Hiding in the Mirror: The Quest for Alternate Realities, From Plato to String Theory (By Way of Alicein Wonderland, Einstein, and the Twilight Zone)

by Lawrence M. Krauss

  C H A P T E R 9

  THERE AND BACK AGAIN

  The theoretical possibilities in a given case are relatively few and relatively simple. . . . Considering these tells us what is possible but does not tell us what reality is.

  —Albert Einstein

  As exciting as the possibility of hidden extra dimensions may have seemed in 1926, within a decade the direct experimental evidence for new phenomena in three dimensions had succeeded in redirecting the imagination of the physics community toward somewhat less esoteric pursuits, or at least more experimentally accessible ones. The half-century following 1930 was one of the most productive periods in the history of physics in terms of changing our picture of the fundamental nature of matter and energy in the universe. This may seem a surprising claim, given the fact that the two greatest single developments in the field in the twentieth century—the development of general relativity, and the discovery of the laws of quantum mechanics—had both been essentially completed by this time. Nevertheless if the theoretical advances made during the first three decades of the century revealed a hidden nature to space and time, the experimental work conducted over the next fifty years revealed a hidden universe of exotic particles and forces. This is not to say that stunning theoretical strides were not made. They were, and I will describe them. But in contrast with general relativity and even quantum mechanics, these developments derived directly from unexpected experimental evidence based on new technologies that opened important new windows on the universe. And each time a new window on the universe has been opened, surprises have inevitably followed.

  In the last years of the 1920s the capstone achievement in the theoretical development of quantum mechanics had been the work of Paul Dirac, who discovered an equation describing the quantum mechanical behavior of an electron in a way that was, for the first time, completely consistent with the principles of special relativity.

  One of the remarkable predictions of Dirac’s equation was that there were always two different independent solutions that satisfied the equation, which described the behavior of electrons of a certain energy. One of these described a negatively charged particle, the electron, and one described a particle with equal mass but opposite—meaning positive—charge. When this prediction first appeared, it caused some embarrassment, because while there was one known particle in nature with equal and opposite charge to the electron—namely, the proton—it had a mass almost two thousand times larger than that of the electron. At first Dirac thought that the positive particle that showed up in his equation might somehow represent the proton. But this interpretation clearly could not hold up under detailed scrutiny. At one point, in desperation, he appealed to another sort of hidden universe: He proposed that perhaps there were other, as of yet unobserved, places in the universe where positives and negatives were reversed.

  Nevertheless, this embarrassing situation turned triumphant when, in the summer of 1932, the second great discovery of the post-1930 era was made. The experimental physicist Carl Anderson, while examining the tracks left by particles in cosmic rays, the high-energy particles that bombard the earth from space every moment of every day, discovered the tracks of a particle that appeared to have a mass identical to that of the electron, but a positive charge.

  The technique he used was quite straightforward. As I have described, Oersted discovered in the nineteenth century that a charged particle will experience a force if it is moving through a magnetic field. The effect of this force will be to cause its trajectory to bend. If it is positively charged, it will bend one way, and if negatively charged, the other. Anderson used a device called a cloud chamber to observe the tracks of incoming cosmic rays. This device causes charged particles to leave a cloudlike track, much like that trailed by airplanes in the sky. By placing the chamber in a large magnetic field, Anderson could determine the charge of the incoming particles by observing the direction in which their trajectories curved. Particles such as protons will indeed curve in the opposite direction to electrons, but, because the former are two thousand times heavier, a proton tends to have far greater inertia, which means its path will tend to bend far less in a magnetic field of a fixed strength than that of a high-energy electron. In one of the photographs of his chamber, taken every fifteen seconds over the course of many days, Anderson saw a track whose curvature was identical to that of the high-energy electrons he was seeing, but the direction of its curvature was opposite. The positron, as it is now known, had been discovered!

