The Universe Within by Neil Turok

the opposite results, with one seeing heads and the other tails, but in four you will agree. What about if the boxes were programmed heads/heads/heads and tails/tails/tails? Well, then you would always disagree. Since every other program looks like one of these two cases, we can safely conclude that however the boxes are programmed, if you open the doors randomly there is always at least a five-ninths chance of your disagreeing on the result. But that isn’t what you found in the experiment: you disagreed half the time.
    As you may have already guessed, quantum theory predicts exactly what you found. You agree half the time and disagree half the time. The actual experiment is to take two widely separated Einstein–Podolsky–Rosen particles in a spin zero state and measure their spins along one of three axes, separated by 120 degrees. The axis you choose is just like the door you pick in the pyramidal box. Quantum theory predicts that when you pick the same measurement axis for the two particles, their spins always disagree. Whereas if you pick different axes, they agree three-quarters of the time and disagree one-­quarter of the time. And if you pick axes randomly, you agree half the time and disagree half the time. As we have just argued with the boxes, such a result is impossible in a local, classical theory. 50
    Before drawing this conclusion, you might worry that the particles might somehow communicate with each other, for example by sending a signal at the speed of light. So that, for example, if you chose different measurement axes, the particles would correlate their spins so that they agreed three-quarters of the time and disagreed one-quarter of the time, just as predicted by quantum mechanics. Experimentally, you can eliminate this possibility by ensuring that at the moment you choose the measurement axis, the particles are so far apart that no signal could have travelled between them, even at the speed of light, in time to influence the result.
    In 1982, the French physicists Alain Aspect, Philippe Grangier, and Gérard Roger conducted experiments in which the setting for the measurement axis of Einstein–Podolsky–Rosen particles was chosen while the particles were in flight. This was done in such a way as to exclude any possible communication between the measured particles regarding this choice. Their results confirmed quantum theory’s prediction, showing that the world works in ways we cannot possibly explain using classical notions. Some physicists were moved to call this physics’ greatest-ever discovery.
    Although the difference between five-ninths and one-half may sound like small change, it is a little like doing a very long sum and finding that you have proven that 1,000 equals 1,001 (I am sure this has happened to all of us many times, while doing our taxes!). Imagine you checked and checked again, and could not find any mistake. And then everyone checked, and the world’s best computers checked, and everyone agreed with the result. Well, then by subtracting 1,000, you would have proven that 0 equals 1. And with that, you can prove any equation to be right and any equation to be wrong. So all of mathematics would disappear in a puff of smoke. Bell’s argument, and its experimental verification, caused all possible classical, local descriptions of the world similarly to disappear.
    These results were a wake-up call, emphasizing that the quantum world is qualitatively different from any classical world. It caused people to think carefully about how we might utilize these differences in the future. In Chapter Five, I will describe how the quantum world allows us to do things that would be impossible in a classical world. It is opening up a whole new world of opportunity ahead of us — of quantum computers, communication, and, perhaps, perception — whose capabilities will dwarf what we have now. As those new technologies come on stream, they may enable a more