There is yet another fascinating consequence of the constancy of the speed of light. It allows us to see the past. In fact, we do it all the time. Looking out in space is looking back in time. And the further out we look, the further into the past we see. This is so because starlight takes time to travel from the distant stars to our eyes. The speed of light is not infinite, so light messages are not transferred instantly. The light from the sun, for example, takes about 8 minutes to reach our eyes. This means that observing the sun at, say, 12:00 noon is actually seeing how the sun was at 11:52 a.m. But Polaris, the North Star, is about 434 light-years away from us (i.e., its light takes 434 years to reach us). So looking at Polaris tonight is actually seeing how Polaris looked 434 years ago. Polaris may not even be there now!
There are still other effects of special relativity. A moving object becomes more massive relatively to its mass at rest. As such an object is approaching c, its mass is approaching infinity, but an infinite mass requires infinite force—which doesn’t exist—to increase its speed to precisely c; thus, c is unattainable by material objects. Also events that are simultaneous for one observer (say two babies are born at the same time) are not so for another observer in motion relative to the first observer (one baby is born before the other). All these so-called relativistic effects become evident only at high speeds, however, those comparable to the speed of light. Because the everyday phenomena involve speeds so much smaller than the speed of light, we are tricked into thinking that Newtonian physics is true. It is nevertheless an excellent approximation of truth, for at the limit of low speeds the equations of special relativity reduce to the Newtonian ones. The equivalence of mass and energy (expressed by the equation E = mc2), length contraction, time dilation, and the relativity of simultaneity, are some of the most startling consequences of special relativity.
Special relativity, published in 1905, deals with the special case of uniform motion (of constant speed in a straight line). General relativity, published in 1916, deals with the general case of accelerated motion (of changing speed and/or direction). Incidentally, since falling objects fall by accelerating, general relativity is really a theory of gravity, more advanced (and with a different vision, philosophy) than Newtonian gravity. Now, space, time, and motion are relative in both special and general relativity. Relative motion means that motion can be discerned or measured only relatively to a reference frame (or an observer). “Every motion [uniform and accelerating] must only be considered as a relative motion,”17 said Einstein. By contrast, Newton thought for example that rotational motion is absolute.
The Relative Motions of the Earth, Sun, and Sky
Hence, in light of special and general relativity, for which space, time, and motion are relative, as regards annual motion, according to the geocentric model, relative to the earth (that is, relative to an earthbound observer), the sun appears to revolve around the earth in 1 year. But equally correct, according to the heliocentric model, relative to the sun (that is, relative to a hypothetical sun-bound observer), it is the earth that appears to revolve around the sun in 1 year. Likewise, as regards diurnal motion, the sky (with the sun and stars) appears to revolve westward relative to the earth daily (and so the sun appears to rise from the east and set in the west relative to the earth daily)—recall that in our earlier analogy the walls appear to revolve clockwise relative to you. But equally correct, the earth appears to rotate eastwardly on its axis relative to the sky daily—you appear to rotate counterclockwise on your axis relative to the walls. This difference (of what is moving with respect to what) “is purely verbal; it is no more than the difference between ‘John is the father of James’ and ‘James is the son of John.’ ”18 The view of the daily eastward rotation of the earth (relative to the sun and all other stars in the sky) is merely more economical (for only one object, earth, is in relative motion) than the view of the daily westward revolution of the sun and of the myriad stars of the sky (relative to the earth).
