In Search of a Theory of Everything

by Demetris Nicolaides

  26Galen, On Medical Experience 15.7, trans. Demetris Nicolaides. Or see Graham, Texts of Early Greek Philosophy, 597 (text 139).

  27Sextus Empiricus, Against the Professors 7.138–139, trans. Demetris Nicolaides. Or see Graham, Texts of Early Greek Philosophy, 597 (text 140).

  28Ibid.

  29Ibid., 7.140, trans. Demetris Nicolaides. Or see Graham, Texts of Early Greek Philosophy, 309 (text 63).

  13

  Atoms of Space and Time

  Introduction

  Epicurus (341–270 bce) expanded on the atomic theory propounded by Leucippus and Democritus. He wrote three hundred books on just about everything, but unfortunately most have been lost. Only the Stoic philosopher Chrysippus (ca. 279–ca. 206 bce) wrote as many. According to legend,1 at fourteen years old he was taught from Hesiod’s Theogony (on the origin of the gods) that “In the beginning Chaos came into being”2 . . . which later gave birth to other things. Where did Chaos come from?, Epicurus inquired. Baffled by the question, his teacher finally replied, saying that such a query was philosophical. Then I want only philosophers as my teachers, Epicurus responded.

  New Features

  The Epicurean theory of atoms has several unique features: (1) The E-atom (Epicurean atom), like the D-atom, is unsplittable, but unlike the D-atom, an E-atom has distinguishable indivisible (uncuttable) parts—it has substructure. (2) In addition to material atoms (smallest cuts of matter), there exist space “atoms” (smallest spatial expanses) and time “atoms” (smallest time intervals)! (3) The motion of an E-atom is dotted, quantum! It moves from one place to the next but without passing through any of the points in between. (4) An E-atom may spontaneously swerve (creating uncertainty in its whereabouts), a feature added by Epicurus in a first-ever attempt to escape the Democritean determinism and subject human free will to a scientific hypothesis—the subject of the next chapter.

  These news features evolved when Epicurus or his students responded to various well-thought Aristotelian attacks on Democritean atomism. Space and time atoms, we’ll see, challenge profoundly the bedrock of modern physics. Space atoms, recall, are an essential requirement of loop quantum gravity. The cause of the most consequential premise of quantum mechanics—the Heisenberg uncertainty principle—and also the cause of the famous quantum jump will be cautiously speculated with two original ideas, using the Epicurean theory of matter, space, time, and motion.

  The Parts of E-Atoms

  E-atoms are physically indivisible but conceptually3 divisible into minimal parts. That is, if we could zoom in on an E-atom, we would notice a substructure, that it has physically distinguishable features, identical parts (although their shape and size is not specified in the extant sources). A part can neither be cut further (into smaller pieces) nor can it be cut from (or added to) an E-atom. It is also fundamental (a part is partless): if we continue zooming into a part, we’ll discover no new parts (no new substructure). Since we can’t really see one, a part is only a mentally identifiable base unit. Different kinds of E-atoms are made from their own unique integral number of parts (although not from one part)4 arranged in multitude ways. Figure 13.1 shows a hypothetical part, and two types of E-atoms in two dimensions. So the range of allowed sizes (and overall geometry) of E-atoms is quantum—for example, 2 parts, 3, 4, 5, . . . , but not, say, 4.7 parts—like the range of energies in the modern chemical atom (or matter in general). By contrast, the size of D-atoms is not quantum—it varies continuously.

  Figure 13.1 (a) a part; (b) E-atom with three parts; (c) E-atom with four parts.

  Democritus speculated the existence of different atomic shapes and sizes with hooks and crevices to explain how D-atoms interact and aggregate to create macroscopic things. Epicurus, by contrast, needed only speculate the notion of a part. Thereafter he imagined parts to have always been connected with each other in various ways, creating thus the varied atomic shapes and sizes.

  But atoms couldn’t move unless space, time, and motion are radically reimagined.

