. That might clear up my confusion, if it were the case.
There is relativity, and there is relativity. The Special Theory of Relativity is concerned with things like speeds close to c, and the speed of information transfer. The General Theory of Relativity is concerned with the curvature of spacetime and gravity. Special Relativity is not at all inconsistent with quantum mechanics, and indeed, QED, one of the theories which combines the two, is the best-tested theory in all of science. General Relativity, however, is to the best of our knowledge incompatible with quantum mechanics (which of course implies that the best of our knowledge is currently still inadequate).
Quoth Lumpy:
Ah, now we’re finally getting at the point of quantum entanglement. The two experimenters can measure any component of spin they want. No matter what direction I measure spin in, and no matter what electron I use (regardless of whether it’s entangled or not), I’ll always get an answer “positive” or “negative”. Once I make that measurement, the spin is definitely in that state, so if I measure the up component of spin and get “positive”, and then measure the up component of that same particle again, I’ll also get “positive”. Note that this breaks any entanglement the particle might (or might not) have had: A particle in a definite state cannot be entangled. If I take a particle which is definitely in an up-down state (like that one I just measured to be up), and measure it horizontally, I can get either positive or negative, with equal probability. And if I measure it at some diagonal angle to the first measurement, I can get either positive or negative, but not with equal probability: It’s more likely to be in the state which more closely matches the original state. In fact, the correlation between the two measurements is equal to the cosine of the angle between the two measurement directions.
That’s for a single particle. What about a pair of entangled particles? If both particles in the pair are measured on the same axis (say, for instance, the vertical component of both is measured), then they’ll always be opposite. That’s not too mind-boggling; that could be explained just fine by a hidden-variable theory like those shoes in shoeboxes. If the axes they’re measured on are perpendicular, then there’s no correlation at all: Half the time they’re the same (both positive or both negative), half the time they’re different. This could also be explained by a hidden-variable theory, albeit one slightly more complicated than the shoeboxes. But here’s the kicker: If the angle between the axes is somewhere between parallel and perpendicular, then the correlation between them is equal to the negative of the cosine of the angle between them. So, for instance, if the angle between the measurement axes is 45 degrees, then they’ll have a correlation of -0.707… Bell’s Theorem guarantees that, no matter what local hidden-variable theory you try to come up with, you’ll never be able to devise one consistent with that result.
What does it mean for two things to have a correlation of -0.707?
Am I right in thinking that means that, prior to the measurement of the near particle, the far particle is not in a definite state concerning spin on the relevant axis? And that this, in turn, means that measurement of the near particle in some way makes the other particle take the state it ends up taking?
Makes it take that state instantaneously?
What does “instantaneously” mean? Instantaneously in what frame of reference?
And does the collapse of a wave function amount to a change in informational state, in the sense of information used by those who say things like “There is no faster than light transmission of information when entangled particles are measured”?
Please forgive this very naive idea (which I’m sure that most or all of you in the thread have considered and discounted).
Could the entangled particles’ separation in spacetime be more apparent than real? In other words, could they be “right beside one and other” in a non-classic dimension. If so, could signals not pass between them via that dimension “instantaneously” despite the fact that in the 4 traditional dimensions they’re very far apart? Is something like this what Chief Pedant was getting at?
Physicists working in quantum mechanics tend not to devote too much thought to various interpretations of the theory, as doing so tends to have no effect other than giving physicists headaches. All that really matters is that you can correctly predict (at least in a statistical sense) the results of experiments.
And I’ll hold off on the precise definition of correlation lest I accidentally mis-state something, but the short version is that it’s a measure of how related two things are. A correlation of 1 means that they’re always exactly the same, a correlation of -1 means that they’re always exactly opposite, and a correlation of 0 means that given one, you don’t know anything about the other.
They could surreptitiously steal your particles, too, and still find out where your buddy is going. All it takes is one look for those particles (yours and your friend’s) to be in a definite state.
Right, but it was determinate that each particle would be in a state opposite to its partner in the other box. And in looking at your particles to see what state they’re in, it is impossible to tell if it was yours or your buddy’s measurement that collapsed their wavefunction.
This is no different, information-wise, than having a bunch of unknown coin halves in your boxes. You didn’t know what they were until you opened the box, but once you open it and look inside, you know your buddy has the opposite set.
That’s what they mean by saying that the information never travels faster than light. Certainly, from the point of view of the particle pair, there is a sense in which the signal “my wavefunction collapsed” is sent instantaneously from one to the other, so it knows to collapse, too. But the overall effect is such that nothing else can take advantage of that to send information faster than light.
That’s what I was asking about. I want to know what the technical notion of information is that makes this not an example of information being transmitted instantaneously.
And I’m still curious to know what “instantaneously” is supposed to mean in these discussions. Instantaneous from which frame(s) of reference?
*"That’s faster than light information transfer, isn’t it?
I don’t see a way to send signals this way, and maybe that’s what is meant by saying no information is transferred. But there are ways to coordinate activities in a way contingent on the measured state of the shoe remaining on Earth, and it seems like that requires faster than light information transfer.
Imagine you create a bunch of entangled pairs of particles. You keep one of each pair here on Earth and you ship the other ones off to the new human colony at Alpha Centauri.
At a predetermined time the Earth team starts measuring the spin of the particles one-by-one: up … up … down … up … down … up … down … down …
At the same time the Alpha Centauri team does the same thing: up … up … down … up … down … up … down … down …
To each team the sequence looks perfectly random. Half the time the spin is up and half the time it’s down and there’s no discernable pattern. But if they get together and compare their results, they discover that they’re exactly correlated.
The state of the particles is clearly linked, but no information is communicated from Earth to Alpha Centuri.
