quantum mechanics - Is there such a thing as "Action at a distance"?

What ever happened to "action at a distance" in entangled quantum states, i.e. the Einstein-Rosen-Podolsky (EPR) paradox? I thought they argued that in principle one could communicate faster than speed of light with entangled, separated states when one wave function gets collapsed. I imagine this paradox has been resolved, but I don't know the reference.

Answer

It's not possible to communicate faster than light using entangled states. All you get out of entanglement is a correlation between the values of two measurements.; the entanglement doesn't allow you to influence the value measured at another location in a non-causal way. In other words, the correlation only becomes evident after combining the results from the measurements afterwards, for which you need classical information transfer.

For example, consider the thought experiment described on the Wikipedia page for the EPR paradox: a neutral pion decays into an electron and a positron, emitting them in opposite directions and with opposite spins. However, the actual value of the spin is undetermined, so with respect to a spin measurement along a chosen axis, the electron and positron are in the state

$$\frac{1}{\sqrt{2}}\left(|e^+ \uparrow\rangle|e^- \downarrow\rangle + |e^+ \downarrow\rangle|e^- \uparrow\rangle\right)$$

Suppose you measure the spin of the positron along this chosen axis. If you measure $\uparrow$, then the state will collapse to $|e^+ \uparrow\rangle|e^- \downarrow\rangle$, which determines that the spin of the electron must be $\downarrow$; and vice versa. So if you and the other person (who is measuring the electron spin) get together and compare measurements afterwards, you'll always find that you've made opposite measurements for the spins. But there is no way to control which value you measure for the spin of the positron, which is what you'd need to do to send information. As long as the other person doesn't know what the result of your measurement is, he can't attach any informational value to either result for his measurement.