In Search of a Theory of Everything

by Demetris Nicolaides

  Other conservation laws are also obeyed, such as that of the electric charge. In this case, the electric charge of the energy from which the pair was created was zero—pure energy always has zero electric charge: the electric charge remains zero when the pair is in existence—for an electron has an electric charge of –1 (in some units) and the positron +1—and continues to be zero when the pair is annihilated as it once again becomes pure energy.

  Let us take the conservation of the electric charge one step further. Since the net electric charge is always conserved, neither type of electric charge has an absolute dominance, as Anaximander would require. Nonetheless, one type of charge has a relative dominance over the other. The negative electric charge dominates temporarily at the vicinity of the electron, whereas the positive electric charge dominates temporarily at the vicinity of the positron. It is this temporary dominance that creates the electromagnetic force of interaction and overall competition between opposite charges. It is the cause of the opposites’ becoming and decaying, their attractions, repulsions, motions, conversions to and from energy, and in general, such temporary dominance is a contributing cause of the phenomena of nature.

  Competing opposites are necessary for Anaximander and modern physics, as they will also be for Heraclitus, if nature is to remain diverse, eventful, and beautiful. There is an electron here but a positron there. They, and other particles and antiparticles from similar processes, convert to light and to heat. The particles form atoms, molecules, and composite objects such as the sea, the trees, the breeze, the earth, the sky, and forms of life. It is summer here but winter there. It is warm now but will be cool later; it is night now but was day earlier. The unity of the world is preserved in harmony by the very competition between opposites. Temporary dominance and the resulting struggle of opposites produce the rich plethora of diverse phenomena while simultaneously, cosmically (universally) absolute dominance is not, should not be allowed, for conservation laws must be obeyed. Not only does Anaximander’s worldview see the nature of nature as being cosmically just, but because of conservation laws so should modern physics. Curiously, however, it appears that nature is not cosmically just, for one of the most puzzling questions of science today is why there is more matter than antimatter in the observable universe, a question to be pondered in a section later after we first elaborate on the notions of opposites and neutrality a bit more.

  Not an Ordinary Thing

  Anaximander reasoned that the primary substance of the universe could not have been any one of the ordinary things, such as water or fire. For they have opposition with one another, and opposites destroy; they do not generate one another. If water were the apeiron—that is, if everything in the universe were initially water—it would be impossible to have its opposite, fire, ever created, for water destroys fire; it does not generate it. And that would be terrible because in such a scenario, eventful beautiful diversity would be absent from the cosmos. Thus, something that has an opposite cannot be the primary substance of the universe for it presents a serious threat to the cosmic justice, to the unity and order of nature, to its diversity, and in fact, to the very existence of nature itself—for such type of substance, with an opposite, would cancel itself out, and thus it would cancel out nature itself!

  Anaximander saved the phenomena—kept nature just, eternal, diverse, and eventful, and without the possibility of absolute dominance by any one of the opposites—by requiring that the primary substance, the apeiron, be neutral, with no competing opposite. It must be neutral to itself and to the opposites that it creates. With such choice, neither opposite is a threat to nature any longer, since their effects cancel each other out, nor is the apeiron, since it has no competing opposite to cancel out. Hence, unlike the opposites, the apeiron is permanent and indestructible. And so then is nature itself, for nature’s essence is the apeiron. The neutrality of the apeiron saves the phenomena, but the opposition of the opposites beautifies them. Both neutrality and opposition are central ideas in the world outlook of Anaximander and of modern physics.

  The modern physicist’s version of Anaximander’s reasoning would be that the presently accepted primary particles of matter, the quarks and leptons, cannot really be primary, for they have opposites—their antimatter versions—the antiparticles of antimatter, the antiquarks and antileptons, and as opposites, a particle and its antiparticle annihilate, not generate, each other. Furthermore, there are six types of quarks and six types of leptons, and the pressing question is why there are so many building blocks of matter and why do they have different general characteristics (different electric charge, mass, spin, etc.)? Why not just have one primary substance, one apeiron-like type particle?

  On this issue, Nobel laureate Werner Heisenberg (1901–1976) has said, “All different elementary particles [particles that are not made of other things, thus have no substructure, such as the quarks and leptons] could be reduced to some universal substance which we may call energy or matter, but none of the different particles could be preferred to the others as being more fundamental. The latter view of course corresponds to the doctrine of Anaximander, and I am convinced that in modern physics this view is the correct one.”2

  We have seen how energy may be regarded as the apeiron, but what kind of material particle of modern physics has apeiron-like properties, including the key property of neutrality?

