**Reality Is Not What It Seems**

**The Journey To Quantum Gravity** (2014, tr 2016)

by Carlo Rovelli (1956-), tr Simon Carnell and Erica Segre

Rovelli is not only a popularizer of science, but a leading physics theorist. This book conveys both his mastery of the subject, and his humility toward its correctness.

Part One, Roots, begins twenty-six centuries ago, in the Greek city of Miletus around 450 BCE. That is when Leucippus went from Miletus to Abdera. He was a student in Anaximander’s tradition, and in turn Democritus was his student. This tradition was the dawn of scientific thought. The concept that Rovelli emphasizes is granularity – the notion that things cannot be infinitely subdivided, but there is a smallest unit. Though Democritus is sometimes credited with the notion of atoms of matter, Rovelli’s discussion reveals additional forms of granularity. Clearly an admirer of Einstein, Rovelli shows how the first proof of atoms, Einstein’s 1905 paper on Brownian motion, in principle could have been discovered centuries earlier. (One of Rovelli’s charms is his habit of mentioning the key characters in the chapter titles by their first names: Isaac, Michael, Albert, Niels, Werner, Paul, Matvei, John.)

Rovelli moves on to other giants: Aristotle, Ptolemy, Copernicus, Kepler, Galileo, Newton. His description of Newton’s recognition of universal gravitation was unfamiliar to me. Galileo had shown that freely falling bodies accelerate at 9.8 meters per second per second. Kepler had found the relation between the time for a planet or satellite to complete an orbit and its distance from its primary body (sun or planet). Newton imagined a satellite orbiting just above the surface of the earth. The radius of the earth, and the period and radius of the moon’s orbit had been measured in antiquity. Newton applied Kepler’s relation and determined the period of his imaginary satellite and found its period to be an hour and a half. Calculating the acceleration of an object in such circular motion, he found it to be 9.8 meters per second per second. In other words, the same gravity that caused a falling body to accelerate downward at earth’s surface moved the planets and their satellites.

Rovelli uses a little diagram to illustrate the developing notions of what the world is made of. In Newton’s system, the components are Space, Time, and Particles. Rovelli quotes a passage that shows Newton didn’t believe this was a satisfactory world-view, which included a force between two pieces of matter acting over the distance of their separation:

It is inconceivable that inanimate brute matter should, without the intervention of something else which is not material, operate upon and affect other matter, and have an effect on it, without mutual contact …

That Gravity should be innate, inherent and essential to Matter, so that one Body may act upon another at a Distance thro’ a vacuum, without the Mediation of any thing else, by and through which their Action and Force may be conveyed from one to another, is to me so great an Absurdity, that I believe no Man who has in philosophical Matters a competent Faculty of thinking, can ever fall into it. Gravity must be caused by an Agent acting constantly according to certain Laws; but whether this Agent be material or immaterial, I have left to the Consideration of my Readers.

Rovelli moves on to Faraday’s and Maxwell’s conception and formulation electric and magnetic forces as based on fields, and updates the Faraday-Maxwell world’s components, splitting Newton’s Particles into Fields and Particles. That ends Part One.

Part Two, The Beginning of the Revolution, addresses Special Relativity, and updates the Einstein 1905 world’s components by combining Space and Time into a single entity: Spacetime, along with Fields and Particles. He then describes how Einstein extended the Faraday-Maxwell notion of fields described by equations to gravity. The Einstein 1915 world view combines the Spacetime and Fields components into a single (extended) notion of Fields, along with Particles. While describing Einstein’s application of General Relativity to cosmology, Rovelli takes a longish detour through Dante, perhaps excusable for an Italian.

Turning to quantum theory, Rovelli begins with Einstein’s other 1905 paper, on the photoelectric effect, then turns to the notion of discrete spectra for the electromagnetic interactions of atoms. He discusses the contributions of Bohr, Heisenberg and Dirac, and summarizes with three key features of the world:

– Granularity. The information in the state of a system is finite, and limited by Planck’s constant.

– Indeterminacy. The future is not determined unequivocally by the past. Even the more rigid regularities we see are ultimately statistical.

– Relationality. The events of nature are always interactions. All events of a system occur in relation to another system.

Relationality was not part of my education in quantum mechanics, being developed in the 1980s and 1990s. Rovelli is credited with the current approach. Rovelli’s summary of the components of the Quantum mechanics world-view has Spacetime and Quantum fields, combining the Fields and Particles components of Einstein’s 1905 theory. (General relativity doesn’t enter into quantum mechanics.)

Part Three, Quantum Space and Relational Time, is the main content of the book. Rovelli also developed this theory of quantum gravity, and it remains challenging. The key concept is that at the Planck Length (~1/1,000,000,000,000,000,000,000,000,000,000,000 cm), space must be quantized. Specifically, there is a spectrum of volumes and areas, establishing a granular nature of space. As I understand what he says, space is subdivided like a foam of soap bubbles, with each the volume of each bubble and the area of each face of each bubble quantized in multiples of the square and cube of the Planck length. The grains of this foam are connected at their faces, and a path from one grain to another can be defined. If such a path is closed by ending at its starting grain, the path forms a loop. Calculations made on these loops determine the effective gravitational field, and the theory is sometimes called “loop quantum gravity”. The key point is that the gravitational field is not quantized on spacetime, as gravitons were once expected to be. Instead, the geometry of space itself, which is the gravitational field, is quantized.

From here the theory gets harder to grasp, but the most interesting aspect to me is that it is only space (gravity) that is quantized, and time doesn’t directly appear in the theory. The explanation of how this difference with the preceding theories was not clear to me. One aspect of this is to change perspective from a classical view of a process involving, e.g., particles colliding. In quantum theory, only the end states of the particles before and after their interaction can be considered observable, and able to be calculated (in probabilistic terms). There is no concept of continuous change “in time”. Also, instead of a trajectory for the particles, there is a sort of sum over all possible paths between end states. In the end, the components of the Quantum gravity worldview collapse to a single kind of component, Covariant quantum fields.

In Part Four, Beyond Space and Time, Rovelli addresses consequences of the theory he has described. He brings in the concept of information (Shannon’s theory), and how modern physics incorporates it. This leads to discussion of thermodynamics, and the notion of thermodynamic time. The connections are not clear to me, but it seems like a plausible sequence of developments can be made to re-create the intuitive sense of time from the new time-less theory.

One of the seldom-mentioned peculiarities of the study of physics is the way it begins with simple concepts as Newton used them, and relatively simple algebra for the equations describing mechanics. Then the mathematics is elaborated with calculus in its various forms, and Newton’s formulations are replaced with other forms (Lagrangian, Hamiltonian, etc.) that are at the same time more esoteric and more simple. When fields are introduced, the elaboration continues. When quantum theory is introduced, the student is shown the simplest forms from the 1920s, then more elaborate forms in the order they were developed. (At some point, I got lost.) The whole process is like studying the history of physics, I don’t think the study of other sciences (e.g., biology, geology, chemistry) proceeds this way. I wonder what physics would be like if it started with loop quantum gravity, and derived the necessary special cases from the more general equations.