  Quantum Motion, Space Atoms, and Time Atoms

  In criticizing Democritean atomism, Aristotle had argued rigorously that a D-atom, which is partless, can’t move unless (a) its motion is discontinuous, quantum, and unless (b) space and time are composed of atoms of space and atoms of time—thus, they, too, have a quantum nature.5

  Concerning notion (a): Aristotle imagined a D-atom to have moved from here to there but without moving through any of the points in between—exactly the meaning of a quantum jump in modern quantum physics (recall the chessboard-pawn analogy)! Incidentally, the Bohr model of the hydrogen atom (recall chapter 6) was the first place to have assumed the exact same type of motion when its electron was making a transition, a quantum jump, from one allowed orbit to the next.

  Concerning notion (b): he argued that, if (a) were to hold, then one should not imagine that there were ever-smaller regions of space so small as to be points of space, and that there were ever-briefer periods of time so brief as to be moments. Instead, if (a) were to hold, then both space and time should be finitely divisible—that is, their division (say, in your mind) can’t go on forever; it should stop at a final cut.6 That is, there should be space and time minima (smallest cuts), indivisible spatial and temporal magnitudes, atoms (the meaning of indivisibles in Greek) of space and atoms of time! So space shouldn’t be made of points but from minimal expanses, and time shouldn’t be made of moments (pass moment after moment) but from minimal periods (pass period after period).

  But Aristotle had also claimed to have successfully shown that all these ideas were impossible. For example, he thought quantum motion (jumps), that something could have moved without moving, is absurd. Hence, for him there can’t be atoms of matter; there can be only a plenum (i.e., matter forms a continuum without a void). Motion can’t be quantum; it must be smooth, continuous, sequential point by point (i.e., as we experience it daily). There can’t be atoms of space; space is divisible ad infinitum. And there can’t be atoms of time; time flows smoothly, moment after moment. Thus, atomism, Aristotle thought, is a mere chimera. But Epicurus is braver. He meets the Aristotelean criticism and boldly embraces exactly all these “absurdities”!7 There are atoms (of matter, of space, and of time) and motion is quantum. Aristotle’s reasoning is a force! Even when we think it might be wrong, it’s been shaping up history and what we think might be right.

  Why Should Atoms Exist?

  Epicurus, like Democritus and Leucippus, insisted on matter-atoms and the void because only then motion (and thus change in nature) made sense. Also, the poet Lucretius (99–55 bce), an ardent Epicurean who preserved many Epicurean ideas through a long poem, lists a variety of observational evidence in support of the atomic hypothesis.8 But a theoretical argument that guided Democritus to atomism had to do with the nature of divisibility of matter (although not of space and time, but since Democritus’s general argument applies to space and time, we’ll include that, too). He argued divisibility had to be finite—it had to stop at some minimal nonzero magnitudes. If it didn’t, if divisibility were infinite, “eventually,” he thought, matter (and space and time, everything) will be reduced to nothing—to zero-size points.9 How could one then reconstruct the universe starting from nothing? Being does not come from Not-Being. Lucretius’s Epicurus adds, “If things were made out of nothing, any species would spring from any source and nothing would require seed. Men could arise from the sea and scaly fish from the earth . . . ,”10 and all sorts of other random things would happen, too. But we have order: “Again, why do we see roses appear in spring, grain in summer’s heat, grapes under the spell of autumn?”11 Order, for Lucretius’s Epicurus, was additional evidence that Not-Being cannot generate Being—thus what is has always been and will always be. And for Being to exist and be reconstructible from fundamentals, divisibility had to stop at a final nonzero cut, giving us a material atom (a smallest bit of matter that couldn’t be zero), a space atom (a smallest expanse of space that couldn’t be zero), a
nd a time atom (a smallest period of time that couldn’t be zero). Parenthetically, the strings of string theory and the space atoms of loop quantum gravity have minimal, nonzero magnitudes, too.

  Nature, for Epicurus is quantum (finitely divisible) in all its essence: not just as a property of matter (and energy), as our current laws state, but as a property of space and time, as some of our most advanced scientific hypotheses claim. With space and time atoms, the philosopher had set sail to uncharted waters with unprecedented consequences that shake sacred modern physics grounds.