The genius of relativity, writes, “Take two bodies, the sun and the earth, for instance. The motion we observe is again relative. It can be described by connecting [considering] the c.s. [coordinate system, relative center] with either the earth or the sun. From this point of view, Copernicus’ great achievement lies in transferring the c.s. from the earth to the sun. But as motion is relative and any frame of reference [center] can be used, there seems to be no reason for favoring one c.s. [relative center] rather than the other.”19
Hicetas (ca. 400–335 bce), a Pythagorean, realized the relativity of motion before Galileo, Bishop Berkeley (1685–1753), Ernst Mach (1838–1916), and Einstein: “The Syracusan Hicetas, according to Theophrastus, believes that the sky, the sun, the moon, the stars and generally all things that lie above are motionless and that nothing in the cosmos moves, except earth; as it rotates around its axis with high speed, it causes the same effect that would have been caused if earth were at rest and the sky moved [rotated].”20 Hicetas’s student, Ecphantus (ca. fourth century bce), adds another important detail, “like a wheel, the earth rotates around its axis from west to east.”21 Of course, everyone (then and now) knows that the sun, moon, and stars (the sky in general) appear to rotate from east to west. This implies that Hicetas and his student understood yet another aspect of the relativity of motion: not only that things can be viewed in motion with respect to one another but also that their relative motions are in opposite directions. Hicetas was cited by Copernicus in his On the Revolutions of the Heavenly Spheres. Newton, too, in his The System of the World “attributes to antiquity (correctly) . . . the Copernican revolution: ‘It was the opinion of the ancient philosophers that in the highest parts of the world the stars remain fixed and motionless, and that the Earth turns around the Sun.’ ”22
Mach’s Principle
In criticizing the absoluteness of space, time, and motion of Newtonian physics, Mach, like Berkeley before him, held that (1) all motion is relative.23 Mach, however, accepted one of the tenets of Newton’s law of universal gravitation, that (2) an object’s motion is affected by the gravity it experiences from all other objects in the universe instantly. Einstein coined ideas (1) and (2) as Mach’s principle and found them inspiring in the development of his relativity.24 But in the end, Einstein embraced only (1).25 He rejected (2), because in relativity the fastest that communication is postulated to travel is only at the speed of light, not instantly. (But don’t dismiss instant interaction just yet; wait until the section on “Quantum Entanglement” in chapter 8.)
I find curiously interesting the following similarity between Plato’s explanation of motion and Mach’s idea (2). Both Plato and Mach rejected atoms and the void, and accepted the plenum (that all space contains matter). Plato explained motion as the rotation of a wheel. Since there is no void, he thought everything is connected (either via direct contact or via matter in-between). Thus, an object can move by pushing its surrounding matter—which is in direct contact with it—while, simultaneously, that matter is pushing its own surrounding matter (and that matter its own), causing everything in the universe to instantly interchange position and direction and move much “like a rotating wheel”26 (where all points/matter on it move/s simultaneously). Hence, every time something is moving, everything in the universe is simultaneously moving with it—for example, if I spin about my body’s axis, everything in the universe spins simultaneously with me, too. Motion is communicated instantly to all objects however far they are, Plato implies, as is Mach’s idea (2). Pythagoreans certainly influenced Plato, who plausibly influenced Mach, who certainly influenced Einstein.
Epicurus (chapter 13), however, who accepted atoms and the void as a theory of matter, derided Plato’s explanation. There are those who “maintain that water yields . . . to the . . . fish that push against it, because they leave spaces behind them into which the yielding water can flow together. In the same way, they [Plato, Aristotle and others who taught the plenum and rejected the void as a means of motion] suppose, o
ther things can move by mutually changing places [as in the analogy of a rotating wheel], although every place remains filled. [But] how can the fish advance till the water has given way? And how can the water retire when the fish cannot move? . . . [The alternative:] . . . things contain an admixture of vacuity whereby each is enabled to make the first move.”27
Conclusion
Within the context of modern physics “things are numbers” but also abstract forms indeed. What’s more, many apparently unrelated things (phenomena) have already been unified; they are found to obey the same fundamental mathematical equation and thus the same natural law (e.g., the electroweak unification). These findings point clearly to the subtle cosmic interconnection (of mathematical nature) anticipated by the Pythagoreans. But in addition to the aid of mathematics, to find the Logos (reason) of such inconspicuous connections, one needs to be unconventional, to be able to unite diverse fields of knowledge, and to focus a keen eye on the elusive. For only then may one unveil the common characteristics that different phenomena have in all of nature’s changes, the perceptible but also the discreet.
* * *
1Aristotle, Metaphysics 987b22. Or see Erwin Schrödinger, Nature and the Greeks and Science and Humanism (Cambridge: Cambridge University Press, 1996), 35.
