“As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.” -Albert Einstein
If you create an entangled pair of particles, and stretch them apart as far as you want, the entanglement remains. If you make a measurement of one particle’s quantum state, you immediately — and this is truly instantaneous — learn the quantum state of the other. This is true whether the other particle is meters, kilometers, astronomical units or light years away.
Schematic of the third Aspect experiment testing quantum non-locality. Entangled photons from the source are sent to two fast switches, that direct them to polarizing detectors. The switches change settings very rapidly, effectively changing the detector settings for the experiment while the photons are in flight. (Figure by Chad Orzel)
And yet, according to relativity, there’s no way for information to travel that fast. Nothing at all, under any circumstances, can travel faster than the speed of light in a vacuum. To a casual (or even a serious) observer, it might appear that we’re violating the laws of physics in some fashion or other. But the truth is even scarier: nature is more surprising than anyone anticipated.
If two particles are entangled, they have complementary wavefunction properties, and measuring one determines properties of the other. But whether the wavefunction is merely a mathematical description or underlies a deeper truth about the Universe and a deterministic, fundamental reality is still open to interpretation. Image credit: Wikimedia Commons user David Koryagin, under c.c.a.-s.a.-4.0.