  Space-Time: Points and Smoothness Versus Magnitudes and Quantum-ness

  Matter atoms (D-atoms, E-atoms, even the QL-atoms) are separated by a spatial interval, the void—thus, matter spreads discontinuously in space. But nothing separates the space atoms or the time atoms. It wouldn’t make sense to say, for example, that space atoms are separated by void for void itself is space and with space atoms Epicurus described space itself.

  Quantum Space

  Space in Newtonian and quantum physics, or even in the more advanced notion of space-time, of relativity, is a smooth, sea-like continuum made of points (thus, it is infinitely divisible). Space in E-physics forms a continuum, too. But it is a granular, a quantum space continuum, made not of points but from connected indivisible identical minimal expanses, the space atoms (thus, space is finitely divisible). (The size and shape of space atoms is not specified in the surviving sources.) Think of granular space as asphalt-like (with the recognizable imperfections of the asphalt as space atoms) or as a Lego structure (with indivisible equal-size Lego pieces as space atoms), or a Minecraft structure (with its indivisible unit blocks as the space atoms), like Picasso’s cubism, a tiled floor, or the game Tetris. Fascinatingly, the space atoms of loop quantum gravity, too, form a granular space and are imagined as interlinked rings.12 Also, in both E-theory and loop theory the granular space entails a quantum geometry—only certain distinct shapes and sizes are allowed. In a simplified example, if E-space is a tiled floor (figure 13.2) and space atoms are the tiles (of side say 1 unit), the allowed (say square) areas are only 1 × 1 = 1 square tile, 2 × 2 = 4 tiles, 3 × 3 = 9, 4 × 4 = 16, and so on. Square areas with numbers in between—such as the “dark gray” area of 2.5 × 2.5 = 6.25—are not allowed; “dark gray” areas are allowed only in a point-by-point space. Recall, in relativity, geometry is gravity. If geometry is quantum, gravity must be quantum, too. This is a basic hypothesis in loop quantum gravity.

  Figure 13.2 Space is quantized in E-theory. Only certain discrete (quantum) areas (geometrical shapes in general) are allowed: the “gray,” but not the “dark gray.”

  Quantum Time

  Time in relativity is relative, but it is classical, not quantum. It flows smoothly, moment after moment (as time flows in Newtonian and quantum physics, too), and all moments are allowed to happen. But E-time is quantum! It passes granularly, period after period, time atom after time atom, and so only certain distinct time durations are allowed to happen. Time atoms are indivisible (not made from moments), identical, minimal periods (although their duration is not stated in the extant writings). Say a time atom is 2 seconds. Time is quantum because only periods 2, 4, 6, 8, . . . seconds occur, all other in-between periods (e.g., 2.5, 7, or 17.2 seconds) are not allowed—they are the “dark gray” periods. But time is quantum also because of the way time passes. In our example, the 2-second time atom passes “whole,” not moment by moment—otherwise there would be a problem (see section “Zeno Can Finally Get the Door,” later)—for moments can’t happen, only durations can: a time atom is indivisible; it is not made from smaller “cuts,” or moments. Analogously, the parts of E-atoms aren’t made from other parts (or material points), and space atoms aren’t made from points of space. That’s basically what is meant by the notion of “indivisibility” of a time atom, a space atom, and the E-part. You may think of this as Aristotle thought of a mathematical line, that such a line contains points but it is not composed of points—for, the nonzero magnitude of a line cannot be reconstructed from points which, by definition, have zero magnitude. As seen earlier, it’s difficult to make a universe from points.

  Quantum Events

  An event in E-physics happens at a spatial expanse, the space atom, and lasts as long as a period of time, a time atom—only when the time atom is up can there be a change into another event. Events therefore are reimagined as space-time magnitudes in E-physics, not as space-time points (as in relativity). And as in quantum physics, the E-events are discrete, quantum, not continuous as in relativity. Events in E-physics also can’t be “singular.” For there are neither moments (of zero time duration) nor points of space (of zero size), not points of matter. Thus, matter can’t accumulate at a singularity—an infinitesimally small, a true point of space, of size zero—for space is made of magnitudes, not of points. Nor could the universe have begun as a big bang singularity, but it could as a big bang magnitude. Singularities in modern physics are undesirable; they pose existential threats. They are as problematic as suggested by the indeterminate answer of 1/0. Their elimination would be a scientific and mathematical breakthrough if we ever manage it. Only time can tell, if it’s not dead.

