In 1976, two physicists, Edward Fry and Randall Thompson, startled the scientific community by performing an experiment that might seem to imply that, under some conditions, subatomic particles can communicate with each other at speeds greater than that of light.
The two major scientific theories of the 20th Century that transformed our understanding of how the world works are Relativity and Quantum Mechanics.
When James Clerk Maxwell worked out his famous equations which explained how electricity and magnetism work and interact, this later led to people seeing radio waves as a consequence of these equations. The equations even told how fast radio waves would travel, and that speed happened to be the same as the speed of light, which had already been measured.
But that meant that if you were on a car in a railroad train, moving towards a source of light, the light from that source ought to be moving more quickly. But if light can move more quickly where you are, even though it is only because you are in motion, that means that the physical laws that led to Maxwell's equations would have to be different for you.
One possibility is that the laws of physics are different when looked at from a moving platform. Perhaps light is a wave travelling through a medium; and that medium might well define what it means to be standing still. Other scientists proposed bolder theories, such as the Lorenz contraction; perhaps things get shorter in the direction of motion, and this hides apparent changes in the speed of light.
Albert Einstein boldly took the premise that uniform motion does not change the laws of physics, and instead of stopping at the beginning, he thought through the unusual consequences of this to the end. This led to the Special Theory of Relativity, which, in addition to the Lorenz contraction, also predicted time dilation in moving bodies, and that the time would be, as viewed by a stationary observer, different at the two ends of a moving body for those within it. As well, it predicted that moving objects would be heavier than stationary ones.
Instead of space and time being absolute, the velocity of light was absolute. Not only couldn't a rocket ship go faster than the speed of light, because its weight would approach infinity as its speed approached that of light, but there was no tricky way to go faster than light either. Just as a sailing ship can sail against the wind by tacking, if there were a way of going even slightly faster than light, by choosing the slower-than-light speed from which you start your journey, you could work things out so as to go somewhere distant, and then return back to where you started at a time before you left. This, though, rests on the assumption that whatever trick you try to use, the laws of physics that describe it are also the same for all viewpoints of observers in regular linear motion.
Originally formulated for the case where the corrections due to relativity can be neglected, Quantum Mechanics is the theory famous for telling us that particles behave like waves, and that microscopic reality is irretrievably fuzzy.
The part of Quantum Mechanics we will be concerned with here is Heisenberg's Uncertainty Principle. Heisenberg showed that measurements that can be made on objects come in complementary pairs, and when one tries to measure the value of one such parameter, the complementary one becomes uncertain. Measuring the momentum of an object is like taking an electrical pulse flowing through a wire, and forcing it to go through a strongly resonant circuit which will give it a well defined frequency, at the cost of spreading out the pulse, and making it last longer. Measuring the position of an object is like forcing the pulse to become an instantaneous spike so that it has a well-defined time.
The product of the uncertainty in the momentum measurement and in the velocity measurement is related to Planck's constant.
In 1930, P. A. M. Dirac discovered the existence of antimatter by working out how Quantum Mechanics needed to be modified for conditions when it was necessary to also take account of Relativity. If one tried to quickly measure the position of a particle by looking for it over a large area, since nothing could travel faster than light, if the particle started out as not having a well-defined position, there was a chance you could find it in two places.
This did not violate conservation laws, however, since to make such a measurement, you had to use so much energy that the energy was adequate to create a new particle out of nothing. But other conservation laws would still be violated, unless there was also a third particle, which was opposite to the extra particle (and the original one) in electric charge and other properties.
Subsequently, Albert Einstein, Boris Podolsky, and Nathan Rosen published a scientific paper in 1935 that showed that, according to the mathematics of Quantum Mechanics, for other kinds of measurement, things didn't work out quite so neatly. If one wanted to measure angular momentum, or spin, measuring angular momentum around one axis was complementary to measuring it around a perpendicular axis. It still took energy to measure angular momentum. But it was possible to measure the angular momentum of an object without contributing any angular momentum to it at all.
Processes were known that result in two particles, with equal and opposite spins, being emitted in opposite directions. If you choose an axis, and measure the spin of one of the particles relative to that axis, in order that no angular momentum is added or lost, when you shoehorn one particle into a state where it really is spinning, say, either up or down, the same thing must happen to the other particle, even though it may be far away!
The equations of quantum mechanics predicted strange things would happen in that kind of experiment. If you test the two particles for spin in the same direction, they always have the same spin. If you test them for spin in two perpendicular directions, then there is no correlation between them: one particle goes left or right each just as often when the other one spins up or down. If you test them for spin in two very similar directions, the proportion of times when the spins don't match goes up as the square of the angle between the two directions. This corresponds to how well a signal is picked up by an aerial as you turn or tilt it from pointing in the ideal direction.
If the particles were really spinning up or down in the first place, then it comes as no surprise that they both match when tested for up or down spin. But then, if they're tested for sideways spin, if both tests are independent, there should be no correlation between their spins. But if the tests were independent, they would then have the possibility of contributing net angular momentum to the two particles. So perfect correlation is found, no matter in which direction one looked at the spin.
One way that was proposed to deal with this problem was called hidden variables. Perhaps the two particles were, in essence, each carrying a little book with them which told them how to behave under every possible form of measurement.
But let's then try testing two such particles for their spins in directions separated by a small angle. The minimum number of times that the two particles might not have matching spins in such a case would be if their little books had the simplest possible description of how to behave: a spin that goes one way for 180 degrees, and then the opposite way for the other 180 degrees (where the detector is upside-down, and really measuring the same spin). But then the chance of two spins not matching is linearly proportional to the angle between the two detectors, since that is the chance the line between the two zones falls within that angle. This means that for small angles, the chance of opposing spins is higher than that predicted by quantum mechanics, proportional to the square of the angle.
This constraint, known as Bell's Inequality, allowed experimenters to disprove the idea that particles "knew" in advance how to behave under all circumstances. Which meant that the perfect correlation found for all angles of spin measurement did imply that somehow one measurement influenced the outcome of the other one, even in cases where for this to happen, the influence had to travel faster than the speed of light.
Yet, because the measurement outcomes were random, this principle only working for unobserved particles, this didn't provide a method of faster-than-light communications people could exploit. Thus, many physicists do not accept this as proof that nature communicates faster than light, but rather merely as an indication that quantum mechanics is "nonlocal", although such a concept is hard to understand.