## Tuesday, May 26, 2020

### Book: At least two philosophers understood background independence

While the fake news media are still obsessed (but less so) with the fake Chinese cough apocalypse, among similar things (and with fake scientists who promote fake theories or irrational hysteria), Tiziana Vistarini, a philosopher at the University of Rome, has published a new book about one of the most important topics in the Universe. Yes, it is
The Emergence of Spacetime in String Theory (Routledge Studies in the Philosophy of Mathematics and Physics Book 5) (click to buy at Amazon)
You may be rather sure that the fake science journalists won't promote this book because it actually has some valuable beef. Hardcover and eVersions of the book are available.

I learned about the book because of the chapter 9 written by Nick Huggett and Christian Wüthrich, professors of philosophy in Chicago and Geneva, respectively, who have clearly understood some essential ideas about the background independence in quantum gravity and string theory.
Chapter 9: The ‘emergence’ of spacetime (Pittsburgh Philosophy Archive)
If you want to quickly get to some of the most crucial ideas in that 40-page-long essay, you may search for the sequence of four letters "Motl". ;-)

OK, among many other things, these wise men have read a 2012 blog post by your humble correspondent, What is background independence and how important is it?, and they noticed that I elaborated upon some rough ideas expressed in the textbooks by Green+Schwarz+Witten and by the late Joe Polchinski – who didn't do a great enough job, however.

I think that they really couldn't because our (and my) understanding of the role of the background in string theory kept on evolving after 1987 when GSW was published and even after 1999 when Joe's Big Book of String was released. Here is one passage that leads me to believe that they understood the background independence much more properly than virtually anyone (or strictly everyone) else who likes to talk about the topic:
First some clarification of its terms: up to now, we have, in line with standard use, referred to $$g_{\mu\nu}$$ as the ‘background’ metric, while in the passage quoted, Motl refers to its metric part as the background! (Of course, because he is addressing the question of whether string theory is independent of this particular ‘background’ structure.) For the purposes of our discussion of this proposal it will help keep things clear to adopt a different terminology: we will call $$g_{\mu\nu}$$ the ‘full’ metric, and its components the ‘partial’ metric and graviton/tensor field. Then we have argued that the full metric is emergent because of its graviton field part; but the question currently addressed is whether the partial metric is a non-emergent spacetime structure. The answer we take from Motl is that the partial metric is no structure at all, just an arbitrary component in a split of the only physical quantity, the emergent full metric. This split is necessitated, not by nature, but by the perturbative formalism currently used to describe string theory.
Exactly right. The spacetime is an emergent structure but the geometric spacetime background (and background values of other fields) is not an emergent structure because it is not an objectively physical structure at all. Instead, it is a choice that the user of the laws of physics has to make. By making this choice, he or she contributes to the "emergence of the spacetime" but "spacetime" has another subjective component because a user-dependent choice was made. He or she has a freedom to do so – and in fact, (as long as he or she wants to do a nonzero amount of science) he or she has a duty to exploit this freedom. Once this separation to the background and excitations is made, physical processes may be quantified. The quantification depends on the exact separation. But there is a one-to-one map between the descriptions that we obtain assuming different (allowed) choices of the background.

The background may be "a lot of things" if not "almost everything" and the theory has the remarkable ability to work for all such choices. These comments incorporate lots of dualities and freedom that we know in string theory. In particular, the coherent condensate of gravitons upon one background must be physically identified with the vacuum state (the state with no gravitons or other particles) of another background. Various dualities (S, T, U, M-IIA, string-string duality, K3/heterotic duality etc.) are also manifestations of a broader principle, and so is the AdS/CFT and ER-EPR correspondence. The theory allows us to make lots of choices.

A primary point that these authors understand – and many others don't – is that the freedom if not the duty to pick a background is a virtue of the theory because the theory is capable of producing answers for many chosen questions by the user of the theory: the multitude of these questions is enhanced by the large number of backgrounds that must be considered a part of the data that define the question that the user of string theory wants string theory to answer (the question has the form "what is the probability amplitude for an outcome of a process").

You shouldn't feel guilty if you choose a background and work with it. On the contrary, you should feel proud because it's really necessary to do anything that may be called physics or even natural science in the conventional sense. Physics and science require the spacetime (or at least time!). The theory remains unique despite the freedom of the user of the theory to make these choices. By the way, in their text, the two philosophers say that the choice of the background is needed for our current perturbative formulations of string theory. Well, I think it holds more generally: even rather nonperturbative definitions of string theory do implicitly contain a particular identification of the classical background and/or the vacuum state.

At some point, I tried to coin another phrase, the "background indifference", to emphasize that the freedom of the user of a theory to choose the background is a good thing. They don't use it, I think, but I am not a kind of person who would care about the choice of the language too much. They got the idea right which is what matters.