However, both E-atoms and photons appear to move slower when they move within a material substance such as water or oil because of their collisions with other particles. The denser the material, the slower their speed; or more precisely, the slower their speed appears to be. This is so because as E-atoms or photons are making their way from one place to the next within a substance they constantly collide with the matter particles of the substance (the other E-atoms, the QL-atoms). Hence, they execute a zigzag, longer motion, take longer to arrive at their destination, and as a result appear to have a slower speed. Just like crossing a crowded room with your usual constant pace: zigzagging around the people in an effort to traverse from the back of the room to the front, gives someone who times your trip the impression that you were moving slower. Photons produced in the center of the sun, for example, take a million years to reach its surface because of collisions and zigzagging. Thus, they appear to have been travelling with a speed much smaller than c, although always, from collision to collision, in the sun or any other substance, they are traveling with c. If the sun were a void (empty), the photons would reach its surface in just a few seconds.
Now despite that all E-atoms have the same speed, Epicurus didn’t ignore the obvious: that some things are motionless, others move slow, and others fast. But he thought “slowness and quickness are just the appearance which collision and non-collision take on,”23 that such difference in speed was merely an emergent (an apparent, not a fundamental) property of composite things, and he explained it via the following ingenious mechanism (of particle interaction).24 Composite objects are made from E-atoms, which all have the same cosmic speed. If it happens that the motion of the E-atoms is random (i.e., those moving in one direction are as many as those moving in the opposite direction), their atomic motion averages out to zero and (while every E-atom in the object is in constant motion) the object itself, as a whole, remains at rest—for example, the E-atoms that push the object, say, right are as many as those that push it left, keeping the bulk of the object at rest. (This is, by the way, the exact same reason that water in a cup doesn’t leap out despite that each water molecule in it is in constant motion.) Now, if but only a few of these E-atoms happen to move in a preferred direction, say right, then these E-toms create a small net push to the right causing the object to move slowly to the right, too. The object’s motion is increasingly faster in a certain direction the more E-atoms happen to move in that direction. But could E-atoms move in various directions?
Cosmic Direction
At first, the answer appears to be no because E-atoms were imagined to move toward some cosmic, absolute direction, “down”—not down toward the earth. I’m absolutely lost, still, however hard I have labored to find Epicurus’s cosmic direction—the extant works don’t elaborate much where this direction might be. Nonetheless, I cannot help imagining absolute direction as something like the experience I have whenever I stare at some of the art of M. C. Escher (1898–1972), follow its pathways, feel certain I’m ascending while suddenly I’m also descending. Especially the 1960 print, Ascending and Descending, which is “showing a staircase that goes on endlessly ascending—or descending, if you see it that way.”25 Maybe some strange space-time continuum could accommodate an absolute direction, but I don’t know!
The Challenge to Make a Universe with Uniform Motion
How could E-atoms ever meet, collide, aggregate, and make a universe of composite things if they always move with a uniform motion, that is, with the same cosmic speed and in the same absolute (cosmic) direction? In the spirit of this book, to read the past from the perspective of modern knowledge, not to really judge it for its weakness, but to be inspired by its insights, I will attempt first a different answer than Epicurus’s.
They couldn’t meet if space is flat, Newtonian-like. In an analogy, imagine space as a flat chessboard. Flat surfaces obey the principles of Euclidean geometry. Since parallel lines (as those of the chessboard) in flat surfaces never meet, E-atoms with their uniform motion could never meet either. (a) A trailing atom moving along a chessboard line couldn’t overtake a front atom for they move in the same direction with the same speed. Also (b) they couldn’t meet when two E-atoms move in the same direction along two parallel lines because parallel lines, we learned from Euclid’s Elements, his superb geometry book, never meet in flat surfaces.
But for case (b) they could meet if the E-atoms move in a curved space, like the surface of, say, a sphere. For according to the principles of Riemannian geometry that describe curved surfaces, parallel lines could meet: two (earth) meridians are parallel as they cross the equator of the earth (or a sphere) but do meet at the north and south poles. Hence, E-atoms moving in the same direction, along different meridians, can collide where the meridians meet, interact, and make a universe.
