Black Holes: Challenges in the Quest for Sameness
A black hole is a supermassive, dense, point-like object with immense gravity. The event horizon is the invisible spherical boundary around it, from within which nothing, not even light, can escape. Thus, the region in space enclosed by the event horizon is black. Since light can’t escape, events that might be occurring within a black hole can’t be seen by us. Consequently, if some kind of civilization existed there, its citizens could see us (as light from us enters the back hole), but we couldn’t see them. Black holes exist in every galactic center, although when they were first predicted by Einstein’s general relativity, Einstein himself dismissed their existence as mere mathematical artifacts. The first-ever image of a black hole was released in the spring of 2019.
Now, a black hole is a tiny object with enormous mass—thus both quantum mechanics and relativity apply. But the properties of black holes are different for each theory.
For example, according to relativity, a book falling into a black hole is crossing a calm event horizon as if it were nothing special to pass through. Eventually, the book is ripped into pieces by the immense gravity and is crushed at the infinitely dense center of the black hole. What once was a distinguishable book is now just matter indistinguishable from all other matter already there. And all information about it is thereafter lost forever.
But the falling book, according to quantum mechanics, is crossing a highly energetic event horizon, a region of fire that burns the book as it goes through. Still though, some energy is radiated10 to us from the region just outside the black hole that amazingly contains subtle information about the fate of the book and all its contents while inside the black hole. Information therefore is preserved.
These conclusions clearly clash: if information is lost, quantum theory is fundamentally wrong, but if information is preserved, it is general relativity that is fundamentally flawed. This contradiction is known as the information paradox, and it is still an open question. General relativity and quantum theory don’t see eye to eye in explaining black holes, but a TOE should lift the contradiction.
The Sage
Thales was regarded as one of the seven sages of the ancient Greek world and the wisest among them. For this he was offered a golden cup, which he respectfully declined by offering it to another of the sages, who offered it to another until the cup was again returned to Thales. He then dedicated it to the god Apollo at Delphi. Thales, a humble man, is credited (among several other Greeks) with the famous aphorism “Know thyself.” He was a philosopher, scientist, astronomer, mathematician, politician, and even a theologian known best for his belief in hylozoism, that “all things are full of gods.”11
But he was also a practical man. As an engineer, for example, he aided the army of King Croesus of Lydia in crossing the Halys River by digging a deep trench in the shape of a crescent and diverting its waters. It was a Herculean feat indeed. The waters initially flowed by one side of the army but later diverted; they flowed by the opposite side. Through his observations of the night sky, he discovered the stars of the Little Dipper (Ursa Minor), which includes the North Star, Polaris, and used them to teach navigation. He also wrote treatises on various calendars such as on the spring and fall equinoxes, on the summer and winter solstices, on the phases of the moon, on solar eclipses, and on the rising and setting of certain stars such as the Pleiades.
While in Egypt Thales is said to have computed the height of a pyramid by first noticing that at a certain time of day his own shadow was as long as his height. He then concluded that the length of the pyramid’s shadow at that same time of day was, according to the law of similar triangles, equal to the pyramid’s actual height. While on land and through the use of geometry, he was able to calculate his distance from a ship at sea. Furthermore, he estimated correctly the angular size of the sun and of the moon relatively to the angular size of their apparent orbit in the sky to be equal to 1/720.12 Angular size of an object is the angle created from your eye to two diametrically opposite points on the object. Say the dot, •, represents the eye, letter I, the object, and that they are situated like so, • I, from each other. The angular size of I is the angle depicted in the following geometry: •
Thales was also known for his weather predictions, a skill proven valuable in teaching his fellow citizens an important lesson about life regarding their negative attitude toward philosophy. In spite of all his knowledge (practical and abstract) and all his wisdom, Thales is said to have been poor. And because of his poverty, some people criticized philosophy by calling it a useless and impractical way of life. According to one account, “As Thales was studying the stars and looking up . . . he fell into a well. A Thracian servant girl with a sense of humor . . . made fun of him for being so eager to find out what was in the sky that he was not aware of what was in front of him right at his feet.”14 But had the great Dante Alighieri (1265–1321) witnessed the incident he would not, I am certain, have made fun of Thales but would, I am still certain, have responded to the girl by saying:
The heavens are calling you, and wheel around you,
Displaying to you their eternal beauties,
And still your eye is looking on the ground.15
Hands-on Thales responded similarly, not in words but through a practical action. “He perceived by studying the sky that there would be a good olive harvest. While it was yet winter and he had some money, he put down deposits on all the olive presses in Miletus [his hometown] and Chios [a neighboring island] for a small sum, paying little because no one bid against him [as it was way too early for anyone to worry about the next harvest that would occur during the next autumn and winter]. When harvest time came and everyone needed the presses right away, he charged whatever he wished and made a good deal of money—thus demonstrating that it is easy for philosophers to get rich if they wish, but that is not what they care about.”16 What they do care about is the rational critique of nature.
