I had recently been typing up a reply to Frylock’s thread on quantum mechanics. Probably a bad move, as I’m not a physicist; it just ended up highlighting for me something I don’t quite understand and couldn’t quickly settle with Internet browsing. To wit, suppose we create a system of entangled particles and send them off far from each other (to what I’ll call the west and east labs). Let A and B be non-commuting observables; suppose the west lab measures A twice and the east lab measures B once, in such a way as, from some reference frames (this is where the relativity enters) the order of measurements was AAB, while from some reference frames, the order is ABA.
Now, as far as AAB goes, performing the same measurement A twice in a row is guaranteed to give the same result both times, right? (The first measurement of A collapses the state into an eigenvector which will be preserved by the second measurement of A). But as far as ABA goes, it’s not guaranteed that both measurements of A will give the same result, as the measurement B in the middle can disturb this (changing the state from an eigenvector of A to an eigenvector of B which can collapse into a different eigenvector of A).
So… what gives? From one reference frame, we’re guaranteed that the west lab sees the same result twice, and from another reference frame, we would expect this to happen only some fraction of the time? What (surely embarrassingly basic knowledge) am I missing?
I guess this is all just a special case of the fact that quantum mechanics tells us the order of measurements matters a lot, while special relativity tells us there’s no such thing as the absolute order of the measurements (if they occur with spacelike separation, which we’d need to use entangled particles to create). Which is presumably a quite basic issue, but I’m also quite ignorant. [If I’ve been talking misguided or meaningless gobbledygook at any point, please set me straight]
The west lab’s first measurement of observable A for its particle collapses the state for the east lab’s particle, but also breaks the entanglement between the two particles.
The west lab can now (spookily) say something about the state of the other particle and hence about the results of what the east lab may see in its measurements. But neither lab can again change the state of the other’s particle by any further measurements on its own particle.
The two measurements of particle A will give the same result. You can think of this as some sort of “communication” between the two particles, but if so, then the communication is faster than light or even backwards in time (depending on reference frame). Yes, this is somewhat disturbing, but then, so is every other possible interpretation of the results of the EPR experiment.
bonzer and Chronos are right that the two measurements of A will produce the same result; as bonzer says, measurement of one of the particles of an entangled state will “break the entanglement”; or, if you prefer, entangle the observer with the state in such a way that further measurements will not demonstrate any further nonlocality. I just came to point out that your premise is flawed, and that this is not spooky (at least, no more than normal EPR). A and B are in fact commuting observables; this is a necessary consequence of the fact that they are being performed in causally separated regions.
That is, to be pedantic, the west lab is measuring an observable we can write as A1 (acting as A on the west particle and, necessarily, as the identity on the east particle) and the east lab is measuring 1B. It is easy to see that these commute. It is also easy to see now that the reference-frame-dependent “order” in which these are measured cannot possibly have any effect on the outcomes, which is also true: no superluminal communication between A and B can be effected by this measurement.
:smack: Thanks everyone, I get it now (or at least, I temporarily think I do). omphaloskeptic’s remark that the observables are actually A tensor 1 and 1 tensor B, and thus commute, was particularly helpful.
I believe the OP’s question is related to a question I’ve always had. (I asked it here once but I don’t think it got answered IIRC). Measurement of one entangled particle is supposed to “simultaneously” affect the other particle. But “simultaneous” is relative to a reference frame. So if the effect is simultaneous, what I’ve been wondering is, what reference frame(s) is it supposed to be simultaneous in?
(Disclaimer: I clearly don’t know anything. But this is my understanding. Those people who do know things, please set me straight if I am misguided or flat-out incorrect.)
Well, in a sense, it doesn’t really have an effect; for example, it doesn’t allow for transmission of information, not even information like “It just happened!”. The supposed non-local effect is collapse of the wavefunction, but there are ways of viewing this as not really an effect, per se, at all. For example, I’ve seen it put that the so-called collapse is akin to the classical situation where conditionalizing a probability distribution (what might be thought of as a classical wavefunction) relative to an event (information received from a measurement) modifies it into a new probability distribution (in the extreme case, into a delta/Dirac distribution), yet no one thinks of this phenomenon as causal. I believe the situation is analogous even in the quantum case, just that this all occurs using a slightly different notion of probability distribution.
Call it an “effect” or call it something else, but it seems like what is said is that an event involving particle A happens simultaneously with an event involving particle B. Whether the relationship is causal or not, the relationship is supposed to be simultaneous, and I’ve never understood what “simultaneous” means here.
Even if we say “Well, non-causally-related events that don’t transmit information can correlate simultaneously” this still invites the question, simultaneous for who? Doesn’t it?
Well, the perspective I mean to indicate is that the relevant things aren’t “events”; they aren’t genuinely spatiotemporally located at all. At least, there aren’t two distinguished spatiotemporal locations being considered simultaneous to each other.