Space in relativity is curved, but Epicurus didn’t know about curved space so he devised another, interesting explanation.
Atomic Swerve
With uniform motion E-atoms can never catch up with each other, collide, interact, and aggregate into composite things. Epicurus addresses the problem by imagining that E-atoms swerve spontaneously. He thought that the swerve solved two problems. (1) It allowed E-atoms to change direction, interact, and aggregate into stars, planets, and people. (2) The spontaneity of the swerve introduced uncertainty in atomic motion, a property that Epicurus thought restored human free will, the topic of the next chapter. Swerving has received the intense criticism from both ancient and modern scholars for Epicurus had never explained it; he had merely postulated it—swerve was cause-less for Epicurus. To the best of my knowledge, swerving has not been explained yet. What is the cause of the famous Epicurean swerve? I’ll speculate.
First Cause: The Pause
In my opinion the swerve doesn’t have to be postulated. Its cause is basically the time atom. First, strike the requirement of the absolute direction of motion (we’ll consider it later). Consequently, the quantization of motion, of space, and of time allows E-atoms to move randomly and swerve. How so?
D-atoms move continuously, smoothly point by point, moment by moment—just as we experience the motion of the everyday. Their flow is absolutely uninterrupted, their momentum directional, deterministic.
But E-atoms differ. Although their speed is constant—they always cover the same distance in a given time—their motion is discontinuous; they pause! While an E-atom is in a space atom (at some “location”), it pauses, and it is at rest there for a period of a time atom—time, recall, passes period by period not moment by moment. This period of stasis—the time atom—is the cause of motion randomness that Epicurus so much wanted as a property of the E-atom. For, when an E-atom’s time atom is up, and with the absence of cosmic directionality, its next quantum move (to a neighboring space atom) must be random, uncertain: in the absence of directionality, and while on stasis, it has no more reason to move in this neighboring empty space atom (“location”) than that one, so it swerves! The swerve is caused by the pause, the time atom, which in essence breaks the flow, the momentum, the directionality and continuity of motion. Time in Epicurean physics is quantum, composed not of “nows” (moments) but of periods, of time atoms entailing a time pause, the cause of the swerve.
In an analogy, a tiled floor (figure 13.3) is a two-dimensional quantum space, and the tiles are space atoms. Imagine a black square E-atom26 occupying a tile. Since (a) the E-atom is at rest (at a pause) there for exactly a period of a time atom, since (b) it must quantum jump (for its speed is constant, though not continuous), since (c) it lacks directionality (cosmic or from a continuous momentum) it has no more reason to jump here than there—arrows indicate the potential jumps—then (d) when its time atom is up and must jump, it jumps randomly into any of the eight tiles around it; thus, it swerves.27 Its motion is a constant quantum swerve constituted by uncertain jumps causing uncertainty in its position and direction of motion. Position and direction uncertainties are also part of the famous Heisenber
g uncertainty principle. What’s the connection?
Figure 13.3 The pause of an E-atom is the cause of its spontaneous quantum swerve.
Cause of Heisenberg Uncertainty: A Hypothesis Involving No Collision
My hypothesis is that the swerve (and the resulting position-direction uncertainty) is a property inherent in the very fabric of the quantum nature of Epicurean time. Based on that I speculate that time quantization, the time atom, the pause, might be the cause of the Heisenberg uncertainty principle, too—more precisely, all (a), (b), (c), and (d) properties, earlier, contribute. In other words, the position uncertainty of, say, an electron (or generally, a QL-atom), as described by Heisenberg’s uncertainty principle, is really caused by the pause—time quantization. Reinforcing my speculation is yet another known truth of the Heisenberg uncertainty principle. That the position-velocity (thus position-direction, for velocity is really speed with direction) uncertainty of an electron is not caused only when we curious observers decide to observe little things by shining photons on them and cause collisions (as discussed in chapter 7). Rather, it is always true, even when we are not observing—an inherent property of nature which now makes more sense in the context of time atoms (time quantization). An electron, I hypothesize, like an E-atom (of figure 13.3), quantum swerves into uncertainty on its own—that is, it obeys the Heisenberg uncertainty principle—because of its pause (time quantization).
