Selections from Reality Is Not What It Seems by Carlo Rovelli
17 August 2022
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From p. 96-99:
To understand the geometry of a 3-sphere, let us return to the ordinary sphere: the surface of a ball, or Earth. To represent the surface of Earth on a plane, we can draw two disks, as is customary when drawing the continents (figure 3.11).
Notice that an inhabitant of the Southern Hemisphere is in a certain sense "surrounded" by the Northern Hemisphere, since in whichever direction he goes to exit his hemisphere, he will always arrive in the other one. But the contrary is obviously true as well: each hemisphere "surrounds," and is surrounded by, the other. A 3-sphere may be represented in a similar fashion, but with everything given an additional dimension: two balls stuck together all along their surfaces (figure 3.12).
When we leave one ball, we enter into the other, just as when we leave one of the disks, in the representation of the globe, we enter into the other disk. Each ball "surrounds" and is surrounded by the other. Einstein's idea is that space could be a 3-sphere: something with a finite volume (the sum of the volume of the two balls), but without borders. The 3-sphere is the solution that Einstein proposes in his work of 1917 to the problem of the border of the universe. This article initiates modern cosmology; the study of the entire visible universe, studied at the grandest scale. From out of it will arise the discovery of the expansion of the universe; the theory of the Big Bang; the problem of the birth of the universe, and much else besides. I speak about all this in chapter 8.
There is one more observation that I would like to make about Einstein's 3-sphere. However incredible it might seem, the same idea had already been conceived by another genius, from an entirely different cultural universe: Dante Alighieri, Italy's greatest poet. In the Paradiso, the third part of his major poem, the Divine Comedy (La Divina Commedia), Dante offers a grandiose vision of the medieval world, calqued on the world of Aristotle, with the spherical Earth at its center, surrounded by the celestial spheres (figure 3.13).
Accompanied by his shining loved one, Beatrice, Dante ascends these spheres in the course of a fantastic, visionary journey up to the outermost sphere. When he reaches it, he contemplates the universe below him with its rotating heavens and Earth, very far down, at its center. But then he looks even higher—and what does he see? He sees a point of light surrounded by immense spheres of angels, that is to say, by another immense ball that in his words "surrounds and is at the same time surrounded by" the sphere of our universe! Here are Dante's verses from Canto XXVII of the Paradiso: Quest alim parte dell'Universo d'un cerchio lui comprende si come quarto lialint "This other part of the universe surrounds the first like the first surrounds the others." And in the next Canto, still on the last "circle," parendo indiuso da quel ch elli inchinde: "appearing to be enclosed by those (circles) that it encloses." The point of light and the sphere of angels are surrounding the universe, and at the same time they are surrounded by the universe! It is an exact description of a 3-sphere!
From p. 134-135:
The third discovery about the world articulated by quantum mechanics is the most profound and difficult—and one that was not anticipated by the atomism of antiquity.
The theory does not describe things as they "are": it describes how things "occur," and how they "interact with each other." It doesn't describe where there is a particle but how the particle shows itself to others. The world of existent things is reduced to a realm of possible interactions. Reality is reduced to interaction. Reality is reduced to relation.
Footnote p. 194:
"All the different elementary particles could be reduced to one united substance which could equally be called energy or matter, and none of the particles should be privileged and considered more fundamental. This point of view corresponds to Anaximander's [c.610 - c.546 BCE] doctrine, and I am convinced that in modern physics this is the correct point of view." Werner Heisenberg, Physics and Philosophy: The Revolution in Modern Science (New York: Harper & Row, 196), p. 4.
From p. 242-243:
The answer is subtle: the way in which the atoms arrange themselves is correlated with the way other atoms arrange themselves. Therefore a set of atoms can have information, in the technical precise sense described previously, about another set of atoms.
This, in the physical world, happens continuously and throughout, in every moment and in every place: the light that arrives at our eyes carries information about the objects it has played across; the color of the sea has information on the color of the sky above it; a cell has information about the virus that is attacking it; a new living being has plenty of information because it is correlated with its parents, and with its species; and you, dear reader, when reading these lines, receive information about what I am thinking while writing them, that is to say, about what is happening in my mind at the moment in which I write this text. What occurs in the atoms of your brain is not any more independent from what is happening in the atoms of mine: we communicate.
The world isn't, then, just a network of colliding atoms: it is also a network of correlations between sets of atoms, a network of real, reciprocal information between physical systems.