"The Order of Time" by Carlo Rovelli

Amazon link

Roy Simpson, who frequently comments here, sent me a review of the book above to post as a guest blogger. He wrote:

"Here is the review of the Rovelli book. ... I am hoping the Philip Ball book might arrive next week.

A remarkably hot topic right now is the Riemann Hypothesis since there are several (doubtful) claims that it has been solved. Since I haven't really studied this equation much, I am finding papers which make all rather interesting.

For example in 1949 Casimir used "zeta function regularization" in QFT to calculate his effect; then in 1976 Hawking used "zeta function regularization" to do most of his quantum black hole calculations. As I remarked in your blog

zeta (-1) = 1+2+3+4+  ... = -1/12

Also String theory requires 2/(2-D) = zeta(-1) for the number of Dimensions - giving D = 26!

The reason that this curious sum forms is because of (a) complex analytic continuation - taking a function out of its domain of definition in a unique way and (b) p-adic theory which messes up what is meant by "=" (zero distance) via a fractal like metric. So the interconnectedness of mathematics seems to be in evidence here (something the String Theorists are always proud of).."

Here is his review.

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Review of C. Rovelli : The Order of Time (2018)

By Dr. Roy Simpson, October 2018

The small (214 page) book by Prof. Carlo Rovelli came to my attention as it featured in a “guest interview” in the blog of physicist S. Hossenfelder in August. That interview was conducted by a lawyer with an interest in physics and time and has generated at least 250 comments.

Rovelli has written several very poetic, but informative, popular physics books in recent years and this book continues that theme by discussing his approach to the question of “time” in physics.

In broad terms the book is divided into three parts: first the lessons from General Relativity on time; second the particular ideas about time proposed by Rovelli from his work on Quantum Gravity; third some broader statements about the philosophy of time. None of these parts conveys the details of the theory that a student of physics or a practising physicist would wish (although there are some equations in the notes), but it does all provide a general overview of where Rovelli's thinking is with respect to “Time in Physics” for a general audience. There are links in the end-notes to detailed papers by Rovelli and books by others which can be studied later.

To understand Rovelli's view of physics we should begin by recognising that he is the author of (another) Interpretation of Quantum Mechanics called “The Relational Interpretation”. The underlying idea here was to spread the relational arguments which drove the development of special relativity (time being relative to observers and frames) onto quantum observers and onto physics theories in general. The quantum interpretation that results has some similarity to the original Everett Interpretation, but without the many worlds. He does not believe that “measurement” is a real activity, but only interactions between quantum objects is real. As evident from Part two his relational viewpoint also applies to physics concepts like Entropy – where he emphasises “Relative Entropy” between two subsystems.

To understand why Time is important we also need to understand his research starting point: Quantum Gravity and an associated equation from the 1960s now called the Wheeler-DeWitt equation. Rovelli is also the author of a rival (to String Theory) theory of quantum gravity called “Loop Quantum Gravity” which originated from the Wheeler-DeWitt equation (the latter equation plays no role in String theory, as yet).

The Wheeler-Dewitt equation was derived by making many assumptions in a 1960s attempt at a quantization of General Relativity. This equation was thus a kind of “Schrodinger Equation” for General Relativity, generated by advanced versions of the quantization procedures found in Quantum Mechanics textbooks. Now the Schrodinger equation, in its full dynamic form, is a time dependent equation concerning the wavefunction Ψ(q1,q2,q3;t) where (q1,q2,q3) are position variables and t is the usual Newtonian time parameter. In the Wheeler-DeWitt equation, in which the system quantized is all of general relativity Ψ becomes Ψ(g_ij(p)). Here p is an event in space-time and g_ij is (derived from) the general relativity metric (distance function). The equation becomes a so-called functional equation in the function (of position and time) g_ij(p). Furthermore this derivation requires (perhaps fortunately) that the Schrodinger time parameter t disappears.

In short the Wheeler-DeWitt equation is timeless - Ψ once calculated never changes and this Ψ is meant to describe the entire Universe – for all time! This is known as the “problem of time” in Quantum Gravity, and is especially relevant to the approach taken by Rovelli.

Now time is still present in this model via the metric g_ij(p) and so is introduced the idea of “external variables” and “internal variables” - in particular “internal time”. Thus in the Rovelli approach time is not a fundamental feature of physics but an emergent concept, which he believes can be understood taking a relational approach. The more fundamental concept he calls “change”.

So in Part One of the book Rovelli is reviewing the results of General Relativity (such as the effect of location in a gravitational field on clocks) and presents this as evidence that in standard physics time should be considered as relative, forming part of a network of time. There is no “order of time” amongst the clocks in General Relativity due to lack of simultaneity etc.

In Part Two Rovelli discusses Entropy (also part of the physics discussion of time) and introduces his equation for “thermal time” - which is a time simply derived from the state of a dynamic thermal system, effectively by inverting the usual equation for the dynamical evolution of a thermal system.

Again thermal subsystems have a relative entropy. There is also a quantum version of the same idea. Interestingly an experiment was reported in 2013 that entangled two photons in such a way that photon A used photon B as a local clock, suggesting that hiding inside “quantum entanglement” could be an emergent notion of clock and thus time.

Another consequence of the work on the Wheeler-DeWitt equation is that there can be quantum solutions in which no emergent time forms. Thus time is not even Universal (in the way that “change” might be) as is commonly assumed in physics and “common sense” (naïve intuition). Rovelli makes some remarks about this, but deeper analysis is needed to understand all of this.

Rovelli takes the view that we are on the cusp of more breakthroughs in time research. We shall see.