Albert Einstein did not like Quantum Mechanics. "God does not play dice!" he is famously known to say. Few know Neils Bohr's reply: "Albert, stop telling God what to do".
Einstein and Bohr were constantly jousting over QM. Einstein had to admit that the theory was stunningly accurate, but did not like it's stochastic nature, it's seeming reliance on statistics and probability. To Einstein, the theory was unpalatable and incomplete, and he would come up with one gedanken - a thought experiment - after another to stymie Bohr.
One such gedanken is the EPR Paradox. The Einstein-Podolsky-Rosen experiment - overly simplified - goes something like this. Let us take a molecule composed of two similar atoms such that the atoms have opposite spins (not like the way a top spins, but no matter). If one atom has spin-axis-up, the other will automatically have spin-axis-down. Now, QM can describe the molecule with a state equation, or a quantum wave equation. With such a description, the two atoms can said to be entangled, they share a fundamental information. We then separate the molecule and send the two atoms whizzing away from each other. How far? Why, as far as you like, billions of light years aparts if you wish. But for the purposes of the paradox, far enough so that, for purposes of communication, light takes a long time to go between them.
Now, we have two experimental detecting machines that these atoms fly into. These detectors will tell you what kind of spin the atoms have. (Keep in mind that the atoms always have opposite spin). If detector #1 tells you it's atom has a spin-axis-up, then the other detector has no choice but to tell you that it's atom is spin-axis-down. In other words, even though the atoms are separated by billions of light years, they are still entangled as if they had never been separated. This is what Einstein referred to as "spooky action at a distance". The paradox is that by measuring one atom you instantaneously receive information about the other atom, even though the other atom may be so far away that the only conventional explanation is that information was sent faster than the speed of light, which violates Einstein's relativity, which is a no-no.
Clear as mud? Well, sorry, but every search entry under "EPR Paradox for Dummies" is not much better. Suffice to say that Einstein set this up as a paradox to show that QM wasn't quite up to snuff when describing the universe.
Only problem is, when experimentalists like Alain Aspect (and theorists like John S. Bell) finally had laboratory set ups clever enough, and laboratory equipment sensitive enough to perform the gedanken for real, that's exactly what happened. Quantum Mechanics won out, Einstein's paradox was no paradox at all, and the universe turned to have nonlocal weirdness to it. (But, bear in mind, the speed of light was never exceeded because there was no classical signal sent, no message or communication. The information just simply was).
It gets worse. Some very clever guys figured out a method called quantum teleportation, which allows for a quantum object (like a photon or an electron, or even a molecule) to teleported from one location to another. It's not Star Trek teleportation, where an object is scanned , and then electromagnetically beamed someplace, and then reassembled. Instead, the information about the particle is teleported rather than the particle itself.
Could it work on people? Extremely doubtful. Not impossible. But highly improbable.
Oh, I suppose you might be able to teleport say me, someday. A silly fictional scenario might have a recipe like... Ionize four hundred pounds of the appropriate elements into a plasma. Cooling that down to a few billionths of a degree above absolute zero to create a Bose-Einstein condensate. Deftly tease that into two two-hundred-pound entangled pieces. Ship one ultracold blob off to Jupiter in a special container that prevents any interaction with the larger universe (because if that happens the delicate entangled state collapses). Somehow take a quantum measurement of me and the entangled ultracold blob left behind (probably involving laser beams and giant magnets). Send off a radio signal with the quantum information to Jupiter, to be received by the other entangled piece. And poof! I appear on Jupiter (or better still, in some orbiting laboratory).
Problem with all this? If you don't do the measurement correctly at either end, I'm toast. Another problem? The process of measurement means I have to die, utterly destroyed, gone, finished, kaput, which opens up legal and philosophical issues for the me on Jupiter (should I make it).
So.... not likely. Although practical applications run the gamut from unbreakable message encryption to ultrafast quantum computers, and who knows what else.
So, now the most astounding thing about all this is the recent news that there may be a time travel version of entanglement. Well, not exactly time travel, as it is only into the future, which we travel into anyway. But two theorists from Australia's University of Queensland have proposed an teleportation scheme that allows quantum information to be sent from one detector in the past to one in the future, while never passing through the interval in between. In other words, the intervening time is skipped over.
This, quite frankly, just completely blows me away.
Applications, if any? Beaming energy into the future? Manipulation of the vacuum to manipulate/store information? Dude, it's all really wild stuff!