The realist approach has a very strange implication, first worked out in the 1957 Princeton Ph.D. thesis of the late Hugh Everett. We can live with that. His latest book is To Explain the World: The Discovery of Modern Science. In an atom the wave function must satisfy conditions of continuity and finiteness close to and far from the nucleus, which similarly limit the possible energies of atomic states. Likewise, if we know the wave function that describes the spin of an electron we can calculate the probability that the electron would have a positive spin in the north direction if that were measured, or the probability that the electron would have a positive spin in the east direction if that were measured, but we cannot ask about the probability of the spins being found positive in both directions because there is no state in which an electron has a definite spin in two different directions. In quantum mechanics these probabilities do not exist until people choose what to measure, such as the spin in one or another direction. In effect the history of the world has split into two streams, uncorrelated with each other. This is strange enough, but the fission of history would not only occur when someone measures a spin. So we still have to ask, how do probabilities get into quantum mechanics? The first shock came as a challenge to the clear categories to which physicists by 1900 had become accustomed. There is not even the possibility of chaos, the extreme sensitivity to initial conditions that is possible in Newtonian mechanics. If nothing is done to interfere with these spins, this entangled state will persist even if the electrons fly apart to a great distance. These are quantities whose details of course we now don’t know. The development of quantum mechanics in the first decades of the twentieth century came as a shock to many physicists. It was emphasized in a 1935 paper by Einstein with his coworkers Boris Podolsky and Nathan Rosen, and arises in connection with the phenomenon of “entanglement.”13. ↩, For instance, Northern Lights by Philip Pullman (Scholastic, 1995), and the early “Mirror, Mirror” episode of Star Trek. (b) What is the approximate value of for a state having an energy of 1.0 eV? If this were not the case, to predict probabilities we would need to make some additional assumption about what happens when humans make measurements, and we would be back with the shortcomings of the instrumentalist approach. The realist approach to quantum mechanics had already run into a different sort of trouble long before Everett wrote about multiple histories. Problems from the simple plugged-ins to increasing order of difficulty are included to strengthen the students’ understanding of the subject. Now that we have the theoretical basis for explaining fields, the only major unsolved problems in theoretical quantum mechanics left are: Questions of the interpretation of quantum mechanics, which are of more interest to philosophers of science than many practicing physicists. Every effort has been taken to make the book explanatory, exhaustive, and user-friendly. This is something like the description of a sound wave in classical physics, except that for a sound wave a number for each position in space gives the pressure of the air at that point, while for a particle in quantum mechanics the wave function’s number for a given position reflects the probability that the particle is at that position. This used to be my view. The introduction of probability into the principles of physics was disturbing to past physicists, but the trouble with quantum mechanics is not that it involves probabilities. One difficulty in developing such a new theory is that we get no direction from experiment—all data so far agree with ordinary quantum mechanics. But in the end the opposition to Newtonianism faded away. The weirdness of quantum mechanics did not matter for most purposes. According to Eugene Wigner, a pioneer of quantum mechanics, “it was not possible to formulate the laws of quantum mechanics in a fully consistent way without reference to the consciousness.”11. Despite its great successes, arguments continue about its meaning and its future. The trouble is that in quantum mechanics the way that wave functions change with time is governed by an equation, the Schrödinger equation, that does not involve probabilities. Physicists learned how to use it to do increasingly precise calculations of the energy levels of atoms, and of the probabilities that particles will scatter in one direction or another when they collide. 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