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There are absolute masterpieces that move us intensely: Mozart’s Requiem, Homer’s Odyssey, the Sistine Chapel, King Lear. To fully appreciate their brilliance may require a long apprenticeship, but the reward is sheer beauty—and not only this, but the opening of our eyes to a new perspective upon the world. Einstein’s jewel, the general theory of relativity, is a masterpiece of this order.
the gravitational field is not diffused through space; the gravitational field is that space itself. This is the idea of the general theory of relativity. Newton’s “space,” through which things move, and the “gravitational field” are one and the same thing.
The sun bends space around itself, and Earth does not turn around it because of a mysterious force but because it is racing directly in a space that inclines, like a marble that rolls in a funnel. There are no mysterious forces generated at the center of the funnel; it is the curved nature of the walls that causes the marble to roll. Planets circle around the sun, and things fall, because space curves.
doctoral thesis of the kind that seems completely useless. The result of Riemann’s thesis was that the properties of a curved space are captured by a particular mathematical object, which we know today as Riemann’s curvature and indicate with the letter R. Einstein wrote an equation that says that R is equivalent to the energy of matter. That is to say: space curves where there is matter.
All of this is the result of an elementary intuition: that space and gravitational field are the same thing.
Genius hesitates.
Why are precisely these elements listed there, and why does the periodic table have this particular structure, with these periods, and with the elements having these specific properties? The answer is that each element corresponds to one solution of the main equation of quantum mechanics. The whole of chemistry emerges from a single equation.
In quantum mechanics no object has a definite position, except when colliding headlong with something else.
Without quantum mechanics there would be no transistors.
Even if we observe a small, empty region of space in which there are no atoms, we still detect a minute swarming of these particles. There is no such thing as a real void, one that is completely empty.
Quantum mechanics and experiments with particles have taught us that the world is a continuous, restless swarming of things, a continuous coming to light and disappearance of ephemeral entities. A set of vibrations, as in the switched-on hippie world of the 1960s. A world of happenings, not of things.
It is hardly surprising that there are more things in heaven and earth, dear reader, than have been dreamed of in our philosophy—or in our physics.
Loop quantum gravity is an endeavor to combine general relativity and quantum mechanics.
Where are these quanta of space? Nowhere. They are not in space because they are themselves the space. Space is created by the linking of these individual quanta of gravity. Once again, the world seems to be less about objects than about interactive relationships.
Heat, as we know, always moves from hot things to cold.
The difference between past and future exists only when there is heat. The fundamental phenomenon that distinguishes the future from the past is the fact that heat passes from things that are hotter to things that are colder.
I may not know something with certainty, but I can still assign a lesser or greater degree of probability to something.
Such issues lead us to the heart of the problem of time: what exactly is the flow of time?
Physics describes the world by means of formulas that tell how things vary as a function of “time.”
I think that the answer lies in the intimate connection between time and heat. There is a detectable difference between the past and the future only when there is the flow of heat. Heat is linked to probability; and probability in turn is linked to the fact that our interactions with the rest of the world do not register the fine details of reality.
We are made up of the same atoms and the same light signals as are exchanged between pine trees in the mountains and stars in the galaxies.
The separation is a subtle one: the antelope hunted at dawn is not far removed from the antelope deity in that night’s storytelling. The border is porous. Myths nourish science, and science nourishes myth. But the value of knowledge remains. If we find the antelope, we can eat.
To be free doesn’t mean that our behavior is not determined by the laws of nature. It means that it is determined by the laws of nature acting in our brains.
When we say that human behavior is unpredictable, we are right because it is too complex to be predicted, especially by ourselves.
It is not against nature to be curious: it is in our nature to be so.
I believe that our species will not last long. It does not seem to be made of the stuff that has allowed the turtle, for example, to continue to exist more or less unchanged for hundreds of millions of years, for hundreds of times longer, that is, than we have even been in existence. We belong to a short-lived genus of species. All of our cousins are already extinct.
Nature is our home, and in nature we are at home.
