20160311, 16:52  #1 
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Entanglement question.
According to relativity, information carrying signals travel at β€c.
Experiments on entangled particles show correlations between measurements of, for example, spin components. These are EPR experiments aimed at testing the Bell inequality. If the particles are measured when they have a timelike separation, information could be transmitted between them consistent with relativity. However, experiments yield the same results when the separations are spacelike. (For those not familiar with the jargon, the latter experiments are synchronized to a smaller time interval than the time light takes to cross the distance between them.) Does anyone know, or can point me to the literature, of any measurements of the minimum velocity of information transfer between entangle particles, assuming that information is transferred? Thanks, Paul 
20160311, 17:46  #2 
Basketry That Evening!
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How do you mean?
I don't see that this is a question particularly related to entanglement. Measurement correlations due to entanglement are *not* information transfer, which is why these correlations are observed even across spacelike intervals. As you say, information can only be transmitted at the speed of light, i.e. within timelike intervals, but theoretically you can make a photon travel, on average, arbitrarily slowly, or any informationbearing mass for that matter. 
20160311, 21:24  #3  
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I quite agree that correlation does not imply causation, and have produced a nonQM thought experiment which shows similar behaviour to quantum entanglement. Nonetheless, on the assumption that entanglement measurements are causally connected, what is the experimentally measured minimum speed at which that information is transmitted? To put specific figures into the question, suppose that the measurements are synchronized to within one second (which can be done by transporting locally synchronized clocks to the experimenters, assuming flat spacetime, (the latter assumption being testable by experiment by measuring tidal spacetime distortions and frame dragging), that the experimenters agree that they are at rest with respect to each other (by exchanging light signals in flat spacetime) and that each measure their separation to be one lightminute (again by exchanging signals). If their results are causally connected, then the information must have travelled at not less than 60c Clearer now? Last fiddled with by xilman on 20160311 at 21:25 Reason: fix parenthesization 

