If you insist on clinging to what's safe and familiar you'll come unstuck with quantum theory. Normal rules just don't apply
The first expression of the famous uncertainty principle came in 1927, when the German physicist Werner Heisenberg proved that you can measure the speed of an electron or its position, but not both at once. More precisely, Heisenberg proved that the better you measure the electron's position, the less accurately you can know its velocity, and vice versa. Measurement is a compromise, and you, the experimenter, must choose what to measure and accept the consequences.
Like so many things in quantum theory, the uncertainty principle arises from the element of probability. Heisenberg thought about trying to measure an electron's position and speed by simply bouncing a photon off it. But when a photon and an electron collide, there is no single predictable outcome but instead a range of possible outcomes. Deducing the electron's properties from the behaviour of the photon that bounced off it must also yield a range of possibilities, rather than one specific conclusion. Hence the uncertainty principle.
In a slightly different guise, this notion has its roots in an old experiment performed by Thomas Young in 1801 to prove that light is a wave, not a particle. Young cut two parallel slits close together in an opaque screen, shone a light on them, and observed stripes of light and dark, an interference pattern, where the light struck a wall beyond the slits. He argued that if light consisted of particles travelling in straight lines, they would go through the slits and create two bright patches. But because light is a wave, the crests and troughs emerging from the slits can either reinforce each other or cancel each other out, creating brightness in some places and darkness in others.
Now switch to photons. They are particles, so they ought to create two bright spots. Except that unlike classical bullets, they interact like waves. They are particles with wavelike properties. Or if you like, they are waves that behave like a stream of particles. Just as the partially silvered mirror in an interferometer "splits" the photons, so Young's slits divide each photon into two pieces, which interfere with each other beyond the screen to create the striped pattern on the wall. These "pieces" of photons aren't detectable: if you place detectors right up against the slits, to see which way the photons are going, you'll destroy the interference pattern. If you demand to see the photons acting like particles, going through one slit or the other, you lose the wave behaviour that creates the bright and dark stripes. You can see photons acting like waves, or you can see them acting like particles, but not both at once.
This general idea is one of the defining qualities of the quantum world. Remember how in the EPR paradox one photon seems to have an instantaneous effect on its distant twin because of probability. Both entangled photons carry with them the potential for many possible outcomes, which aren't settled until they are actually measured. And when you choose to measure one thing, you have to forgot knowledge of something else.
Famously, Einstein couldn't accept the idea that God "plays dice with the Universe ..." It wasn't simply the notion of probability that upset him, but all the unsettling consequences it led to. Quite a few physicists have shared Einstein's conviction that something about quantum theory can't be quite right, and over the years they have come up with some ingenious attempts to put matters straight. In 1952, David Bohm, an American physicist who had worked with Einstein, came up with a version of quantum mechanics that seemed to resolve Einstein's disquiet.
In Bohm's theory, quantum particles have "hidden variables" -- intrinsic properties that are specific and definite for each particle. When you make a measurement these hidden variables interact with the measuring device to produce a result. A collection of quantum particles, no matter how carefully prepared, always has a range of hidden variables within it, just as in a conventional gas some atoms move faster than average and some slower.
Measurements, in this version of quantum theory, yield a range of outcomes because the particles being measured have a range of intrinsic properties. The uncertainty principle survives. For practical purposes, Bohm's theory is exactly equivalent to conventional quantum theory. It is, in fact, a mathematical recasting and reinterpretation of the standard equations, and so produces the same results.
But therein lies the sting: quantum theory has some distinctly non-classical characteristics, so even though Bohm tried to restore classical definition to quantum particles, his theory can't be truly classical. And it isn't.
In the two-slit experiment, for example, Bohm's theory says that a photon definitely goes through one slit or the other. So how does it create an interference pattern on the other side? The answer is something called the pilot wave. Bohm says there are both waves and particles, and they are quite distinct. The pilot wave goes through the two slits just as a classical wave does, and creates an interference pattern. The particle then follows this pilot wave - hence the name. Photons going through the slits in a stream all have slightly different energies and directions, and they follow the pilot wave like marbles rolled across corrugated cardboard, following different paths depending on how they started out. The photons arrive at the screen, having been guided by the pilot wave, and create the expected interference pattern.
