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In this talk, I want to ask how far can we go in our search for understanding and knowledge. Will we ever find a complete form of the laws of nature? By a complete form, I mean a set of rules that in principle at least enable us to predict the future to an arbitrary accuracy, knowing the state of the universe at one time. A qualitative understanding of the laws has been the aim of philosophers and scientists, from Aristotle onwards. But it was Newton's Principia Mathematica in 1687, containing his theory of universal gravitation that made the laws quantitative and precise. This led to the idea of scientific determinism, which seems first to have been expressed by Laplace. If at one time, one knew the positions and velocities of all the particles in the universe, the laws of science should enable us to calculate their positions and velocities at any other time, past or future. The laws may or may not have been ordained by God, but scientific determinism asserts that he does not intervene to break them.
At first, it seemed that these hopes for a complete determinism would be dashed by the discovery early in the 20th century; that events like the decay of radio active atoms seemed to take place at random. It was as if God was playing dice, in Einstein's phrase. But science snatched victory from the jaws of defeat by moving the goal posts and redefining what is meant by a complete knowledge of the universe. It was a stroke of brilliance whose philosophical implications have still not been fully appreciated. Much of the credit belongs to Paul Dirac, my predecessor but one in the Lucasian chair, though it wasn't motorized in his time. Dirac showed how the work of Erwin Schrodinger and Werner Heisenberg could be combined in new picture of reality, called quantum theory. In quantum theory, a particle is not characterized by two quantities, its position and its velocity, as in classical Newtonian theory. Instead it is described by a single quantity, the wave function. The size of the wave function at a point, gives the probability that the particle will be found at that point, and the rate at which the wave function changes from point to point, gives the probability of different velocities. One can have a wave function that is sharply peaked at a point. This corresponds to a state in which there is little uncertainty in the position of the particle. However, the wave function varies rapidly, so there is a lot of uncertainty in the velocity. Similarly, a long chain of waves has a large uncertainty in position, but a small uncertainty in velocity. One can have a well defined position, or a well defined velocity, but not both.
At first, it seemed that these hopes for a complete determinism would be dashed by the discovery early in the 20th century; that events like the decay of radio active atoms seemed to take place at random. It was as if God was playing dice, in Einstein's phrase. But science snatched victory from the jaws of defeat by moving the goal posts and redefining what is meant by a complete knowledge of the universe. It was a stroke of brilliance whose philosophical implications have still not been fully appreciated. Much of the credit belongs to Paul Dirac, my predecessor but one in the Lucasian chair, though it wasn't motorized in his time. Dirac showed how the work of Erwin Schrodinger and Werner Heisenberg could be combined in new picture of reality, called quantum theory. In quantum theory, a particle is not characterized by two quantities, its position and its velocity, as in classical Newtonian theory. Instead it is described by a single quantity, the wave function. The size of the wave function at a point, gives the probability that the particle will be found at that point, and the rate at which the wave function changes from point to point, gives the probability of different velocities. One can have a wave function that is sharply peaked at a point. This corresponds to a state in which there is little uncertainty in the position of the particle. However, the wave function varies rapidly, so there is a lot of uncertainty in the velocity. Similarly, a long chain of waves has a large uncertainty in position, but a small uncertainty in velocity. One can have a well defined position, or a well defined velocity, but not both.