Does the experimentally observed magnetic field of electrons and protons actually arise from the spinning rotation of elementary particles? Technically, the answer is no. The simplest reason why not is that neutrons, the other fundamental particle found within atomic nuclei, which have nearly the same mass as protons but are electrically uncharged, also possesses an internal magnetic field! If the magnetic field of the proton arose from the fact that as a charged object, its rotation could be described as a series of electrical current loops, each of which generates a magnetic field, then the rotation of an electrically uncharged object should not generate a magnetic field.17
Moreover, even if we did not know that neutrons existed, we still could not explain the magnetic field of electrons as arising from their rotation about an axis passing through their center. The magnitude of the measured magnetic field of the electron is such that it would require that these particles spin at a rate so fast that points on their surface would be moving faster than the speed of light!
What experimental question does the proposal of intrinsic angular momentum (that is, spin) answer? In 1922 Otto Stern and Walther Gerlach passed beams of atoms through special magnets, looking for interactions between their laboratory magnet and the internal magnetic field of the atom. They were trying to probe the magnetic field that would arise from the electron’s orbital motion about the nucleus. For atomic systems where they did not expect to see any orbital motion, they nevertheless observed an intrinsic magnetic field of elementary particles and, moreover, that this came in two values. It was if the electron had a built-in magnetic field with a north pole and a south pole that was allowed to point in only two directions, relative to the magnets used in Stern and Gerlach’s experiment. The electron either pointed in the same direction as the external magnet, so that its north pole faced the south pole of the lab magnet, or exactly oppositely aligned, so that the electron’s north pole faced the lab magnet’s north pole.
While Stern and Gerlach’s experiment clearly suggested that electrons possessed an intrinsic magnetic field, spin was actually first proposed to account for features in the absorption and emission of light by certain elements that indicated that there had to be some internal magnetism inside the atom. A variety of careful experiments confirmed that this magnetic field did not arise from the electrons orbiting around the positively charged nucleus, but was somehow coming from the electrons themselves.
So, why do we say that electrons, protons, and neutrons have spin that is associated with their internal magnetic fields? The origins of this phrase go back to, shall we say, a “youthful indiscretion.” Two Dutch graduate students in Leiden, Samuel Goudsmit and George Uhlenbeck, wrote a paper in 1925 suggesting that an internal rotation of the charged electron generated a magnetic field necessary to account for the atomic light-emission-spectra anomalies. They showed their paper to their physics adviser, Paul Ehrenfest, who pointed out various problems with the electron literally spinning about an internal axis. Hendrik Lorentz, Ehrenfest’s predecessor, soon calculated, as the students’ argument required the electron to rotate faster than light speed, that, thanks to E = mc2, this would make the electron heavier than the proton. (Neutrons, which would have indicated to them immediately that the observed magnetic field could not result from a spinning charged particle, had not yet been discovered.) Defeated, Goudsmit and Uhlenbeck intended to drop the whole matter. They were surprised when Ehrenfest told them that that he had already submitted their paper for publication. He consoled them, indicating that he had recognized their error but thought that there was merit in their suggestion, and argued that they were “young enough to be able to afford a stupidity.”
On one level it is unfortunate that Goudsmit and Uhlenbeck employed the term “spin” for the intrinsic angular momentum and magnetic field possessed by subatomic particles. The term is so evocative (and the fact that an electron, for example, can have an intrinsic angular momentum of either +(1/2)h/2π or -(1/2)h/2π, but no other values, makes it easy to think of in terms of “clockwise” or “counterclockwise” rotation) that it is difficult to remember that the electron is not actually spinning like a top. The 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 acts like a negative charge.