20160311, 21:58  #4 
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You seem to be misusing one or two terms here. Information *can not* travel faster than \(c\), despite what you appear to claim here:
You seem to be having the same confusion as EPR so famously did. Entanglement between two particles means that their states are mathematically related: if you know one, you may deduce the other. What this means physically is that if you measure an observable property of an entangled particle, you immediately know what a measurement on its entangled partner will produce, regardless of the spacetime interval separating the pair. This is, as we both agree, a correlation among the measurements. But this correlation is neither causal (in the relativistic sense) nor information transfer. You can not communicate in any way by measuring an entangled particle (because you can not control the outcome of the measurement, i.e. there is no way to input something to the system). The thing that freaked out EPR (and in several senses, rightly so) is that it *seems* as though one particle "tells" the other "oh, I was just measured this way, so you must be measured that way". This is not the case. The correlation is completely determined by how the entanglement was produced, i.e. before the particles were separated by a spacelike interval (as of course this whole discussion is pointless if they are only separated by a timelike interval). One way you can think about it is that the measurements were already "decided" somehow at the time of entanglement, and the particles merely carry that decision without communicating, until such time as they are measured. This explanation would have satisfied EPR, except of course that as you seem to know, it is a description of a local hidden variable theory, which are ruled out by experimental tests of Bell's inequality. So we must suffice ourselves that the two particles share an indeterminate state, and that collapsing the state of one of the particles also means that if/when the other's state is collapsed, it will yield the particular measurement that the entanglement measurement dictates. This is one of the extreme oddities of quantum mechanics, but it does not and cannot transmit information, and so does not violate relativity. Having said all that, one possible answer to your question (as I understand it) is that the "transfer of the state collapse" may happen at any "speed" whatsoever, fast or slow or superluminal or slower than molasses in January. A better answer, IMO, is that it is meaningless to talk about such a "speed". Regardless of the interval between the two measurements, spacelike or timelike or whatever, they are correlated. In fact, if they are separated by a spacelike interval, you cannot even say definitively which measurement comes first, and so talking about the "speed of the propagation of the particular collapse of the state" is meaningless in the specific way of you can't say which particle is "telling" the other. (In your specific example, even if the people in their own mutual rest frame can agree on an order of measurement, there will always exist other frames (moving relative to the locations of measurement) that mutually disagree on the order of things.) This, in sum, is what freaked out EPR. State collapse of two entangled particles happens regardless of spacetime interval, and without a meaningful speed, and it cannot be explained by local hidden variables. It is simply one of the fundamental oddities of the universe, and (fortunately?) doesn't violate relativity. tl;dr quantum mechanics is weird enough that talking about such "speeds" is a meaningless Edit: Precisely how freaked out you are about this heavily depends on your interpretation of quantum mechanics and the meaning of wave function collapse. Warning: this is a massive rabbit hole. (Edit2: Another related article: https://en.wikipedia.org/wiki/Quantum_pseudotelepathy) Last fiddled with by Dubslow on 20160311 at 22:24 
20160312, 04:15  #5 
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http://inspirehep.net/search?ln=en&p..._search=Search
http://www.nature.com/news/thequant...etime1.18797 Last fiddled with by jwaltos on 20160312 at 04:16 Reason: added info 
20160312, 06:53  #6 
Basketry That Evening!
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I can't speak for the physicist in question, but the Nature article greatly confuses "entanglement" with "quantum nonlocality of collapse of entangled superposition", using the former when they mean the latter. Entanglement, i.e. the correlation/relationship between the states of two particles, is also a classical phenomenon (e.g. consider a grid of gears. The binary state of direction of rotation one individual determines said state of all the other gears on the grid  they are all mutually entangled. In quantum physics, as opposed to classical physics, the gears may be said to be rotating both ways at once, and you can't say which direction until you measure one  and measuring one instantaneously and nonlocally collapses the wavefunctions of all the other gears. It is this nonlocal collapse that is fundamentally weird about quantum mechanics.)
Edit: Ah yes, I recall reading this article some months ago, because the physicist they mention at UIUC is the one from whom I took my undergraduate quantum course. (I didn't really get much out of the lectures, I just read Griffiths  but he wrote the exams, at any rate.) Last fiddled with by Dubslow on 20160312 at 06:56 
20160312, 07:29  #7  
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20160313, 22:34  #8 
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You're welcome. Your reasoned insights on this topic are always appreciated.

20160314, 14:29  #9  
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First, I'm a good little relativist and know that one of the tenets is that information transfer is bounded by \(c\). My claim was in the form of a counterfactual "Ifcondition, what then?". Let's drop all reference to speed, information transfer, arbitrary observers and the like. Let two experimenters verify that spacetime around them is flat (around meaning for the duration of the experiment and throughout a continuous volume of space which encloses them both. Let them manoeuvre themselves with rockets, gyros, or whatever, so that they each measure themselves to be at rest with each other. Let them synchronize their clocks to within a precision of Ξt seconds using a purely Einsteinian procedure. Let them each measure their separation and agree that the value is l metres. Let them both perform their entanglement measurement at time t=0 as measured on their local clock. Let them compare their observations at a subsequent time using any method they wish  carrier pigeons and messenger boys for all the difference it makes. My question is: what is the greatest experimentally measured value of l/Ξt? 

20160314, 15:45  #10  
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Quote:
Quote:
Moving on: Quote:
My confusion is, what does the precision of the clocks' synchronization have anything to do with their (simultaneous) measurement? 

20160314, 16:41  #11  
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Yes, I know that I'm spouting heresy and I'm well aware that the Bell inequalities (which are based on extremely plausible assumptions) forbid hidden variable formulations of quantum mechanics. Nonetheless, I am trying to get my head around the pilot wave interpretation of QM and find that setting up thought experiments to compare with lab measurements a helpful way do develop my intuition. 
