The chancy (probabilistic) nature of wave function collapse is just one of numerous puzzling aspects of quantum mechanics. Another deep mystery associated with microphysical systems is a phenomenon called quantum entanglement. According to quantum mechanics, physical systems can be related to each other in a way that makes it impossible to represent their states with separate wave functions. Two systems are said to be entangled when the state of one system is correlated with the state of the other, so that their behaviors cannot be predicted independently. In other words, the two systems cannot be adequately represented using separate wave functions, but must be described using the same wave function, as though they were a single system. If something happens to one system, its entangled partner is simultaneously affected.

What makes this especially puzzling is that the two systems don’t have to be located close together in order to be entangled. Quantum entanglement can occur with systems arbitrarily far away from each other. This seems to violate Einstein’s special theory of relativity, as illustrated by the following example.

According to quantum mechanics, two photons (“particles” of light) can become entangled so that the polarization of one photon is always orthogonal to the polarization of the other, even if the photons are far apart. If the polarization of one photon changes, the other photon’s polarization will change too, no matter how far away it is.

For example, whenever one photon has horizontal polarization, the other has vertical polarization, and *vice versa*. Now recall that horizontally or vertically polarized photons are in a superposition of 45° and -45° polarization states. If the horizontally polarized photon hits a 45° polarizing filter, it has a 50% chance of collapsing to a 45° polarization (in which case it will pass through the filter) and a 50% chance of collapsing to a -45° polarazition (in which case it will be blocked).

But here’s the really surprising thing: if the horizontally polarized photon collapses to a 45° polarization, its entangled partner (which had vertical polarization) will collapse to a -45° polarization so that their polarizations remain orthogonal. And this will happen no matter how far apart the two photons are, and no matter which collapse happens first. In fact, the photons will maintain opposite polarizations even if the two collapse events have spacelike separation, which means—according to special relativity—that there is no fact of the matter which collapse happened first!

In 1935, Einstein and two of his colleagues, Boris Podolsky and Nathan Rosen, co-authored a famous paper criticizing the theory of quantum mechanics.The paper, entitled “Can Quantum-Mechanical Description of Physical Reality be Considered Complete?”, is available here. According to the traditional way of understanding Born’s rule, the collapse of a wave function is a fundamentally *chancy* event, as explained previously. When a photon collapses from a superposition to a definite polarization state, the outcome of this collapse is not predetermined, but is simply a chance event that occurs when the photon’s polarization is “measured” by the polarizing filter. But if the polarization of a photon really does change in a fundamentally chancy way, as the theory claims, then entangled photons would have to influence each other at faster-than-light speeds in order to maintain opposite polarizations at all times.

Einstein, Podolsky, and Rosen pointed out that if this aspect of the theory is correct, then quantum entanglement violates the principle of locality, which says that no causal influence can travel faster than light. This problem—the fact that quantum entanglement violates the principle of locality—is known as the EPR paradox. (EPR stands for Einstein, Podolsky, and Rosen.)