Consider this (classical) analogy: there’s a factory which produces a random number and then places identical copies of it in two sealed boxes. The sealed boxes are then mailed out to locations far, far away from each other. You are the recipient of one of these boxes. You have some method of pressing a button upon your box and receiving some information about the number within it. Prior to pressing the button, you would describe the probability distribution of the contents of the other box one way; immediately after pressing the button, you would describe the probability distribution of the contents of the other box some other way (as it would now be relativized to the information you just learnt). In this sense, a button-pressing in one location causes a simultaneous collapse of a probability distribution at another, far-distant location. That’s the kind of simultaneity involved, but the thing is, this “probability distribution collapse at the other box” isn’t really a genuine spatiotemporal event at all; it’s more an artifact of our conventions for how to represent our having carried out certain measurements. Any observer in any reference frame would be willing to describe a collapse as occurring at whatever time they first find out the relevant information.
I believe the quantum phenomenon you refer to, while of course different in interesting ways, behaves exactly analogously so far as your question goes.
Your analogy relies on the idea of probability as a measure one’s own epistemological state. But I think that in Quantum Physics, though the math they use is the mathematics of probability, what they’re measuring isn’t supposed to be the measurer’s own epistemological state, but rather something metaphysically “out there,” independent of the measurer’s epistemological state. I thought this was part of the import, for example, of Bell’s Theorem. You’re analogy is like saying there’s a “hidden variable” (the code locked in the box) that explains everything that happens, but Bell’s Theorem shows that no “hidden variable” theory can explain this kind of thing.
In other words, it’s my understanding that measuring one of the particles in an entangled pair correlates (causally or not) with a change in state of the other particle in the pair–not just a change in someone’s epistemological position respecting that particle, but rather a change concerning the particle itself.
'T’d be nice if someone who actually knows the physics would chime in here, though!
ETA: Your analogy is suggestive of a possibility I hadn’t considered before–that “simultaneous” as used in formulations of entanglement phenomena means “simultaneous from all reference frames.” From any reference frame, the time of the measurement of one particle is simultaneous with the time of the waveform collapse of the other particle. You explained this simultenaity in epistemological terms, but even if that’s not the right way to explain the simultanaity, the simultanaity may nevertheless be from all reference frames after all, as far as I can tell.
It doesn’t really matter. You can imagine an experiment where the two measurements are occurring in different reference frames with different notions of what order things are happening. The results are still the same. From the perspective of tester A his measurement came first and he instantaneously collapsed the wave function of the B particle. From the perspective of B his measurement came first and he instantaneously collapsed the wave function of the A particle. The “spooky action at a distance” is a temporal phenomenon as well as a spatial one – apparent effects can precede apparent causes.
I used to think that, too. Unfortunately the EPR experiment is usually explained poorly enough that that would be a reasonable conclusion. Let me see if I can explain it better.
Let’s say that our entangled system is a pair of fermions, with total angular momentum zero and no orbital angular momentum (thus, the spin of the two particles must be opposite; a fairly typical case for entangled particles). I take the two particles and separate them by an appropriate distance, into two far-away laboratories, and in each laboratory I have an apparatus for measuring the component of spin of a particle in a particular direction (in quantum mechanics, you can’t measure the whole spin, only a single component, and that component will always be +1/2 or -1/2, never anything in between). If the apparati in the two labs are oriented in the same direction, they’ll always give opposite results: One will be +, and one will be -. If they’re oriented in opposite directions, they’ll always give the same result: Either both +, or both -. If they’re oriented at right angles to each other, there will be no correlation between the results: No matter what result you get from one, the other still has a 50-50 chance of either. And if you put them at some other angle to each other, you’ll get something in between: If they’re at an angle less than 90 degrees to each other, then they’ll usually be opposite, but sometimes the same, for instance.
Now, so far, all of this could be explained easily enough by hidden variables: The particles are boxes with some actual value printed inside, and the results of the measurements are determined in some deterministic way from what’s written inside, even though we can never directly read the writing. The problem comes in that diagonal case, where the measurements are at some angle other than 90 degrees, if we ask just how often the measurements should agree. John Bell was able to prove mathematically that, in any system based on local hidden variables, there is some minimum value for the correlation at any given angle. However, quantum mechanics predicts a value for that correlation which is not within the bounds of Bell’s inequality, and experiments have proven that particles really do follow the predictions of quantum mechanics, not Bell’s result. Thus, quantum mechanics, and reality in general, is not and cannot be based on local hidden variables.