  Dirac’s theory was vindicated, and Dirac stated, regarding his own timidity in believing in the existence of positrons, “My equation was smarter than I was!” . One of the related striking predictions of Dirac’s theory was that relativity implied that all charged elementary particles should have “antiparticles” (as they have become known): particles with identical mass and opposite electric charge. Moreover, electrons and their antiparticles—indeed all particles and their antiparticles—should be able to annihilate each other, producing pure electromagnetic radiation as an end product. Anderson was able to show that the reverse process also occurs: Very energetic electromagnetic radiation, called a gamma ray, could convert into electron–positron pairs as it traversed matter. The annihilation of these particles and antiparticles back into gamma rays was also observed. The fact that particles and antiparticles could be created in pairs from pure energy (i.e., radiation) completely changed our thinking about matter. This was the most obvious vindication of Einstein’s famous relation E = mc 2. Even more importantly, perhaps, it has forever changed our thinking about empty space. The reason stems from that other crown jewel of quantum mechanics, the Heisenberg uncertainty principle. As I have mentioned, the uncertainty principle states that there are certain combinations of physically observable quantities that cannot be measured at the same time with a combined accuracy better than some amount fixed by the laws of nature, not by an experimental apparatus. The most famous such combination involves the position of a particle and its momentum, both of which cannot be measured at exactly the same time. The more accurately you can determine a particle’s position, for example, the less accurately you can measure in precisely which direction it is moving. A less-known combination involves energy and time. Here, the uncertainty principle tells us that the longer we measure something, the more accurately we can determine its total energy. Since all measurements take merely a finite time, however, there is always a residual uncertainty in the value of the energy that can be measured in any system. Now, as Faraday and Maxwell told us, if an electron is moving through space it can act as the source of electromagnetic radiation. But what if some of this electromagnetic radiation were to spontaneously convert into an electron–positron pair? Classically we would say that this is impossible, because the electron and positron together weigh twice as much as the original electron, so unless the original electron is moving so fast that its total energy is more that three times its rest mass energy, it is impossible to end up with three particles after starting with one. But we don’t live in a classical universe. Quantum mechanics is, as I like to say, just like the White House: As long as no one can measure what is going on, anything goes! In this case, the uncertainty principle tells us that during some time interval that is short enough so that the energy uncertainty is large enough—larger, say, than twice the rest mass of the electron—we cannot say how many particles exist within a region we may be measuring.

  There is a finite probability that there might be, for some short period, two extra particles present. For example, an electron–positron pair could spontaneously appear for a short time, and then these particles could annihilate, leaving just the original system. As long as the particle–antiparticle pair exists for a time short enough so that the uncertainty principle indicates that we cannot measure the violation of energy conservation implied by their brief presence, the laws of quantum mechanics and relativity together suggest that such a configuration is allowed. This represents another complete revision in our funda
mental understanding of the nature of space. According to this new picture, empty space is not empty at all, but involves a boiling, bubbling brew of these particle–antiparticle pairs popping in and out of nothingness. Here is yet another hidden universe lying just beyond our perception, and one that ultimately played a key role in motivating physicists to consider the possibility of yet more radical revisions in our picture of space and time. Before jumping on the virtual particle bandwagon, one might wonder whether suggesting particle–antiparticle pairs popping in and out of the vacuum is really any different than fantasizing about psychics popping in and out of extra dimensions in order to untie knotted ropes and recover objects inside of boxes. In cooking, the proof is in the tasting. In physics, it is in the testing.