One phenomenon that was analyzed rationally was the annual overflow of the waters of the Nile River—an unexpected phenomenon within the context of the generally dry Mediterranean summers when it begins to occur—that puzzled several Greek thinkers including Anaxagoras, Democritus, Herodotus, and Euripides. The occurrence was explained in a naturalistic way first by Thales, who ascribed seasonal northerly winds as its cause that hindered the river from emptying into the Mediterranean Sea and forced its waters to spill over its banks. Ancient Egyptians attributed the flooding to the tears of their mourning goddess Isis over the loss of her husband, Osiris. Today we know that the Nile’s overflow is due to seasonal precipitation (mainly rain) on the highlands of Ethiopia (south of Egypt), where one of the sources of the Nile can be traced. Incidentally, Democritus’s explanation was similar to ours.17 That Thales was wrong is not as important as is his attempt to offer a rational explanation for this natural occurrence. Similarly, Thales and the other natural philosophers in general treated eclipses as natural phenomena, whereas the Babylonians viewed them as omens, despite the fact that the latter kept fairly accurate records for their repeated cycles. Comets, too, were generally thought of as bad omens, but not by the natural philosophers. Anaxagoras and Democritus, for example, thought that comets “are a conjunction of planets that, when coming nea
r each other, create the illusion that they touch,”18 an explanation, which although incorrect, is logical because it explains why a comet appears to be a strip-like light in the sky instead of point-like, as planets and stars are. Today we know that the strip-like appearance is due to a comet’s tail. It is created from the sublimation of some of its ices, while a comet approaches the sun in its elliptical orbit around it.
Naturalistic interpretations of nature were the approach of all natural philosophers and remain the approach of modern scientists.
Conclusion
By reasoning that all things are ephemeral transformations of one primary substance of matter, Thales attempted to attribute an all-encompassing, common, and unifying principle to all the phenomena of nature, the main goal of physicists today, as well as to understand a notion of great importance in science—namely, change. The concept of change (and the degree of change) has been hotly debated for centuries. Some have accepted it as self-evident, and others have flatly denied it as an illusion. Consensus has yet to be found. Every scientist, past and present, has looked to identify a permanent principle in all of the apparent changes. What that principle might be has varied from one scientific theory to another and from one epoch to the next.
Thales was more of a practical man who accepted change undeniably. His student Anaximander was practical but also an abstract thinker. His primary substance of matter was imperceptible and although he, too, accepted change as self-evident, he also required that change in nature obeys laws and happens with measure for only then cosmic justice is preserved. But in all the conspicuous changes, he reasoned, something subtle must endure. He called it apeiron.
* * *
1Aristotle, Metaphysics 983b6–13, 17–27. Or see Daniel W. Graham, The Texts of Early Greek Philosophy: The Complete Fragments and Selected Testimonies of the Major Presocratics (Cambridge: Cambridge University Press, 2010), 29 (text 15); Aëtius 1.31, 1.10.12. Or see Graham, Texts of Early Greek Philosophy, 29 (text 16); Simplicius, Physics 23.21–29. Or see Graham, Texts of Early Greek Philosophy, 29 (text 17).
2Aristotle, Metaphysics 983b6–13, 17–27. Or see Graham, Texts of Early Greek Philosophy, 29 (text 15).
3Aëtius 1.31, 1.10.12. Or see Graham, Texts of Early Greek Philosophy, 29 (text 16).
4Ibid.
5Ibid.; Aristotle, Metaphysics 983b6–13, 17–27. Or see Graham, Texts of Early Greek Philosophy, 29 (text 15).
6Stephen Hawking, A Brief History of Time: From the Big Bang to Black Holes (New York: Bantam Books, 1988), chap. 5.
7Charles W. Misner, Kip S. Thorne, and John Archibald Wheeler, Gravitation (Princeton, NJ: Princeton University Press, 2017), 5.
8Brian Greene, The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory (New York: W. W. Norton & Company, 1999), 144; Michio Kaku and Jennifer Trainer Thompson, Beyond Einstein: The Cosmic Quest for the Theory of the Universe (New York: Anchor Books, 1995).
9Carlo Rovelli, Reality Is Not What It Seems (New York: RiverHead Books, 2017) (Kindle ed.); Carlo Rovelli, Seven Brief Lessons on Physics (New York: RiverHead Books, 2016) (Kindle ed.).
10Hawking, A Brief History of Time, chap. 7 (“Black Holes Ain’t So Black”).
11Aristotle, On the Soul 411a7–8, trans. Graham, Texts of Early Greek Philosophy, 35 (text 35).
12Diogenes Laërtius 1.24. Or see Graham, Texts of Early Greek Philosophy, 21 (text 1).