Yes, I understand that the violation of Bell’s inequality means there aren’t actual local hidden variables (in fact, that’s what I was originally going to post in the other thread before I got caught in my own confusions), so we can’t use an actual classical probability distribution to model the situation. But that’s why I said it was different but analogous. I didn’t mean to imply that there were actual counterfactually definite values hidden in the box, but simply that the kind of phantom simultaneity displayed by classical probability distribution collapse is the same kind displayed by non-classical wavefunction collapse. Can we not still consider the case to be that the apparent collapse of the (complex-valued, its square modulus gives the probability, etc.) wavefunction is simply its relativization to the result of a measurement (I thought this was what the relative state interpretation does)?
(That would be my reply to the following quote as well. I am not proposing that there are actual local hidden variables; the discussion of a classical probability distribution collapse is meant to simply be an analogy for the kind of collapse the wavefunction undergoes; I am not proposing that the wavefunction is simply a means of describing an underlying hidden variable theory, just pointing out the kind of thing that is meant by “simultaneous collapse”.
(So, again, just to make it clear: the analogy I posted was specifically meant to take place in a classical, not quantum, framework. It wasn’t meant to say “Hey, here’s what’s going on with quantum indeterminacy”; it was meant to say “Hey, here’s another, different kind of situation but with exactly the same kind of ‘Simultaneous according to everyone’”, which could help clarify the latter notion. The presence of underlying definite hidden values was meant to be acknowledgedly part of the difference (why I described it in parentheses as classical), not part of the similarity.).
Got it. But it’s hard for me to see how to separate the simultanaity-according-to-everyone in your analogy from the hidden-variable-and-probability-as-empistemological-measuremnt in your analogy.
Remove the idea “There is an underlying definite, albeit hidden, value in the box” but retain the idea “There is absolutely no experiment at the distant spatiotemporal region which would have any difference in value between the situations where the collapse did and did not occur; in this sense, the collapse is not a ‘real’ event and merely an epistemological one, if you would like to use that terminology, and, in particular, has no spatiotemporal location. Specifically, what I mean by this is that there is some function W(M)§ of two variables, the first (M) being some corpus of observed measurements and the second § being a point in spacetime. For any particular fixed value of the first argument, the resulting function W(M) of one variable can be thought of as a field of values varying over all of spacetime, with the particular use that from this field’s values in some region, certain (probabilistic) predictions can be made about the results certain experiments would have in that region, with the ability to be confident in these predictions if one has actually made the observations M. The so-called ‘instantaneous everywhere collapse’ of this field is simply a description of our shift in interest from looking at W(M_1) to looking at W(M_2) in response to a particular observation/measurement changing the corpus of historical observations we are interested in from M_1 to M_2; however, just as there is no distinguished global value of what the corpus of interest is (M), there is no distinguished global value of what the field is (W(M)), and so, in particular, at any given point, there is no distinguished value of this field at that point (W(M)§). Since points in spacetime do not have distinguished associated values, we cannot speak of distinguished events/points in spacetime defined via the geometry of those values (e.g., ‘where/when they change’). ‘Collapse’ is not actually about how W(M)§ changes as P varies, but about how it changes as M varies; it is not associated with a particular location in spacetime as one shifts between those with one property and another, but rather with shifts between corpuses with different properties.”
Everything I’ve written there is true when W(M)§ is taken as the function defining the probability of some property holding at point P relative to corpus M in a situation of classical indeterminacy, and I believe everything I’ve written is also true regarding when W(M)§ is taken as corresponding to “the wavefunction” in quantum mechanics, albeit in that case W contains not just simple probabilistic information but “phase” information as well, allowing for destructive interference and eliminating the possibility of being modelled by underlying local hidden variables.
(Well, technically, one could always, trivially, take the position that at the very beginning of the universe, all the particles huddled together in the Big Bang and said ‘Alright, here’s how the entire rest of history will go’, keeping a secret copy with them to this day determining their every move. Local hidden variables, that. But contrived and unhelpful as a model, lacking any predictive power if one has no grounds to say anything about what they decided upon for history. More to the point, regarding the Bell’s inequality violating experiment Chronos mentioned, if the far-off labs choices of detectors’ orientations are considered as probabilistically independently nondeterministic, then there really absolutely cannot be any local hidden variable theory describing the results.)
OK, gotcha. What you were posting before sounds similar to what many folks say when they don’t grasp the real subtlety, and one can go pretty far in one’s physics education without ever seeing it explained properly, so I thought I should play it safe and explain.
On another note regarding my post #17 afterthought, though I just ran out of the edit window
I suppose the bolded bit is really just a kind of locality condition in itself, a slight strengthening of spacelike-separation. That is, not only do we ask of the two labs that they be spacelike-separated, but also that they be able to take nontrivial information-theoretic advantage of this, via access to local information-producers (sources of probabilistic nondeterminism, i.e., randomness).
Anyway, #17 was all rather trivial pedantry, so there’s no point continuing with it. I’m sure everyone who’s ever considered the issue has understood the implicit presence of this condition as well.