Second Cause: Overcrowding Is Against the Law
Let’s use the tiled-floor analogy to explain the swerve but now by preserving the cosmic direction of motion. For even now E-atoms can meet and interact. For example, with the Riemannian geometry of a sphere in mind, two E-atoms may move in the same direction, north, and still come face to face as long as one moves along the 0-degree meridian, and the other along the 180-degree meridian.
So a black E-atom, which comes from left (figure 13.4.a), moves toward a gray E-atom, which comes from right. The arrows indicate where the atoms have come from. If the E-atoms are initially an odd number of tiles apart, they will eventually face off with a single tile in between them. What then? They pause the usual period of a time atom and when that time is up, each has to quantum swerve to a different tile (figure 13.4.b shows one possibility) simply because overcrowding is against the law (Pauli exclusion principle): E-atoms are absolutely rigid; they can’t occupy the same tile at the same time.
In a variation, E-atoms will still quantum swerve even if initially they are an even number of tiles apart—only now, they’ll swerve after they face off by being right next to each other.
Figure 13.4 (a) After two E-atoms have “collided” (interacted), (b) they must quantum swerve because overcrowding is against the law; they can’t occupy the same tile at the same time.
Cause of Heisenberg Uncertainty: A Hypothesis Involving Collision
The face-off between E-atoms basically describes a collision between them, even if they don’t touch. Electrons collide in this manner, for electrons too “know” that overcrowding is not allowed. And as we learned, a collision is the first step of the uncertainty principle. True for E-atoms, too, for after they face off, which tile each will jump into is uncertain. It is as uncertain as an electron’s quantum jumps: for, due to the Heisenberg uncertainty principle, an electron (or any microscopic particle) may jump/be only in one of several allowed positions. Here is a more concrete connection: imagine the black E-atom to be an electron and the gray E-atom to be a probing photon used to “see,” locate the electron (figure 13.4.a). The Heisenberg uncertainty in the position and direction of the electron is easily justified within the Epicurean physics by figure 13.4.b: after the photon collides with the electron, the electron (the black E-atom) must quantum jump into any one of the eight neighboring tiles around it (or to other nonneighboring ones), but which one it is uncertain—thus, both its position and direction are uncertain. Specifically, the distance between the initial tile and the tile that the electron jumps into is the uncertainty in its position.
Particle Claustrophobia
The Heisenberg uncertainty principle is the cause for particle claustrophobia. The smaller the confining space of, say, an electron, the faster it moves away from it—the less time it stays there. The constancy of the speed of E-atoms is the cause of their claustrophobia. The E-atom of figure 13.3 stays on one tile (a small confining space) only for the period of a time atom (short period of time), but in a vicinity of say the eight tiles (a bigger confining space) that surround it, it stays at least two such periods (for the E-atom can move back and forth). Could there be a connection between these two seemingly different causes of claustrophobia especially in light of Einstein’s realization that in the four-dimensional space-time all objects move with the same speed always? We have no answer so far. However, the realization that claustrophobia—a phenomenon of Heisenberg uncertainty—is also explainable in the context of E-theory (of space and time quantization) is to me another hint that the Heisenberg uncertainty might be caused by space and time quantization.
Challenges
Additional challenges in the Epicurean theory deal with how the size and shape of an E-atom (or its parts) relate to those of a space atom. Can an E-atom, for example, underflow, fit exactly, or overflow a space atom? Epicurus thought an E-atom must fit exactly in the space atoms it occupies. For our examples the E-atom is either totally within a tile or not at all: it can’t be partially in it. Or, can a quantum jump occur into a faraway tile, skipping the immediate next? Relativity imagines objects attached on the fabric of space-time. Since loop quantum gravity attempts to reconcile relativity and quantum mechanics, I anticipate similar challenges between loop quantum gravity’s space atoms and QL-atoms.
