Reality Is Not What It Seems: The Journey to Quantum Gravity
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Science is a continual exploration of ways of thinking. Its strength is its visionary capacity to demolish preconceived ideas, to reveal new regions of reality, and to construct new and more effective images of the world. This adventure rests upon the entirety of past knowledge, but at its heart is change. The world is boundless and iridescent; we want to go and see it. We
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Science is made up of experiments, hypotheses, equations, calculations, and long discussions; but these are only tools, like the instruments of musicians. In the end, what matters in music is the music itself, and what matters in science is the understanding of the world that science provides.
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For thousands of years, they had given themselves answers that all resembled one another: answers that referred to elaborate stories of spirits, deities, imaginary and mythological creatures, and other such similar things. From cuneiform tablets to ancient Chinese texts; from hieroglyphic writing in the pyramids to the myths of the Sioux; from the most ancient Indian texts to the Bible; from African stories to those of aboriginal Australians, it was all a colorful but basically quite monotonous flow—of Plumed Serpents and Great Cows, of irascible, litigious, or kindly deities who create the ...more
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The Milesians understand that by shrewdly using observation and reason, rather than searching for answers in fantasy, ancient myths, or religion—and above all by using critical thought in a discriminating way—it is possible to repeatedly correct our worldview and to discover new aspects of reality that are hidden to the common view.
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This new approach to knowledge works quickly and impressively. Within a matter of a few years, Anaximander understands that Earth floats in the sky and the sky continues beneath Earth; that rainwater comes from the evaporation of water on Earth; that the variety of substances in the world must be susceptible to being understood in terms of a single, unitary, and simple constituent, which he calls apeiron, the indistinct; that animals and plants evolve and adapt to changes in the environment, and that man must have evolved from other animals. Thus gradually founding the basis of a grammar for ...more
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This is the immense legacy of Miletus, cradle of philosophy, of the natural sciences, and of geographical and historical studies. It is no exaggeration to say that the entire scientific and philosophical tradition, Mediterranean and then modern, has a crucial root in the speculations of the thinkers of Miletus, in the sixth century BCE.1
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Together, these two thinkers have built the majestic cathedral of ancient atomism. Leucippus was the teacher. Democritus, the great pupil who wrote dozens of works on every field of knowledge, was deeply venerated in antiquity, which was familiar with these works. “The most subtle of the Ancients,” Seneca called him.3 “Who is there whom we can compare with him for the greatness, not merely of his genius, but also of his spirit?” asks Cicero.4
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The idea of Democritus’s system is extremely simple: the entire universe is made up of a boundless space in which innumerable atoms run. Space is without limits; has neither an above nor a below; is without a center or a boundary. Atoms have no qualities at all, apart from their shape. They have no weight, no color, no taste. “Sweetness is opinion, bitterness is opinion; heat, cold and color are opinion: in reality only atoms, and vacuum.”5
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Just as by combining letters of the alphabet in different ways we may obtain comedies or tragedies, ridiculous stories or epic poems, so elementary atoms combine to produce the world in its endless variety. The metaphor is Democritus’s own.6
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On this foundation Democritus wrote dozens of books articulating a vast system, dealing with questions of physics, philosophy, ethics, politics, and cosmology. He writes on the nature of language, on religion, on the origins of human societies, and on much else besides. (The opening of his Little Cosmology is impressive: “In this work I treat of all things.”) All these books have been lost.
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If, in some cataclysm, all scientific knowledge were to be destroyed, and only one sentence passed on to the next generation of creatures, what statement would contain the most information in the fewest words? I believe it is the atomic hypothesis, or the atomic fact, or whatever you wish to call it, that all things are made of atoms—little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another. In that one sentence you will see an enormous amount of information about the world, if just a ...more
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Therefore we cannot think that matter is made of points without extension, because no matter how many of these we manage to put together, we never obtain something with an extended dimension. The only possibility, Democritus concludes, is that any piece of matter is made up of a finite number of discrete pieces that are indivisible, each one having finite size: the atoms.
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But is this really the correct solution in the real world? Do arbitrarily short strings really exist? Can we really cut a piece of string an arbitrary number of times? Do infinitely small amounts of time exist? This is precisely the problem that quantum gravity will have to face.
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Whether this abstract argument is correct or not, its conclusion—as we know today—contains a great deal of truth. Matter does indeed have an atomic structure.
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I will speak a lot about this young man in the rest of this book, and about the three articles he sent to the most prestigious physics journal of the time, the Annalen der Physik. The first of these articles contained the definitive proof that atoms exist and calculated their dimensions, solving the problem posed by Leucippus and Democritus twenty-three centuries earlier.