13Pliny, Natural History 2.53. Or see Daniel W. Graham, The Texts of Early Greek Philosophy: The Complete Fragments and Selected Testimonies of the Major Presocratics (Cambridge: Cambridge University Press, 2010), 25 (text 5).
14Plato, Theaetetus 174a4–8, trans. Graham, Texts of Early Greek Philosophy, 25 (text 7).
15Dante, Divine Comedy, trans. BookCaps (BookCaps Study Guides, 2013), Kindle Locations 10900–10901.
16Aristotle, Politics 1259a5–21, trans. Graham, Texts of Early Greek Philosophy, 25 (text 8).
17Diodorus of Sicily 1.39.1–3. Or see Graham, Texts of Early Greek Philosophy, 563 (text 84).
18Aristotle, Meteorology 342b25, trans. Demetris Nicolaides. Or see Graham, Texts of Early Greek Philosophy, 303 (text 48).
4
Cosmic Justice
Introduction
Anaximander (ca. 610–ca. 540 bce) thought water is a bad idea for a primary substance of the universe because it’s not neutral—it has an opposite, fire. And opposites destroy; they don’t create one another. He taught that everything is generated from the apeiron:1 a timeless, neutral substance, encompassing the universe and constantly transforming into competing transient opposites, but with measure to conserve the cosmic justice—without absolute dominance by either opposite. In physics, it’s ubiquitous energy that’s constantly transforming into ephemeral competing opposites—matter and antimatter—with measure. Curiously, however, matter (“water”) is more plentiful than antimatter (“fire”). Why? Nobody knows. Where’s the cosmic justice? The Higgs boson, too, is strikingly similar to the apeiron.
The Apeiron
While itself intangible, the apeiron transforms into all concrete things of every day. Thus, it is the true beginning of everything, animate and inanimate. It is also neutral, having no competing opposite. But it transmutes into opposites in struggle with one another—water versus fire, hot versus cold, wet versus dry, light versus darkness, sweet versus sour, and so on. The unjust dominance of one opposite over the other is ephemeral, for eventually it is rectified at annihilation; then, neutralized, both opposites transform again into the neutral apeiron. And since eventually the effects of one opposite cancel those of the other, their endless creations and annihilations neither add anything to the apeiron nor subtract. Thus, even through its transformations, the apeiron remains eternally conserved. In modern physics, it is energy that is conserved through its transformations into competing opposites, that of matter and antimatter, and, like the apeiron, energy is also limitless and everywhere.
Energy and the Apeiron
In physics the notion of energy includes mass, too, since, according to Einstein’s famous equation E = mc2, from his theory of special relativity, energy (E) and mass (m) are equivalent and transmutable into each other—they are connected via the speed of light (c). Like the apeiron, energy is limitless, timeless, indestructible, and omnipresent even in “empty” space. Even more, energy causes change by continually transforming from one form to another (e.g., from light to heat) and from pure energy (e.g., light) into matter (e.g., electrons) and antimatter (e.g., antielectrons, also known as positrons). But even with these transformations, the total energy content of the universe is always constant. This is known as the law of conservation of energy. One can neither add more energy to the universe nor subtract any from it. Conservation laws, of which there are several in physics, ensure that changes in nature occur with measure, as in the theory of Anaximander. Measure, in modern physics, means that in all of nature’s changes some things or properties remain numerically equal (e.g., energy). This equality (this measure) is in basic agreement with the view of Anaximander, who (as we’ll see), to save nature and keep cosmic justice, reasoned that neither of two opposites could ever dominate totally. Now, to appreciate further the notion of measure and the similarities between energy and the apeiron, we need to first understand matter and antimatter since these, in modern physics, are opposites in struggle with each other, created from energy, and into energy once again they return.
Every particle of matter has a corresponding antiparticle of antimatter. A particle (like the negatively charged electron) and its antiparticle (the positron, which is really a positively charged electron) have the same mass and opposite electric charge (of equal magnitude). They are regarded as competing opposites since when they meet they annihilate each other by transforming completely into pure energy—like Anaximander’s water and fire that neutralize each other and transform into the apeiron. Furthermore, as opposites, not only do they compete—interact via the forces of nature they ob
ey—but, since their effects cancel each other out, they compete with measure, by obeying conservation laws such as the conservation of energy.
For example, an electron and its competing opposite, a positron, can be created out of energy, interact—they initially move apart but after a brief time in existence they recombine—and ultimately annihilate (neutralize, cancel) each other by converting their masses entirely back into the energy from which they came. Just like Anaximander’s opposites, which are created and annihilated from and into the apeiron. Just as the apeiron remains constant during such processes, so does the energy since, according to the law of conservation of energy, the energy content of the universe is the same before the creation of the electron-positron pair, during its existence, and after its annihilation. The energy content never changes, only the forms in which it manifests itself.
In Search of a Theory of Everything Page 3