2Diogenes Laërtius 8.46. See G. S. Kirk, J. E. Raven, and M. Schofield, The Presocratic Philosophers (Cambridge: Cambridge University Press, 1983), Kindle Locations 9294–9295.
3Aëtius 2.1.1, trans. Demetris Nicolaides. See Greek book Βας. Α. Κύρκος (Vas. A. Kyrkus), Οι Προσωκρατικοί: Οι Μαρτυρίες και τα Αποσπάσματα τόμος Α (The Presocratics: Testimonies and Fragments, vol. A) (Αθήνα: Εκδόσεις Δημ. Ν. Παπαδήμα, 2005), (Athens: Publications Dem. N. Papadima, 2005), 247.
4Aristotle, On the Heavens 290b12, trans. Demetris Nicolaides. See also Kirk, Raven, and Schofield, Presocratic Philosophers, Kindle Locations 9131–9133.
5Johannes Kepler, The Harmonies of the World, quoted in George N. Gibson and Ian D. Johnston, “New Themes and Audiences for the Physics of Music,” Physics Today 55, no. 1 (January 2002): 44.
6Arnold Sommerfeld quoted in Gibson and Johnston, “New Themes and Audiences for the Physics of Music,” Physics Today 55, no. 1 (January 2002): 43.
7The Elegant Universe: Part 1, PBS, October 28, 2003.
8Plato, Timaeus 53 c – 57 e.
9Aristotle separated heaven from the earth but we know today heaven and earth are made from the same stuff; and that, for a civilization on an exoplanet, our earth is in their heaven just as their “earth” (exoplanet) is in our heaven.
10Plato, Republic, Book V to Book VII; Bertrand Russell, The History of Western Philosophy (New York: Simon & Schuster, 1945), 119–132; Karl R. Popper, Conjectures and Refutations: The Growth of Scientific Knowledge (London: Routledge, 1989), 90–96.
11Schrödinger, Nature and the Greeks, 122; Werner Heisenberg, Physics and Philosophy: The Revolution in Modern Science (New York: Harper Torchbooks, 1962), 45–46.
12Popper, Conjectures and Refutations, 87.
13Schrödinger, Nature and the Greeks, 45.
14Ibid.
15Russell, History of Western Philosophy, 214.
16Ibid., 217.
17Albert Einstein, Relativity: The Special and General Theory [New Kindle Edition with Readable Equations] (Kindle Locations 615–616).
18Russell, The History of Western Philosophy, 540; Isaac Asimov, Understanding Physics (Dorset Press, 1988), vol. II, 117–119.
19Albert Einstein and Leopold Infeld, The Evolution of Physics (London: Cambridge University Press, 1938), 222–223.
20KIK. Acad. Pr. II 39, 123, trans. Demetris Nicolaides. See Greek book Προσωκρατικοί (Presocratics), vol. 13 (Athens, Greece: Kaktos, 2000), 73, https://www.kaktos.gr/001110 (accessed July 14, 2019).
21Aëtius 3.13.3, trans. Demetris Nicolaides. See Greek book Προσωκρατικοί (Presocratics), vol. 13 (Athens, Greece: Kaktos, 2000), 73, https://www.kaktos.gr/001110 (accessed July 14, 2019).
22Isaac Newton quoted in Carlo Rovelli, Reality Is Not What It Seems (New York: RiverHead Books, 2017), 72 (Kindle ed.).
23Popper, Conjectures and Refutations, 169, 171–172.
24Ibid., 172.
25Albert Einstein, Relativity: The Special and General Theory [New Kindle Edition with Readable Equations] (Kindle Location 751).
26Plato, Timaeus 79 c; see also 80 c, 79 b, 52 e, 57 d.
27Lucretius, On the Nature of the Universe 1.373–384, trans. R. E. Latham (London: Penguin Books, 2005), 19.
