Free Seven Brief Lessons on Physics by Carlo Rovelli Page B

there is nothing more. A vision—that space curves—became an equation.
    But within this equation there is a teeming universe. And here the magical richness of the theory opens up into a phantasmagorical succession of predictions that resemble the delirious ravings of a madman but have all turned out to be true.
    To begin with, the equation describes how space bends around a star. Due to this curvature, not only doplanets orbit around the star but light stops moving in a straight line and deviates. Einstein predicted that the sun causes light to deviate. In 1919 this deviance was measured and the prediction verified. But it isn’t only space that curves; time does too. Einstein predicted that time passes more quickly high up than below, nearer to Earth. This was measured and turned out to be the case. If a person who has lived at sea level meets up with his twin who has lived in the mountains, he will find that his sibling is slightly older than he. And this is just the beginning.
    When a large star has burned up all of its combustible substance (hydrogen), it goes out. What remains is no longer supported by the heat of the combustion and collapses under its own weight, to a point where it bends space to such a degree that it plummets into an actual hole. These are the famous “black holes.” When I was studying at university they were considered to be the barely credible predictions of an esoteric theory. Today they are observed in the sky in their hundreds and are studied in great detail by astronomers.
    But this is still not all. The whole of space can expand and contract. Furthermore, Einstein’s equation shows that space cannot stand still; it
must be
expanding. In 1930 the expansion of the universe was actuallyobserved. The same equation predicts that the expansion ought to have been triggered by the explosion of a young, extremely small, and extremely hot universe: by what we now know as the “big bang.” Once again, no one believed this at first, but the proof mounted up until “cosmic background radiation”—the diffuse glare that remains from the heat generated by the original explosion—was actually observed in the sky. The prediction arising from Einstein’s equation turned out to be correct. And further still, the theory contends that space moves like the surface of the sea. The effects of these “gravitational waves” are observed in the sky on binary stars and correspond to the predictions of the theory even to the astonishing precision of one part to one hundred billion. And so forth.
    In short, the theory describes a colorful and amazing world where universes explode, space collapses into bottomless holes, time sags and slows near a planet, and the unbounded extensions of interstellar space ripple and sway like the surface of the sea . . . And all of this, which emerged gradually from my mice-gnawed book, was not a tale told by an idiot in a fit of lunacy or a hallucination caused by Calabria’s burning Mediterranean sun and its dazzling sea. It was reality.
    Or better, a glimpse of reality, a little less veiled thanour blurred and banal everyday view of it. A reality that seems to be made of the same stuff that our dreams are made of, but that is nevertheless more real than our clouded, quotidian dreaming.
    All of this is the result of an elementary intuition: that space and gravitational field are the same thing. And of a simple equation that I cannot resist giving here, even though you will almost certainly not be able to decipher it. Perhaps anyone reading this will still be able to appreciate its wonderful simplicity:
    R ab - ½ R g ab = T ab
    That’s it.
    You would need, of course, to study and digest Riemann’s mathematics in order to master the technique to read and use this equation. It takes a little commitment and effort. But less than is necessary to come to appreciate the rarefied beauty of a late Beethoven string quartet. In both cases the reward is sheer beauty and new eyes