Free The Amazing Story of Quantum Mechanics by James Kakalios

intrinsic angular momentum of the electron is properly accounted for in the Dirac equation, a fully relativistic version of quantum theory. Solving the Dirac equation, one finds that the electron is characterized by an extra “quantum number” that corresponds to an internal angular momentum of (1/2) h /2π and a magnetic field of magnitude exactly as observed. In a sense it is an intrinsic feature of the electron, just like its mass and its electric charge. 18 Goudsmit and Uhlenbeck managed to get the right answer for the wrong reasons. For this work they were awarded several elite prizes and medals. Publish in haste, celebrate at leisure.
    I have promised that this internal angular momentum, possessed by electrons, protons, neutrons, and all other elementary particles, is the key to understanding the periodic table of the elements, chemistry, and solid-state physics. In Chapter 12 I will describe the Pauli exclusion principle, which states that when two electrons (or two protons or two neutrons) are so close to each other that their de Broglie waves overlap, they can both be in the same quantum state only if one electron has a spin of +h /2π and the other has a spin of − h /2π. This has the consequence of “hiding,” except in certain cases, the magnetism associated with the intrinsic angular momentum.
    Electrons can spin either “clockwise” or “counterclockwise” (once an axis of rotation has been specified), which indicates that their intrinsic magnetic fields can point either “up” or “down.” All magnets found in nature have both north and south poles. If we make a magnet in the shape of a cylinder, like a piece of chalk, then, as shown in Figure 10, there will be a magnetic field emanating from the north pole that will bend around and be drawn into the cylinder’s south pole. The spatial variation of the magnetic field is the same as for an electric field created by two electrical charges, positive and negative, at either end of a cylinder (see Figure 10b). We call such an arrangement of electric charges a “dipole,” and as the magnetic field distribution described earlier has the same spatial variation, we refer to it as a magnetic dipole. Inside an atom, the preferred configuration of the protons and neutrons in the nucleus, and electrons “orbiting” the nucleus, is such that they orient themselves so any pair of particles will have their magnetic fields cancel; thus, if the north pole of one magnet points “up,” then the north pole of the second magnet will point “down.”
    The electric dipole field differs from a single positive or negative charge, which is called a “monopole,” as shown in Figure 10a. We have never observed in the universe a single free magnetic pole, that is, just a north pole or a south pole, despite extensive investigations and theoretical suggestions that they should exist. They always come in pairs, forming a magnetic dipole. It must be said, though, that an unsuccessful search does not mean that they do not exist—simply that we haven’t found them yet.
    We need to figure out magnetism if we want to understand how hard drives work. Furthermore, without appreciating the role that spin plays, chemistry would be a mystery (unlike when most of us studied it in high school, when it was a hopeless mystery). Similarly, absent our understanding how the spin of electrons governs their interactions in metals, insulators, and semiconductors, there would be no transistor, and hence no computers, cell phones, MP3 players, or even television remote controls, and humanity would be reduced to a brutal state that would test the imagination of the writers of the most dystopian science fiction stories.

    Figure 10: Sketch of the electric field from an isolated positive and negative charge (a) and from the two charges forming a dipole pair (b). The same field lines are found for a magnetic dipole, where the north pole plays the role of the positive charge, and the south pole