What I don’t like about the coin analogy, Dr Cube, is that it suggests the particles are in some determinate state like the coins, but you are right that whether they are or not doesn’t change the constraint, which was that our boxes contain opposites. But it is good in all the important ways.
Frylock, on a physics forum out there in the wild, wild interweb I noticed a person raising the point that having a decision procedure based on a random outcome is different from transferring information. What is weird about the quantum entanglement, though, is not that one person makes a decision based on a random outcome, but that two people who cannot communicate would agree on the outcome of a single random event. But this is no weirder than entanglement in the first place. Since entanglement is so weird, it is hard to grasp this situation.
That said, I think the “information is already contained in the experiment setup” line is a bit throwaway. The key is in considering what counts as information. If I decided that 01101101 represented Saturn instead of Eris then I could not communicate this to my parter faster than light. In fact, I am not communicating anything at all, I am merely mapping a set of possible outcomes to a set of locations. In this respect, the coin analogy is fair. The key to this is that (a) some correspondence exists and (b) that neither of us know which will be selected. So really what we are talking about here is the difference between “an event happened” and “I am telling you what event happened.” But all I can tell you with entanglement is what you already know from entanglement, that just this event happened. So no additional information has been added.
Information is a measure of the “surprise value”, “non-obviousness” or “improbability” of an event, message, etc. In this case, the information is all exchanged at slow speeds: 1) The information that the pair of particles are entangled was extracted when they were both very close together. 2) The determination of which state one particle is in is found when we measure it, which also takes time. With those two bits of information, we already know what state the other particle is in, there is nothing new coming from the other, distant particle in all this. There are no surprises, in other words.
That’s from anyone else’s perspective. From the particle’s perspective, it is a little bit trickier, and that’s where people say things like “nobody REALLY understands quantum physics”. What people are talking about when they say “information isn’t being transmitted faster than light” is the rest of the universe’s perspective. I’m not sure what you can say about the particle’s perspective, but that’s why this is an interesting scenario, and people write about it in books, and talk about it on message boards and stuff. Otherwise it would be no different than a left shoe being really far away from the right.
Well, that’s why I brought up the coin analogy in the first place. Quantum indeterminacy is what confuses people into thinking the information is moving faster than light. By analogizing with coins, it helps people see that from our point of view, the information travels no differently than it would if these were everyday macroscopic objects in a well-defined state.
I have to say, though, I only understand information from its use in communication theory. I’m not completely sure how it is used in physics. That’s why I don’t understand how to explain things from the particle’s perspectives. It really does seem like one particle “knows” instantaneously what its pair is doing light years away. All I know is if that information does travel faster than light, there is no way for it to help us send messages.
I said “I don’t see a way to send signals this way,” but you are apparently paraphrasing that as “signals are sent”? That doesn’t appear to you to be a very bad paraphrase? Since what I said implies signals are not sent?
But it gives people the false impression that the the two particles are somehow “synched” when they’re together: They’re both put into matching states, so you’d expect them to be correlated when you measure them later. But that’s not what’s happening.
The key, as Chronos pointed out, is Bell’s Theorem. If both Earth and Alpha Centauri measure spin using the same reference axis they get matches 100% of the time. If they measure spin using perpendicular reference axes they get matches 50% of the time … the same result you’d get with two random unentangled particles.
What if they measure spin using reference axes at 45 degrees to each other? You’d expect them to match up 75% of the time. (It’s pretty easy to see why if you draw a circle and divide it into octants.) This translates to a correlation of 0.5.
But quantum mechanics predicts (and experiments have proved) that the correlation in this case is actually much higher: 0.71. That’s impossible if all that’s happening is that both particles start off in matching states. It’s as though at the instant one particle is measured the other one realigns itself to match.
This is one of those topics where the most ignorant (me) and the most knowledgeable guy in the class get to ask the same question, so it’s a lot of fun to bandy about.
FWIW (and that’s nothing) I’m not quite so convinced that the particles need to be proximate in some sort of sense currently defined within our construct of spacetime. I do recognize that’s one explanation, and no nuttier than non-locality. I think we just haven’t figured out what particles are, and what space is. For sure particles are not shrunken down baseballs. And maybe they aren’t something that flies through space; maybe they are space, moving, and don’t become “particles” until they hit (interact) with something else. So when the waveform describing the system collapses (so to speak), what was space, moving, becomes two disentangled “particles.” Sure, light propagates at a constant speed “in” space but until we figger out what space and particles are, we don’t know that two entangled particles are not actually the same ezzak perturbation of space across as long a distance as we want to imagine. There’s nothing to say space has to behave like an aether; it can have properties all its own.
I haven’t finished mentally masturbating with all this, so I definitely did not put it into words well, but on the other hand even I could, I’m not sure the Dope is the place to lay out a really good idea. I do not want to be victimized by an actual smart guy cribbing my ideas and preventing me from being the stupidest man to win a Nobel.
You could think of waveform collapse with quantum entanglement as communicating information instantaneously, if you really insist on it. But the sense of “communication of information” in which this occurs is different from the sense used in stating that information cannot be sent faster than light.
When people say “information cannot be sent faster than light”, they mean something like “there’s no way to set-up a causal link between a sender at spacetime location A and a receiver at spacetime location B such that, for any method the sender uses to produce a message, the receiver learns about that message.” You could not accomplish this with quantum entanglement; the entanglement will not communicate arbitrary messages of the sender’s choosing. Rather, it will, in a sense, produce a message of its own choosing and give it to both parties involved (i.e., no party is able to act as a sender).
That having been said, you can always think of quantum mechanics in terms which avoid pretending there is an actual event such as waveform collapse at all, which I think makes it much easier to analyze the situation.