  Is Old Chronos Dead?

  On April 6, 1922, during a dialogue between the great philosopher Henri Bergson (1859–1941) and Einstein, the great physicist famously provoked the philosopher by saying that “the time of the philosophers did not exist.”13 He said that in the context of his relativity for which time “flows” deterministically, and the future has already been written (since all moments of time exist always in the block universe). However, the philosopher insisted that “the future is in reality open, unpredictable, and indeterminate.”14 Determinism versus indeterminism, as properties of the universe, is still very much an open question and will be discussed further in the next chapter in the context of free will.

  For now, if space and time atoms turn out to be the new reality of nature, it is the time of the physicist that will not exist. For time and space, in Einstein’s relativity, although relative (i.e., not universal) and revolutionary, are not made of time and space atoms; they are made of points.

  Nonetheless, time could be dead, really dead, for both physics and philosophy, but for a different reason. Time, in loop quantum gravity, is hypothesized to not exist—it’s an emergent property (and it’s not part of the theory’s main equations).15 Physicist Carlo Rovelli (1956–), a founder of loop theory, writes: “For a hypothetically supersensible being, there would be no ‘flowing’ of time: the universe would be a single block of past, present, and future. But due to the limitations of our consciousness we perceive only a blurred vision of the world and live in time.”16 “Similarly, [in Epicurean philosophy] time by itself does not exist”17; it is an emergent property for “nature is twofold, consisting of . . . matter and the space [void].”18

  Is Einstein’s idea of a cosmic, absolutely constant speed (not just for light), required by his relativity, a truth for E-atoms, too?

  Cosmic Speed

  E-atoms move always with the same constant speed “as quick as thought.”19 It is so because for Epicurus, “Empty space [or in modern physics, the absence of the Higgs field] can offer no resistance to any object in any quarter at any time, so as not to yield free passage as its own nature demands. Therefore, through undisturbed vacuum [before the Higgs field was activated] all bodies [E-atoms, QL-atoms, photons] must travel at equal speed.”20 Epicurus, therefore, according to Lucretius, justifies the constancy of the E-atom speed as a consequence of the void, which offers no resistance to the motion of E-atoms. Analogously, in modern physics, during the early superhot stages of the expanding universe, before the Higgs field was activated, nature allowed QL-atoms to move with their natural cosmic speed, that of light. They slowed down only when the universe cooled a bit and triggered the Higgs field that endowed QL-atoms with their mass (an emergent not a fundamental property) via the Higgs mechanism.

  The constancy of
speed in E-physics can be justified also in another way. Assuming they move, E-atoms must move with the same constant speed since all space atoms have the same size and all time atoms last the same interval of time. An E-atom then takes 3 time atoms to travel 3 space atoms, and 5 time atoms to travel 5 space atoms, and so on. Its speed is always constant, 1 space atom per time atom. Speed constancy is inherent in the very quantum nature of Epicurean space and time.

  Interestingly, Einstein too thought that space and time are the cause that all objects move with a constant speed, that of light! “Einstein proclaimed that all objects [not just light] in the universe are always traveling through space-time [space-time] at one fixed speed—that of light [even those that appear to move slower].”21 He means “an object’s combined speed through all four dimensions—three space and one time— . . . that is [always] equal to that of light.”22 The consistency of both relativity and Epicurean physics relies subtly on speed constancy! The phenomenon of time dilation, in relativity, implies that time passes ever-slower at ever-greater speeds, and stops at the speed of light. Now, since, in the sense just discussed, everything moves with the speed of light, then time (old Chronos) might indeed be dead.

  The constancy of the speed of light (of photons) is a foundational premise in Einstein’s special relativity. It safeguards causality and saves the universe from paradoxes (recall chapter 6). Photons travel with the same constant cosmic speed always: when they are emitted from moving or stationary sources, when they collide with other particles and change direction, even when they move through other substances. E-atoms too move in the same exact manner (although not with the speed of light).