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I often think that the loss of the works of Democritus in their entirety is the greatest intellectual tragedy to ensue from the collapse of the old classical civilization.
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Take a look at the list of his works in the footnote; it is difficult not to be dismayed, imagining what we have lost of the vast scientific reflections of antiquity.* We have been left with all of Aristotle, by way of which Western thought reconstructed itself, and nothing by Democritus. Perhaps if all the works of Democritus had survived, and nothing of Aristotle’s, the intellectual history of our civilization would have been better.
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The closure of the ancient schools such as those of Athens and Alexandria, and the destruction of all the texts not in accordance with Christian ideas was vast and systematic, at the time of the brutal antipagan repression following from the edicts of Emperor Theodosius, which in 390–391 declared that Christianity was to be the only and obligatory religion of the empire. Plato and Aristotle, pagans who believed in the immortality of the soul or in the existence of a Prime Mover, could be tolerated by a triumphant Christianity. Not Democritus.
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Here is a passage in which Lucretius provides a “living proof” of the notion of atoms: This process is illustrated by an image of it that is continually taking place before our very eyes. Observe what happens when sunbeams are admitted into a building and shed light on its shadowy places. You will see a multitude of tiny particles mingling in a multitude of ways in the empty space within the light of the beam, as though contending in everlasting conflict, rushing into battle rank upon rank with never a moment’s pause in a rapid sequence of unions and disunions. From this you may picture what ...more
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Einstein resuscitated the “living proof” presented by Lucretius, and probably first conceived of by Democritus, and made it solid by translating it into mathematical terms, thus managing to calculate the size of the atoms.
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The Catholic Church attempted to stop Lucretius: in the Florentine Synod of December 1516, it prohibited the reading of Lucretius in schools. In 1551, the Council of Trent banned his work. But it was too late. An entire vision of the world that had been swept away by medieval Christian fundamentalism was reemerging in a Europe that had reopened its eyes. It was not just the rationalism, atheism, and materialism of Lucretius that were being proposed in Europe. It was not merely a luminous and serene meditation on the beauty of the world. It was much more: it was an articulate and comp...
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There is a feeling of deep universalism, in the wake of the splendid words of Democritus: “To a wise man, the whole earth is open, because the true country of a virtuous soul is the entire universe.”25
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The physics of Aristotle is still rough; it is not quantitative (we cannot compute with it), but it is coherent and rational, and it enables correct qualitative predictions to be made. It is not for nothing that it remained for centuries the best available model for understanding motion.1
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left a momentous legacy to the entire world: the discovery of the theoretical utility of mathematics: “Number”—he is said to have asserted—“governs forms and ideas.”2
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Driven by this conviction, it was Plato who posed the momentous question: the question out of which, after a long detour, modern science would emerge. Of his disciples who studied mathematics, he asked if they could find the mathematical laws followed by the celestial bodies visible in the heavens.
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We know of the triumphs of this science thanks to a single book, the only one to have survived: the Almagest of Ptolemy.
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But the time is now ripe, and more than a thousand years after Ptolemy, Copernicus is able to make the leap forward that generations of Indian, Arab, and Persian astronomers had not been able to make: not simply learning, applying, and adding small ameliorations to the Ptolemaic system, but thoroughly improving it—with the courage to change it in depth. Instead of describing heavenly bodies turning around Earth, Copernicus writes a sort of revised and corrected version of Ptolemy’s Almagest, in which the sun is at the center and Earth, together with the other planets, runs around it.
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In this way—Copernicus hopes—the calculations would work even better. In reality, they did not work much better than those of Ptolemy; in fact, in the end, they turned out to work less well.
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While Kepler in the cold north calculates movements in the sky, in Italy it is with Galileo Galilei that the new science begins to take off. Exuberant, Italian, polemical, argumentative, highly cultured, exceptionally intelligent, and overflowing with inventiveness, Galileo gets sent from Holland a new invention—the telescope—and makes a gesture that changes human history. He points it toward the sky.
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For the first time in the history of mankind, an experiment is made.
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Experimental science begins with Galileo.
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We call “gravity” the force causing objects to fall. Newton understands that it is this same gravity that makes the little moon turn around Earth. Without this gravity, it would run away in a straight line. But then also the real moon must orbit Earth because of gravity! And the moons that orbit Jupiter are attracted by Jupiter, and the planets that turn around the sun are attracted by the sun! Without this attraction, every celestial body would move in a straight line. So the universe, then, is a large space where bodies attract one another by means of forces; and there is a universal force, ...more
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Newton knew that his equations do not describe all the forces that exist in nature.