Tidy enough. But the big difficulty is explaining just what this pilot wave is, and how it guides the photons. It can't be a classical wave, exerting a force to steer the photons, because then the photons' energies would change -- which they don't.
The curious nature of the pilot wave becomes more apparent in an EPR experiment. There, the pilot wave literally conveys information from one entangled particle to the other, so that measurements on the pair always come out right. But it has to do so instantaneously. The pilot wave is a physical embodiment of the old notion of "action-at-a-distance", which is precisely what Einstein was trying to avoid.
Five years after Bohm produced his hidden-variable version of quantum theory, a Princeton physicist, Hugh Everett, had a quite different inspiration. In an EPR experiment, for example, you might know that one photon in a pair is vertically polarised, so that the other must be horizontal. But it could easily have been the other way round. The puzzle is why one possibility happens and the other does not.
Everett said that both possibilities do happen -- but in different universes. He proposed that whenever a quantum measurement is made, different universes "split off" -- one for each of the possible outcomes. We see one particular result because we are in the universe in which that one happens. In the other universes, our counterparts are seeing one of the other results, and so on through as many universes as you like.
Everett's many universes proposal leaves the technical content of quantum theory quite unchanged. It is, if you like, a metaphysical gloss on the same old theory. Even the question of whether these other universes are real is a moot point. Getting a glimpse of a universe other than your own amounts to a violation of the uncertainty principle. It would mean, for example, measuring an electron's speed in one universe, measuring its position in another, and then combining results from both universes to beat Heisenberg's restriction.
Therefore, once a measurement has generated these separate universes, they have to remain strictly and absolutely separate. Are they real or not? You decide. Argument over "interpretations" of quantum theory has been long and, some might say, ultimately pointless, since by design they all produce the same practical results. It's really a question of which mental picture of the quantum world you find most pleasing.
It has been possible, however, to prove that quantum theory is fundamentally different from classical physics. In 1964, John Bell came up with the simple and elegant theorem that now bears his name. It concerns an EPR experiment where pairs of particles are entangled and sent off in different directions, as usual. Bell thought about what would happen if the two experimenters were not obliged always to measure the polarisation of a photon in one prescribed direction, for example, but could randomly choose between polarisation measurements at different angles.
Classically, two EPR particles can't influence each other once they have been sent their separate ways. According to quantum theory, the spooky connection is retained, but it's hard to say what that connection is, or to find any way of quantifying it. Bell's theorem does just that: it says that in a series of measurements on successive pairs of EPR particles, statistical differences between the quantum and classical pictures emerge. Quantum particles are more highly correlated than classical ones, and you can tell this by performing simple mathematical tests on the results obtained from a series of measurements on EPR pairs.
Bell formulated a mathematical quantity that, according to quantum theory, would be larger than any classical picture would allow. It was not for another 20 years that Bell's theorem was successfully tested. The requisite experiments were hard to do with sufficient reliability and precision. But in 1982 Alain Aspect succeeded at the University of Paris.
Quantum theory gave the right answer, which if nothing else demolished any lingering hope that classical physics might one day be restored to its former glory. More subtly, Aspect's test of Bell's theorem showed that any attempt to recast quantum mechanics as a pseudo-classical theory was bound to be inadequate. Quantum theory is and always will be truly different.
The nature of the difference is, fundamentally, a concept called "non-locality." Classical physics embodies a strictly local law of cause and effect. What happens at point A can have an immediate effect only at point A, and if the effect makes its presence felt at point B, some physical influence has to travel from A to B, taking some finite time to do so.
Quantum theory is non-local. In an EPR experiment, a measurement at point A has an elusive, instantaneous and - through Bell's theorem - quantifiable influence at point B. Whether anything physical travels from A to B is debatable. In Bohm's theory, the pilot wave carries that instantaneous influence. In Everett's idea, non-locality is dispersed throughout the many universes. However you look at it, non-locality just happens in the quantum world. There's no getting away from it.