  How can we test for the existence of unobservable particles? We do it just as we might work to uncover evidence of a crime we did not witness directly: by looking for indirect evidence. And so it turns out that while one cannot measure virtual particles directly, one can nevertheless measure their effect on processes we can both calculate and measure. Niels Bohr’s first great success in his emerging quantum mechanics was to correctly predict the spectrum of light emitted by hydrogen gas when it is heated. During this process, an electron can jump between discrete allowed orbits about a proton by absorbing or radiating electromagnetic waves that we can observe as visible light. The fixed nature of the frequencies/colors emitted by hydrogen was a mystery until Bohr proposed that electrons were somehow confined to such orbits. It was the great success of Schrödinger and Heisenberg that they presented a self-consistent mechanics that allowed a precise calculation of these energy levels in hydrogen that agreed well with the measured frequencies of radiation emitted by hydrogen atoms. However, as measurements became more and more precise, a tiny discrepancy between the predicted energy levels and the levels inferred from observation emerged. In other areas of science, such a small discrepancy might have been ignored. But such was the precision afforded by the new merging of quantum mechanics, relativity, and electromagnetism—a theory that became known as “quantum electrodynamics”—that this experimental anomaly presented a major challenge for theoretical physicists. Shortly after World War II the physicists who had otherwise been occupied with developing the atomic bomb returned to their fundamental investigations of nature. At one of the most famous meetings in twentiethcentury physics, held on Shelter Island off Long Island in New York, a group of young turks demonstrated that a proper accounting of the effects of virtual particles could yield the critical missing component that could resolve the aforementioned shift in energy levels between theory and experiment. This shift was by then known as the Lamb shift, after the experimentalist Willis Lamb, who first discovered it.

  At the time the different mathematical methods used to calculate these effects were diverse, complex, and almost mysterious, representing the similarly diverse approaches to physics of the scientists involved, from the formal and prodigiously brilliant Julian Schwinger, to the informal and sometimes irreverent genius Richard Feynman, and independently by the quiet Sin-Itiro Tomonaga, all of whom would later share the Nobel Prize for their efforts. Nevertheless, with hindsight and after a “translation” paper published by the equally brilliant Freeman Dyson, it became clear that the different approaches all reflected the same underlying physical reality. The central point of all these approaches was that it is incorrect to calculate the orbit of an electron around a proton as if these were the only two particles present. For if virtual particle–antiparticle pairs can spontaneously appear for short periods out of nothing, then the electric field experienced by the orbiting electrons must be affected by these virtual particles. Working independently, Feynman and Schwinger used this technique to calculate the values of the energy shifts. Their method is now known as QED—an acronym for quantum electrodynamics—and its agreement with the empirically observed values is better than one part in a million, a result that remains the best-measured prediction in all of science. With the recognition that empty space was anything but empty, a manifest need arose to try to explicitly understand what processes take place on the smallest scales that can be imagined, and in turn understand how these processes might affect the nature of physical reality on more familiar scales. As we shall see, this program would set into motion a simmering set of internal conflicts in physics that would ultimately drive theorists to new extremes of speculation.

  Alert readers will note that I referred to the discovery of antiparticles as the “second great discovery” in the post-1930 era. The first occurred about four months earlier, in February 1932, although its origins date back to the dawn of the modern era. In 1896 the French physicist Henri Becquerel found that certain substances, such as uranium, spontaneously emit a strange new sort of radiation. Mystified, he called this radiation U-rays, although his contemporaries called them Becquerel rays. Ultimately it was shown that there were actually three different kinds of radiation given off by radioactive substances, which Lord Rutherford later creatively labeled alpha, beta, and gamma rays.

  Over the next decade or so Rutherford and his student James Chadwick, as well as the Polish-French physicist Marie Curie, demonstrated that gamma rays were energetic forms of electromagnetic radiation, while beta rays were energetic electrons, and alpha rays consisted of the nucleus of helium, the second lightest element, with a weight about four times that of hydrogen.

  At around this time the nature of recently discovered atomic nuclei such as helium was puzzling. Since atoms were neutral objects, the charge of an atomic nucleus is precisely equal and opposite to the total charge of the electrons orbiting it. But for some reason, nuclei weighed far more than the amount that could be accounted for if they simply contained protons, the heavy, positively charged objects Rutherford identified in 1919. In 1920 Rutherford imagined two different possibilities to account for this discrepancy: First, some of the protons in a nucleus were paired with electrons inside the nucleus, canceling their charge. Alternatively, perhaps there were new neutral particles in nature with a mass almost identical to that of the proton. Neither possibility had any real evidence in support of it, but the emerging laws of quantum mechanics began to argue strongly against the former.

