There are many outstanding books explaining the latest developments at the frontiers of theoretical physics to general audiences. This is not an easy thing to do, but the physicists who have stepped up tend to be very good writers and expositors: I am thinking of people like Roger Penrose, Julian Barbour, and Lee Smolin.
The latest such book that I have read is Carlo Rovelli’s Reality is not what it seems, published (in English translation) by Allen Lane last year.
In brief, what distinguishes this book is that the author’s research is in loop quantum gravity, one of the more successful approaches to quantum gravity, and his feeling is that this approach has been successful so far. (Of the other main contender, string theory, whose main concern, he says, “is not so much studying the quantum properties of space and time, but rather writing a unified theory of all known fields, an objective that might be premature given current knowledge”.
There are chapters devoted to classical physics (Newton), special and general relativity (Einstein), and quantum mechanics (Einstein again, Heisenberg, Dirac), before we come to the viewpoint he proposes, that space and time are not fundamental properties of the universe, but emerge from quantum processes on a very small scale.
But the book has a couple of features that distinguish it from the average popular physics book.
First, the endeavour is traced back to the journey of Leucippus from Miletus (then the centre of Greek philosophy, with Thales, Anaximander, Hecataeus, and others) to Abdera in about 450BCE. There, he found a disciple, Democritus, and together they developed the philosophy of atomism. Crudely, this says that the world is made of atoms and the void, and the achievement of quantum gravity is to get rid of the void. But there is much more to it: the philosophy of these two was based on the notion that “the world can be comprehended using reason”, and science has no need to appeal to the authority of gods or ancient texts. Atomism was also a richer theory than is often portrayed: Democritus regarded atoms as like letters, which can be combined so as to obtain “comedies or tragedies, ridiculous stories or epic poems”. Incidentally, atomism resolves Zeno’s paradox of Achilles and the Tortoise: if space is not infinitely divisible, the paradox simply does not arise.
Democritus was extremely prolific, but almost all his works have been lost. (Rovelli lists them in a footnote which takes up the best part of an entire page.) What we know of his thought is almost all contained in the poem De rerum natura by the Latin poet Lucretius. Rovelli speculates on what might have happened if we had retained the work of Democritus and lost that of Plato and Aristotle.
The second feature is that Rovelli is not afraid to write down equations, not accepting the “wisdom” that every equation halves the sales. Figure 7.7 is a schematic picture of a T-shirt with the equations of loop quantum gravity on it (though I don’t think he expects most readers to understand them: the point is that the formulation is concise and elegant). Other equations are more important to the flow of the argument.
For example, he tells the story of Matvei Bronštein, the Soviet physicist who first showed that general relativity and quantum mechanics, taken together, show that there is a smallest scale of length. The argument goes like this. Suppose we want to measure a small region of space. We must place something in this space in order to identify it. The finer our measurement, the more confined the particle is. According to the Uncertainty Principle, this implies more uncertainty in its momentum, and hence (I will come back to this) in its energy. Special relativity shows that energy is equivalent to mass, and general relativity that mass bends spacetime; so a sufficiently energetic particle in a small region of space will produce a black hole, and our proposed measurement will become impossible. Rovelli remarks that the argument is much more precise and general than indicated, and leads to a calculation of this minimal length (now called the Planck length) in terms of the gravitational constant, Planck’s constant, and the speed of light. The equation is at the top of page 130.
My caveat is that, except for zero-rest-mass particles like photons, the energy is not determined by the momentum. I am not sure how to get around this.
Rovelli goes on to tell the fate of Bronštein. When Stalin came to power, he (and other physicists) who had followed Lenin, were mildly critical of Stalin; Bronštein was arrested and condemned to death, and executed on the same day. Let us all hope that such things are not going to return in our lifetime!
The main message of the book, then, is that everything, even space-time, is “granular”; infinity does not exist in nature. This view disposes of the infinities that have troubled physics, which result from the possibility of things becoming arbitrarily close (for example, a point charge interacting with itself).
As I said earlier, Rovelli gives the impression that loop quantum gravity has provided us with a workable basis for the union of relativity and quantum theory. But, like Democritus, he realises that we are not at the end of the journey. Signs from these and other investigations suggest that the basic currency of the universe might be, not space-time, but information; time might arise from the entropy of the small-scale structure. But he admits that he doesn’t know how this might work. A refreshing view after the premature announcement of the “theory of everything” a couple of decades ago.