A Briefer History of Time by Stephen Hawking Page B

universe are not of much interest to us ordinary mortals. It seems better to employ the principle of economy known as Occam’s razor and cut out all the features of the theory that cannot be observed. This approach led Heisenberg, Erwin Schrödinger, and Paul Dirac in the 1920s to reformulate Newton’s mechanics into a new theory called quantum mechanics, based on the uncertainty principle. In this theory, particles no longer had separate, well-defined positions and velocities. Instead, they had a quantum state, which was a combination of position and velocity defined only within the limits of the uncertainty principle.
    One of the revolutionary properties of quantum mechanics is that it does not predict a single definite result for an observation. Instead, it predicts a number of different possible outcomes and tells us how likely each of these is. That is to say, if you made the same measurement on a large number of similar systems, each of which started off in the same way, you would find that the result of the measurement would be A in a certain number of cases, B in a different number, and so on. You could predict the approximate number of times that the result would be A or B, but you could not predict the specific result of an individual measurement.
    For instance, imagine you toss a dart toward a dartboard. According to classical theories—that is, the old, nonquantum theories—the dart will either hit the bull’s-eye or it will miss it. And if you know the velocity of the dart when you toss it, the pull of gravity, and other such factors, you’ll be able to calculate whether it will hit or miss. But quantum theory tells us this is wrong, that you cannot say it for certain. Instead, according to quantum theory there is a certain probability that the dart will hit the bull’s-eye, and also a nonzero probability that it will land in any other given area of the board. Given an object as large as a dart, if the classical theory—in this case Newton’s laws—says the dart will hit the bull’s-eye, then you can be safe in assuming it will. At least, the chances that it won’t (according to quantum theory) are so small that if you went on tossing the dart in exactly the same manner until the end of the universe, it is probable that you would still never observe the dart missing its target. But on the atomic scale, matters are different. A dart made of a single atom might have a 90 percent probability of hitting the bull’s-eye, with a 5 percent chance of hitting elsewhere on the board, and another 5 percent chance of missing it completely. You cannot say in advance which of these it will be. All you can say is that if you repeat the experiment many times, you can expect that, on average, ninety times out of each hundred times you repeat the experiment, the dart will hit the bull’s-eye.
    Quantum mechanics therefore introduces an unavoidable element of unpredictability or randomness into science. Einstein objected to this very strongly, despite the important role he had played in the development of these ideas. In fact, he was awarded the Nobel Prize for his contribution to quantum theory. Nevertheless, he never accepted that the universe was governed by chance; his feelings were summed up in his famous statement "God does not play dice."

    Smeared Quantum Position
    According to quantum theory, one cannot pinpoint an object’s position and velocity with infinite precision, nor can one predict exactly the course of future events.
    The test of a scientific theory, as we have said, is its ability to predict the results of an experiment. Quantum theory limits our abilities. Does this mean quantum theory limits science? If science is to progress, the way we carry it on must be dictated by nature. In this case, nature requires that we redefine what we mean by prediction: We may not be able to predict the outcome of an experiment exactly, but we can repeat the experiment many times and confirm that the various possible