  By 1930, after Heisenberg and Schrödinger had completed their seminal work, it was recognized that to confine an electron within a region the size of an atomic nucleus would require an energy far greater than that which was available from the electric attraction of protons and electrons. Thus there seemed no way that one could resolve the apparent paradox of nuclear masses merely by adding proton-electron pairings to nuclei. This left the possibility of a new neutral particle as the most likely option, and motivated by this the German physicists Walther Bothe and his student Herbert Becker began to utilize radioactivity itself to explore the atomic nucleus. In 1930 they reported that when they bombarded beryllium atoms with alpha particles emitted by a radioactive source made from the element polonium (named after her native Poland by Marie Curie), a strange new type of neutral radiation was emitted that could penetrate a brass plate several centimeters thick without slowing down. This was over twenty times farther than protons with comparable energy can penetrate. Moreover, this radiation did not efficiently knock electrons out of atoms in targets, ionizing them, as charged proton beams would do. The assumption was made that this penetrating neutral radiation was a type of gamma ray, that is, high-energy electromagnetic radiation.

  A key clue to the true nature of this radiation was obtained via experiments performed by the daughter of Marie Curie, Irène Joliot-Curie, and her husband, Frédíric Joliot-Curie, although this pair actually misinterpreted the data. They placed a paraffin wax target in the path of this radiation and discovered that the radiation knocked protons out of the paraffin with a very high energy. Since a similar process was known to occur in which high-energy electromagnetic radiation impinging upon atoms could knock out electrons, Joliot-Curie and her husband interpreted this new effect as an analogous phenomeno
n caused by even higher energy gamma rays.

  Because the proton is, however, almost two thousand times as heavy as the electron, to knock it out of an atom would require far more energy than appeared to be available in the original beryllium emission process. Rutherford and Chadwick recognized this fact, and in February 1932

  Chadwick announced the result of a series of experiments he had performed analogous to those that had been performed by Joliot-Curie and her husband. By using different targets he demonstrated convincingly that the mystery particle could not be a massless photon, but instead had to have a mass almost identical to that of the proton. Chadwick had discovered the neutron, one of the major components of all matter, and in so doing he solved the mystery of what makes up the missing mass in atomic nuclei. For this achievement he was awarded the Nobel Prize in 1935. (In a happy coincidence, Joliot-Curie and her husband, who did not share the prize with Chadwick because of their misinterpretation of their data, won the chemistry prize that year for their discovery of artificial radioactivity.) Chadwick’s discovery revealed a whole new world, previously hidden, inside of every atomic nucleus. It is amazing, when you think about it, that less than seventy-five years ago the most abundant component in all matter, including the very atoms in our bodies, was unknown. Moreover, what is equally remarkable in retrospect is the fact that the consideration that led Chadwick to discover the neutron is really a principle that is taught in high school physics. It can be restated in a perhaps more intuitive way as follows: If I want to knock the headlight out of an oncoming truck, I could choose to throw a piece of popcorn at it, but I would have to throw it much faster than I am likely to be able to in order to cause any damage. However, if I use a rock, I don’t have to throw it very fast to achieve my goal. Chadwick used precisely this line of reasoning to work out the details of his experiment, and to demonstrate that knocking protons out of nuclei required a massive, rather than a massless, projectile. Perhaps more than anything else, however, Chadwick’s discovery of the neutron opened a Pandora’s box of new mysteries in elementary particle physics. Gone was the simple world of protons and electrons, gravity and electromagnetism. Suddenly the nuclei of atoms became complex amalgamations of protons and neutrons, held together by some unknown new force.