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This may be a foolish question given my limited understanding of QM but here it is.

As I understand quantum entanglement basically means that two particles evolve as a single "unit", i.e., are described by a single wave function. Now, it seems to me that production of entangled pairs (or n-tuples?) of particles must be a common occurrence and assuming that these particles may then travel a long way away from each other, does this not mean that the whole universe must be a mess of entanglements, effectively breaking the principle of local action? I believe, I understand the reasons why information cannot propagate faster than light from one region of space to another in spite of entanglement but it still seems to me that a universe of "disentangled" particles would behave quite differently from the universe where many particles are entangled. Is there a flaw in this reasoning?

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I think your confusion comes because you are thinking of the state function as a physical function describing the physical location of all particles in the universe coherently.

In truth, the square of it is a probability function describing coherently where all particles might be if you measured them in the universe.

The density matrix formulation allows one to think of any number of particles contained by one state function.

density matrix

Here the psi's are the individual wave function solutions for the zillions of atoms etc. ( their squares give the probability for measuring each individual at that (x,y,z,t).

Each atom in the universe and each free floating particle will be contributing its bit in this density matrix and the off diagonal elements describe the "entanglement" /coherence relation between the individual wave functions. As we know from the laboratory that the probability is infinitesimally small, for example, of an electron around an atom to exist a centimeter away from the nucleus, as the ensemble and the distances covered grow, the off diagonal elements become infinitesimally small, unmeasurable.

Thus, though theoretically everything is mathematically connected to everything else, in practice, once we reach dimensions where h_bar is to all intents and purposes zero, the classical framework is attained very fast , and it is only in our immediate locality, with instruments that can examine dimensions where h_bar is significant and quantum behavior is important, one needs to bother with all this entanglement stuff. The classical limit where probability functions are useless in describing/predicting observations is reached very fast.

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  • $\begingroup$ I think, I understand. Basically, the whole universe is described by one wave function, accounting for all observable particles. I guess my question is about those off-diagonal elements in the density matrix. I could be wrong about this, but as I wrote in the original question, if appearance of entangled particles, e.g., in stars, is a common occurrence they could then travel a long way in inter-galactic space without interacting with anything else and remain entangled(?). Would that not mean that a significant proportion of the off-diagonal entries could be non-zero? $\endgroup$ – Daniel Genin May 20 '14 at 13:11
  • $\begingroup$ Stars are just matter like earth except athigh temperatures. This means that the wavefunctions will attenuate fast ( and thus the off diagonal elements).So not a significant amount. Some two photon production if it is from electron positron annihilation (as an example) and the photons meet nothing on the way, then those two photons will have off diagonal elements in the density matrix. In the primordial universe, the inflation and quark gluon plasma period, then one could say that most of the off diagonal elements have some entries. en.wikipedia.org/wiki/File:History_of_the_Universe.svg $\endgroup$ – anna v May 20 '14 at 13:38
  • $\begingroup$ I chose stars because they produce a lot of radiation as compared to something cool like Earth. If there are processes in stars that could produce entangled photons would not they even today lead to many non-zero off-diagonal entries? $\endgroup$ – Daniel Genin May 22 '14 at 15:25
  • $\begingroup$ The radiation they produce is mostly incoherent, the sun for example. It is only in lasing conditions that coherence can be quaranteed, and then one could talk of entanglement, but I do not think that such a situation arises in stars. electron positron annihilations would be a very small part of what radiates from a star. $\endgroup$ – anna v May 22 '14 at 18:43
  • $\begingroup$ Ah, I see. So production of entangled particles is actually a rare event. That was the flaw in my mental model. Thank you for clarifying. $\endgroup$ – Daniel Genin May 23 '14 at 20:35
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What do you mean with "quite differently"?

The answer to your first question -

does this not mean that the whole universe must be a mess of entanglements

would be "yes", that's what it means.

But, it seems that entangled particles cannot be used to transmit information without also having a classical information channel available, which is bound by the speed of light. As such, the answer to your second question, if I understand it correctly, would be "no" - a universe of "disentangled" particles would not behave quite differently from the universe where many particles are entangled. Or perhaps more precisely: there is no way to tell the difference.

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  • $\begingroup$ Yes, let me try to clarify what I mean by "quite differently". Take an extreme example -- a universe in which all particles are entangled. Is there no measurement, or sequence of measurements, we could perform to distinguish it from a universe in which particles are disentangled? $\endgroup$ – Daniel Genin Apr 20 '14 at 2:43
  • $\begingroup$ I don't think there is. Since you need a classic information channel to find out if a particle is entangled or not, I don't think that we can tell the difference. $\endgroup$ – user1459524 Apr 20 '14 at 4:48

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