  The Higgs Particle

  The search for a universal neutral substance that addresses Anaximander’s concern and saves the phenomena has never been more intense. The particle with the most qualities required by such a substance is the Higgs boson. It has been mathematically predicted to exist by various physicists in the 1960s, including Nobel laureate Peter Higgs (1929–), from whom it took its official name. In fact, it is required to exist in order to save the phenomena as described by the standard model of physics: the Higgs particles are thought to give mass to all material particles (such as quarks and leptons) by pulling on them, thus forcing them to slow down, clump, and form all the composite objects in the universe, from nuclei, atoms, molecules, plants, animals, planets, and stars, to galaxies, and in general, all the complexity in the universe. (The mass-giving mechanism of the Higgs is a more relevant topic for chapter 12.) With the Higgs we can explain mass, and as a result the universe is diverse, beautiful, and saved. Without the Higgs, all particles would be massless, would fly around at light speed, and would not be able to come together and form atoms or in general composite objects, including us; the universe in such a case would exist in one boring, undiversified state, which of course would be in contradiction to the actual diversified universe we live in. Indeed, then, the Higgs saves the phenomena!

  Like the apeiron, the Higgs particle is intangible, neutral (in a few interesting ways, as we will explore in the next section), and the field that represents it permeates all of space. (Use of the term “field” means that something exists everywhere, whereas “particle” implies that something exists only somewhere. In quantum theory, particles are manifestations of field fluctuations. Consider this analogy: if the sea is a field, a splash in the sea—a fluctuation, an excitation—is a particle that can be detected. Because of its all-pervasiveness, the Higgs field was related to Anaximander’s apeiron by Nobel laureate Leon Lederman [1922–2018].3) But while itself neutral, the Higgs also manifests itself as the competing opposites, as particles of matter and antiparticles of antimatter, and as some of the forces that matter and antimatter obey. In fact, it is not expected to be observed directly (analogously, neither was the apeiron); instead, its existence was confirmed indirectly by studying the behavior of various other particles that the Higgs decays into. Thus, the observed opposites in nature are in a sense different aspects of the same thing, the Higgs—or, analogously, the apeiron. Anaximander proposed the apeiron to put his opposites, and Peter Higgs proposed the Higgs field to put his opposites (the particles and antiparticles) in order to explain why they have mass.

  Neutrality

  T
o save the phenomena, neutrality must be an essential characteristic of a primary substance. The Higgs is neutral in various ways: (1) it is electrically neutral; thus, it is its own antiparticle—it is both matter and antimatter, and in this respect it has no warring opposite to be destroyed by. (2) It is also color-neutral—“color” (or more precisely, color charge) here is a property of the quarks and of the nuclear strong force (like the electric charge that is a property of the electromagnetic force) and not the color of everyday sense. (3) Moreover, its spin is zero; thus, it is direction-neutral, an unusual notion that we need to elaborate on further.

  Spin (like electric charge) is an intrinsic quantum property of elementary particles. In a simplistic view, imagine the spin of a particle to be like the spin of a top around its axis. However, unlike a spinning top, which may spin slow or fast and in every direction, an elementary particle spins with a fixed magnitude and only in certain directions. Now, the direction of a particle’s spin is related to the direction of its motion through space. For example, a neutrino (an electrically neutral point-like particle, belonging in the family of leptons as electrons do) is observed to always be left-handed. This means that a neutrino moves through space like a left-handed screw: it advances (moves forward) by spinning counterclockwise. An antineutrino, on the other hand, is always observed to be right-handed. It moves like a right-handed screw: it advances (moves forward) by spinning clockwise. Unlike a neutrino, an electron can be ambidextrous—or move in space by spinning in either direction. The important point is that all particles are directional—the direction of their motion through space is restricted by how they spin.

  But a primary substance must itself be free of such restriction; it must be nondirectional, direction-neutral, that is, isotropic (with no preferred direction of motion)—because a left-handed substance would, in Anaximander’s terms be like, say, fire, and a right-handed substance like water. If a primary substance’s own motion were restricted, it would not have been able to generate the existing particles with all their various observed directionalities, which collectively are isotropic. In other words, if Anaximander’s cosmic justice is to hold, a preferred (special) direction in the universe, toward which particles would be moving, should not exist. In fact, on a grand scale, the view of the universe is similar in all directions; thus, the universe itself is isotropic (there is no special direction in it). One piece of evidence for this is the observation of the so-called cosmic microwave background, light that comes to us from every direction in the universe, showing that the matter that emitted it had almost exactly the same temperature, about 3 degrees above absolute zero.4 Now, since the universe is made of galaxies and stars, which in essence are made of particles, then the isotropy of the universe must really be a consequence of the isotropy of its constituent particles. And if we believe that one day we will conceive a theory of everything, describing one primary substance, such a substance must have the property of isotropy, for only then it can generate the universal isotropy that we observe today. Well, to be isotropic, direction-neutral, the spin of such a primary substance must be zero since without spin the direction of its motion cannot be restricted. The Higgs boson particle is electrically neutral as well as color-neutral, and being the only particle of the standard model with zero spin, it is direction-neutral, too! Anaximander’s notion of neutrality should be a vital property of the primary substance of the universe and, consequently, of the universe itself. Nonetheless, it seems that the universe does not obey this fundamental notion of neutrality. For although it is isotropic and thus cosmically just (neutral) direction-wise, it is also unjust matter-wise; matter appears to dominate antimatter. What happened to the cosmic justice?

  Why Is There More Matter Than Antimatter?