SECTION 2
CHALLENGERS OF THE UNKNOWN
CHAPTER FIVE
Wave Functions All the Way Down
In 1958, Jonathan Osterman (Ph.D.
in atomic physics, Princeton University) began his postdoctoral research position at the Gila Flats Research Facility in the Arizona desert. There he participated in experiments probing the nature of the “intrinsic field.” This is the collection of forces responsible for holding all matter together, aside from gravity. This would include electromagnetism, to account for the negatively charged electrons attracted to the positively charged protons in the atom’s nucleus. Electricity is much stronger than gravity, so much stronger, in fact, that the electrostatic attraction between the electrons and the protons in an atom’s nucleus is more than one hundred trillion trillion trillion times stronger than their gravitational attraction to one another. Consequently we can indeed neglect gravity’s contribution to the intrinsic field holding matter together.
In addition to electromagnetism, the intrinsic field must be comprised of additional forces that act on the protons and neutrons within each atom’s nucleus. While opposite electrical charges are attracted to each other, similar electrical charges are pushed away. The nucleus contains positively charged protons that are electrostatically repelled from one another and electrically uncharged neutrons that are immune to the electrostatic force. The closer two charges are, the greater the electrical force between them. Given that the protons within a nucleus are less than ten trillionths of a centimeter from each other, the electrical repulsion between protons is very powerful, and any force capable of overcoming this must be very strong—so strong, in fact, that physicists named it the strong force,19 and it is also therefore a component of the intrinsic field binding matter together. The strong force was originally believed to operate between protons and neutrons within the nucleus, holding them together. With theoretical and experimental investigations indicating that each of these nuclear particles is composed of quarks (which are in turn electrically charged), the strong force is now identified as the force that holds the quarks together and bleeds outs to neighboring particles within the nucleus. The experimental evidence for this force is indirect, as it turns out to be very difficult to slice protons and neutrons open and probe the quarks directly. But clearly there must be an attractive force operating within the nucleus that is able to overcome the electrostatic repulsion between protons at very close quarters.
In addition, physicists were unable to explain why certain elements’ nuclei decay and emit high-energy electrons despite the binding glue of the strong force. The neutron, discovered in 1932 by James Chadwick, was found to be unstable. A neutron out in free space has a half-life of roughly fifteen minutes. That is, in a quarter of an hour, a neutron outside of a nucleus has a 50 percent chance of decaying into a proton, an electron, and a neutrino (technically an antineutrino). As the neutron is uncharged, this has nothing to do with electromagnetism, and as it is outside of a nucleus, the strong force does not apply. This decay is also found to occur for neutrons inside certain nuclei.
There must be some other type of force that can turn a neutron into a proton. This additional force can’t be stronger than the strong force (or else nuclei would not hold together at all), but it appears to be not simply electromagnetism. This somewhat weaker force is termed, creatively enough, the weak force, and it is the third component of the intrinsic field. The strong force within the nucleus is roughly a hundred times stronger than electromagnetism (which is why nuclei with 90 to 100 protons, such as uranium and plutonium, are stable), while the weak force is one hundred billion times weaker than electromagnetism.
Physicists at the Gila Flats facility in the late 1950s, attempting to investigate the nature of the intrinsic field that governed the inner working of the atom, studied what happened when the intrinsic field was removed. This was essentially a variation on the traditional experimental technique to study subatomic matter—smash the atoms together. Actually these “atom smashers” study collisions not of atoms but of their building blocks, such as protons and electrons. Particle accelerators push protons20 around a ring at velocities very near the speed of light. When they collide with a fixed target or with another beam of protons traveling in the opposite direction, the large energy of the collision can enable the generation of other, exotic particles, providing a practical application of Einstein’s relation E = mc2. It is through such violent reactions that the structure of matter has been elucidated.
The physicists attempting to explore the intrinsic field took essentially a subtler, though no less destructive, approach. To isolate and remove the intrinsic field, they created another intrinsic field that was completely “out of phase” with the original field. Here they applied the same principle of interference, illustrated in Figure 4b, that certain sound-elimination devices employ—creating sound waves that are 180 degrees out of phase with the ambient sound such that the two wave fronts completely cancel each other, resulting in the removal of the original sound. Similarly, in order to cancel the intrinsic field of matter, one must identify the frequency and phase of the field and create an identical field with the same amplitude but exactly out of phase with the original. Thus, it takes an intrinsic field generator to perform an intrinsic field subtraction.