7
The Changing Universe
Introduction
Everything is constantly changing, and nothing is ever the same, Heraclitus of Ephesus (ca. 540–ca. 480 bce) proposed, and in accordance with Logos, the intelligible eternal law of nature. Thus, everything is in a state of becoming (in the process of forming into something) instead of being (reaching or already being in an established final state beyond which no more change will take place). This means that things, permanent things, no longer exist—for they contradict his theory of constant change—only events and processes exist. His doctrine has found strong confirmation in modern physics, for, according to it, absolute restfulness and inactivity are impossibilities. Points in Einstein’s four-dimensional space-time continuum are events, and so are the quarks and leptons—for, unlike in deterministic Newtonian physics, matter in probabilistic quantum physics lost its permanence and identity because of the Heisenberg uncertainty principle. Moreover, all happenings, evidence suggests, are consistent with a single universal law.
Strife and Harmony
For Heraclitus everything in nature is characterized by opposites that are struggling. “We must recognize that war [the competition between opposites] is common, strife is justice, and that all things happen according to strife and necessity.”1 So without strife, as Homer had wished, the universe would be led to its destruction because events and processes could not have existed without some force that promotes change: “Heraclitus criticizes the poet who said, ‘would that strife might perish from among gods and men’ [Homer, Iliad 18.107]; for there would not be harmony without high and low notes, not living things without female and male, which are contraries.”2 Hence, “strife is justice” because change, for Heraclitus, is caused by the strife of the opposites. Without strife, change would not occur.
Now, like Anaximander, Heraclitus, too, requires cosmic justice by such strife. In fact, he argues that not only is absolute dominance not allowed by any of the opposites but quite the reverse, that harmony is born from their strife. “Attunement [harmony] of opposite tensions, like that of the bow and the lyre.”3 This harmony of strife is the result of a subtle underlying unity shared by the opposites; generally, it is the result of the common characteristics that different things have. For example, the property of mass is common to both the different objects the earth and the sun. As a result (according to Newton’s third law discussed later), each body attracts the other with the same strength! Discovering and understanding such unity is understanding Logos, but to manage this is difficult because “nature loves to hide.”4 Nonetheless, Newton and several scientists thereafter have managed it.
Action-Reaction
Newton’s action-reaction law, his third law of motion, describes the strife of opposite forces but also their subtle unity and harmony. According to it, for every action force there is an equal reaction force in the opposite direction. For example, the force exerted on a nail by a hammer has the same strength and is in opposite direction to the force exerted on the hammer by the nail. The competing opposites are the competing forces acting in opposite directions, but they do so with equal strength—so their unity in strength is mathematically expressible, in other words, action force = reaction force. A force (the action) cannot exist by itself; it exists only in relation to its opposite (the reaction)—thus, Homer’s wish to eliminate strife is unrealizable in Newton
ian physics. In fact, generally in physics “physical action always is inter-action, it always is mutual.”5
Analogously, in Newtonian gravity, the earth is attracting you downwardly with the same exact force as you are attracting the earth upwardly! Your weight is the strength of this mutual force. The earth and sun attract each other with forces of equal strength (unbelievable but true) and opposite directions, and as a result both celestial bodies move harmoniously through space and time. Both bow and lyre obey Newton’s third law, too. In a bow, the cord is pulling each of the two limps (the flexible upper and lower parts of a bow) in one direction—the action force, which is along the cord and toward its midpoint. Whereas the limps respond by pulling the cord in the opposite direction—the reaction force, which is also along the cord but away from its midpoint. Furthermore, action and reaction are forces of equal strength. So the bow’s apparent rest is really the result of the constant strife between opposite equal tensions, the action and reaction. Newton’s third law applies even while the cord is being drawn in order to shoot an arrow (or as the cord is being released and shooting the arrow); or as the strings of lyre are at rest, or as they are plucked, producing their sweet notes of music. Even more impressive is that the apparent inactivity, at the macroscopic level, of the bow or lyre at rest (or any other object), is, at the microscopic level, really a frantic and endless activity of particle exchange; for force, on the microscopic level, is really an eventful process. And constant change, even the imperceptible, is indeed a fact.
Force in Quantum Theory
In Search of a Theory of Everything Page 8