  In modern cosmology, there is an open question: why is there more matter than antimatter in the observable universe? In Anaximander’s terms, this problem might have been phrased: Why is there more water than fire in the observable universe? This observation makes no sense if indeed the universal substance is a kind of neutral, which transforms into equal amounts of opposites with properties that cancel each other out through the conservation laws they obey—so that the universal substance can remain neutral. Absolute dominance by any one opposite should not be allowed. Yet matter appears to have an absolute dominance in the universe. If true, and our observations are correct, where is Anaximander’s cosmic justice? Are the laws of physics as we now know them really incorrect? The answer does not yet exist, but I will speculate cautiously.

  Think of a creation process like that of an electron-positron pair. It obeys cosmic justice. During its existence, the region where the electron is located is dominated by matter, and the region where the positron is located is dominated by antimatter. But such dominance is relative and ephemeral. No law forbids equal and relative dominance by matter and antimatter in various regions of the universe. In fact, this would be expected if indeed equal amounts of matter and antimatter are generated by a neutral-type universal substance. What is forbidden is absolute dominance, for which the amount of either matter or antimatter in the universe is absolutely more. Now, with relative dominance in mind, we can speculate on why there is, or actually, why there appears to be more matter than antimatter in the observable universe.

  First, the universe is immense, some 93 billion light-years across, and we haven’t observed all of it yet. So an unseen part of it might be composed of mostly antimatter that could balance out the matter we see; hence, we have cosmic justice.

  Second, what if our universe is not the universe, but rather only a mere region in it? In fact, we should not be rash in dismissing such a view, for until the early twentieth century we thought the entire universe was what we now call the Milky Way galaxy—whereas now we think there are some 170 billion galaxies. If this hypothesis holds, the puzzle of the observed asymmetry between matter and antimatter might then be resolved. Matter might be dominating temporarily in our part of the universe, but antimatter could be dominating temporarily in another part of the universe, and in such a way that neither can claim absolute dominance in the universe. Because such temporary dominance can be neutralized when such parts collide or interact, converting their matter and antimatter to pure neutral energy. Anaximander’s cosmic justice would then be restored.

  Cosmology

  In addition to the hypothesis of the abstract apeiron, Anaximander makes another conceptual leap by holding that the earth is motionless in space and without any physical support. This happens, he argues, because earth’s equal distance from everything in the sky—so it appears, anyway—is causing earth to have an equal tendency to move in every direction (e.g., equally to the right as to the left), that in turn, cancels out any potential motion and keeps earth at the center in equilibrium.5 This is in contrast with Thales’s view of an earth floating on water and thus supported by it—for in that case, what would support the water, and what that? Philosopher Karl Popper (1902–1994) remarked, “In my opinion this idea of Anaximander’s is one of the boldest, most revolutionary, and most portentous ideas in the whole history of human thought. It made possible the theories of Aristarchus and Copernicus. But the step taken by Anaximander was even more difficult and audacious than the one taken by Aristarchus and Copernicus. To envisage the earth as freely poised in mid-space, and to say ‘that it remains motionless because of its equidistance or equilibrium’ (as Aristotle paraphrases Anaximander), is to anticipate to some extent even Newton’s idea of immaterial and invisible gravitational forces.”6 Aristarchus of Samos (310–ca. 230 bce), sometimes called the ancient Copernicus, was the first to advance the heliocentric model, revived in the sixteenth century by Nicolaus Copernicus (1473–1543) (perhaps Copernicus could be viewed as the modern Aristarchus).

  As commended by classicist John Burnet (1863–1928),7 Anaximander’s doctrine of innumerable worlds, each with its own earth, heaven, planets, stars, and especially its own (relative) center and diurnal rotation, is inconsistent with the exi
stence of an absolute center or preferred direction of motion in the universe. With the lack of an absolute direction of motion, Burnet continues, Anaximander’s argument that an earth that happened to be equidistant from everything in its world has no reason to move in any direction is quite sound. This is in fact a clever use of symmetry, a notion of central significance in modern physics. Symmetry, as in a circle, implies a certain constancy, a similarity that persists without change. The circle, for example, looks the same from its center at all angles, or, in Anaximander’s case, the earth remains in equilibrium because of its equidistance from its own sky. Symmetry in physics does not describe just appearance. It also underlies conserved abstract properties of nature such as the conservation of energy, momentum, and electric charge. For example, conservation of energy is a consequence of the hypothesis that the laws of nature are symmetric (invariant) with respect to time translations: they work the same today as they have in the past and are expected to continue so tomorrow. Because this hypothesis has been true so far, we accept conservation of energy as a law of nature. The great mathematician Emmy Noether (1882–1935) proved mathematically various conservation laws of nature by associating them with a specific symmetry.

  The absence of a special direction in space was employed by Democritus in describing the motion of his atoms as random (chapter 12). Though true, abandoning the notion of an absolute direction is still difficult today. We are tricked by the phenomena (such as falling objects or “the earth being under our feet and the sky up above us”), and so we often think of up above and down below as if they were really absolute up and absolute down. We don’t realize that for those living on the opposite side of the earth, our relative up is really their relative down, and our relative down is really their relative up.