Without the electromagnetic, strong, or weak forces, there is nothing to hold atoms or nuclei together, and all matter would rapidly and violently be torn apart. Unfortunately for Dr. Osterman, just such a fate befell him when he was accidentally locked in the intrinsic field chamber during one such test run in 1959. Osterman, along with concrete block no. 15, which was the intended target of that day’s intrinsic field removal experiment, was completely dematerialized once his strong, weak, and electromagnetic forces were negated. Through a process that remains poorly understood to this day, Osterman was able to re-create himself, atom by atom, cell by cell, to become the superpowered being known as Dr. Manhattan.
Jon Osterman (also known as Dr. Manhattan) was created by Alan Moore and Dave Gibbons in the graphic novel Watchmen (originally published in 1986-87 as a twelve-issue miniseries). Figure 11 shows the scene from Watchmen when Osterman first manifests in his post-intrinsic field extraction form. One of the most striking aspects of the reborn Dr. Manhattan is that his skin is bright blue, while Osterman had been a fairly typical Caucasian male. (Another feature of Dr. Manhattan that is hard to miss is that when he first successfully reintegrated his corporeal existence over the lunch tables in the Gila Flats cafeteria, he was completely naked. This aspect of the story turns out to be accurate—we physicists are extremely secure in our sexuality!)
Figure 11: Physicist Jon Osterman when he first reassembled himself following the removal of his “intrinsic field” in the graphic novel Watchmen.
Purely from a practical standpoint, the molecular chemical bonds that link the trillions and trillions of atoms in a person represent a vast amount of stored electrostatic energy. In order to cancel out, the “intrinsic field” for a person would require the energy of a nuclear power plant at full capacity. Even assuming that we could turn off the strong, weak, and electromagnetic forces, there is no way that any poor scientist subjected to such a procedure would be able to reconstitute himself following this ordeal. But, in considering the array of abilities that the character Dr. Manhattan displays in the pages of Watchmen, there does appear to be some interesting physics at play.
In addition to his now bright blue appearance, Osterman gained the ability to alter his size at will, to teleport himself and others instantly from one location to another, and to be aware of the future, that is, to experience time—past, present, and future—simultaneously. That is to say, following the removal of his intrinsic field and subsequent rebirth as Dr. Manhattan, Jon Osterman appears to have gained independent control over his quantum mechanical wave function.
His quantum mechanical what? We have now reached the point in our amazing story where we consider what a wave function is, and why gaining control over it would be akin to possessing superpowers. Here’s the short answer: The quantum mechanical aspect of any object is reflected in its wave function. By performing simple mathematical
operations on the wave function, one can calculate the probability density (that is, the probability per unit volume) of finding the object, whether it is an electron, an atom, or a large blue, naked physicist, at any point in space and time. If you could indeed alter your wave function at will, you would gain the ability to instantly appear at some distant location, without ever technically traveling between your initial and final points; you could change your size (from either very large to tiny); you could diffract into multiple versions of yourself; and you would be cognizant of your future evolution. And you’d likely give off a blue glow, though as we’ll see later, that is more a consequence of leaking high-energy electrons—a side effect of rebuilding yourself at the atomic level.
While Jon Osterman is not a real person, nor is there a wave associated with an “intrinsic field,” nor any such thing as an “intrinsic field,” for that matter, the rest of the preceding discussion about the fundamental forces of nature (that is, electromagnetism and strong and weak nuclear forces) was correct. The experiments described in Section 1 demonstrated that there is a wave associated with the motion of electrons and atoms, and in fact with the motion of any and all matter. The concept of a wave function, introduced by Erwin Schrödinger in his “matter-wave equation,” is the key to understanding all atomic and molecular physics. It might as well be called the “intrinsic field” for the central role it plays in the understanding of chemical bonding, by which all matter is held together.
The Amazing Story of Quantum Mechanics Page 6