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The first surprise is that almost all phenomena we see are governed by a single force, other than gravity: the force that today we call “electromagnetism.”
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The second and biggest surprise, crucial to the story I’m telling, is that understanding this force requires an important modification to the world of Newton: the modification out of which modern physics was born, and the most important notion to keep in focus, to understand the rest of this book: the notion of “field.”
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Without knowing mathematics, he writes one of the best books of physics ever written, virtually devoid of equations. He sees physics with his mind’s eye, and with his mind’s eye creates worlds. James Clerk Maxwell is a rich Scottish aristocrat, and one of the greatest mathematicians of the century. Despite being separated by a gulf in intellectual style as well as social origin, they succeed in understanding each other—and, together, combining two kinds of genius, they open the way to modern physics.
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His intuition is this: we must not think of forces acting directly between distant objects, as Newton presumed. We must instead think that there exists an entity diffused throughout space that is modified by electric and magnetic bodies and that, in turn, acts upon (pushes and pulls) the bodies. This entity, whose existence Faraday intuits, is today called the “field.”
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Thus two distant charged objects do not attract or repel each other directly, but only via the medium interposed between them.
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Newton is deeming his very own masterwork to be absurd, the very same work that was to be praised for centuries to come as the ultimate achievement of science! He understands that behind the action at a distance of his theory, there must be something else, but he has no idea what, and leaves the question . . . “to the Consideration of my Readers”!
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Today, Maxwell’s equations are used daily to describe all electric and magnetic phenomena, and to design antennae, radios, electric engines, and computers. And this is not all: these same equations are needed to explain how atoms function (they are held together by electrical forces), and why the particles of the material that forms a stone adhere together, or how the sun works. They describe an amazing number and range of phenomena. Almost everything that we witness taking place, with the exception of gravity and little else besides, is well described by Maxwell’s equations.
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But there is more. There is still what is perhaps the most beautiful success of science: Maxwell’s equations tell us what light is.
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Light is thus nothing more than a rapid vibration of the spiderweb of Faraday’s lines, which ripple like the surface of a lake as the wind blows. It isn’t true that we “do not see” Faraday lines. We only see vibrating Faraday lines. To “see” is to perceive light, and light is the movement of the Faraday lines. Nothing leaps from one location in space to another without something transporting it. If we see a child playing on the beach, it is only because between him and ourselves there is this lake of vibrating lines that transport his image to us. Is the world not marvelous?
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Our entire current technology is founded on the use of a physical thing—electromagnetic waves—that was not discovered empirically: it was predicted by Maxwell, simply by searching for the mathematical description accounting for the intuition Faraday got from bobbins and needles. This is the outstanding power of theoretical physics.
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The theories of Newton and of Maxwell appear to contradict each other in a subtle way. Maxwell’s equations determine a velocity: the velocity of light. But Newton’s mechanics are not compatible with the existence of a fundamental velocity, because what enters Newton’s equations is acceleration, not velocity. In Newton’s physics, velocity can only be velocity of something with respect to something else.
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Einstein has claimed that he was not put on the right track by any experiments, but only by reflecting on the apparent contradiction between Maxwell’s equations and Newton’s mechanics. He asked himself whether there was a way of rendering Newton’s and Galileo’s core discoveries and Maxwell’s theory consistent.
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In doing so, Einstein arrives at a stupefying discovery.
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Between the past and the future of an event (for example, between the past and the future for you, where you are, and in the precise moment in which you are reading), there exists an “intermediate zone,” an “extended present”; a zone that is neither past nor future. This is the discovery made with special relativity.
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This is why it is impossible to hold a smooth conversation between here and Mars. Say I am on Mars and you are here; I ask you a question and you reply as soon as you’ve heard what I said; your reply reaches me a quarter of an hour after I had posed the question. This quarter of an hour is time that is neither past nor future to the moment you’ve replied to me. The key fact that Einstein understood is that this quarter of an hour is inevitable: there is no way of reducing it. It is woven into the texture of the events of space and of time: we cannot abbreviate it, any more than we can send a ...more
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A first result of this restructuring is that as space and time fuse together in a single concept of spacetime, so the electric field and the magnetic fields fuse together in the same way, merging into a single entity that today we call the “electromagnetic field.”
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There is another implication of the theory, freighted with heavy consequences. The concepts of “energy” and “mass” get combined in the same way as time and space, electric and magnetic fields are fused together, in the new mechanics.
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