Zeno Can Finally Get the Door
With space and time atoms, and quantum motion, Zeno’s paradoxes may be addressed more easily. Imagine there exist five space atoms (five tiles in our simplified quantum space) between here and the door. Zeno (an E-atom) quantum jumps from tile to tile and in a mere five jumps and only five time atoms (five periods of time) he finally gets the door, and (dichotomy) problem solved! That’s roughly the solution proposed by loop quantum gravity, which assumes space atoms exist.28
Note that the paradox would not have been resolved if motion is not quantum, that is, if an E-atom is assumed sliding smoothly, passing sequentially via every point. For in such case an E-atom would have Zeno’s original challenge (created by space divisibility ad infinitum) to cover any distance such as that of a single space atom (tile). Moreover, if motion were continuous, then part of an E-atom’s body (shaped like an arrow in figure 13.5, for simplicity) would have always been moving into the space already occupied by the E-atom itself (figure 13.5.a), but that’s impossible because E-atoms are impenetrable; they can’t move where they already are because overcrowding is not allowed. Thus, an E-atom must quantum jump, as in Figure 13.5b: the arrow has moved to its dotted position without moving through any of the points (locations) in between (since these points were already occupied by itself). Interestingly, this type of reasoning explains the cause, the why QL-atoms, too, must quantum jump; because they, too, are impenetrable.
Figure 13.5 (a) An E-atom in continuous motion would always be moving into a space already occupied by itself—an impossibility because E-atoms are impenetrable. (b) But an E-atom in quantum motion (as in the chessboard-pawn analogy) can never move into a space already occupied by itself. Thus a possible cause of an E-atom’s (or generally a QL-atom’s) quantum jump may be its impenetrability.
Time atoms also solve a time-like dichotomy paradox (mine, not Zeno’s). First, assume time is infinitely divisible (i.e., no time atoms). To have, say, 1 second pass, time must first flow half a second, then half of the remaining time, then half of the new remaining time, ad infinitum. Since there will always exist a smaller last half to flow/pass last, 1 second can never pass. It’s a paradox because I’ve been growing older by the second.
A second can pass, however, if we suppose time is
finitely divisible, that there exist, say, half-second time atoms and that time passes time-atom after time-atom—that is, the time interval of the time atom passes whole, not moment by moment. One second has passed when first, the first half-second atom has passed, whole, and then the second half-second atom has passed, whole, too. That is, the time duration of 1 second has passed (half-second after half-second) without passing (from each moment for there aren’t moments; there are only periods). So we can’t have either a “dark gray” square or a “dark gray” time duration—for our example, ¼, ¾, or 3¼ seconds are “dark gray” durations and can’t occur, but 3 or 3½ seconds are allowed.
Epicurus and Planck
How big are the space and time atoms? The Epicureans simply said they are small. Max Planck (1858–1947) speculated an answer (although I’m not sure if he studied Epicurean philosophy). For fun, he played around with the three most important, fundamental constants of nature, the speed of light, c (a cosmic speed limit); the gravitational constant, G (a measure of the strength of gravity); and Planck’s constant, h (a measure of the microscopic scale where quantum effects become measurable), by rearranging them in two different ratios. One ratio expresses length, now known as Planck length, an unimaginably small expanse of space, 10–35 meters; the other ratio expresses time, known as Planck time, an unimaginably small period of time, 10–43 seconds. If space and time turn out to be composed of such small magnitudes, their smallness would make their effects unnoticeable in everyday phenomena. We would be naturally tricked by it and think that space and time are smooth, made of points of space and moments of time—not granular, made of finite magnitudes, the space and time atoms. Planck length is speculated to be the size of space atoms in loop quantum gravity and the size of the strings in string theory.
In Search of a Theory of Everything Page 21
