Wednesday, September 27, 2006

What's New in Quantum Gravity

I read Lee Smolin’s new book, The Trouble with Physics. I’m not going to review it in detail (here is a good review;UPDATE 3_Oct. see also review up at Cosmic Variance), but will instead focus below on the section where he discusses some newer approaches to quantum gravity.

The largest part of the book diagnoses the reasons for the slow progress in solving the big outstanding problems in theoretical physics. (Some of my earlier posts on this topic and referencing Smolin are here, here and here). The focus is on his perception of the shortcomings of string theory and also on the “sociological” issues which have led to string theory’s dominance of the field. He also makes suggestions for improving the situation so the next generation of physicists can make better progress.

While the focus is on string theory, it is also clear that the Loop Quantum Gravity program (with which Smolin has been most identified) has also made only slow progress – if it had been more successful, this book would not exist.

While these parts of the story left me a bit depressed, I still recommend the book for those interested in the topic: Smolin is a great writer and is well positioned to speak on the issues. (The book is frequently being reviewed in conjunction with Peter Woit’s new book, which I plan to read; in the meantime I continue to follow Woit’s interesting blog.)

Amidst the gloominess, Smolin does make some optimistic comments about the development of alternative background-independent (BI) approaches to quantum gravity (Chapter 15). In BI approaches, he says, one does not “start with space, or anything moving in space.” Instead, one starts with an abstract quantum mechanical structure, then looks for spacetime to emerge at larger scales. Early attempts proceeded by quantizing Einstein’s spacetime geometry directly (in the spirit of quantizing the classical electromagnetic field). These didn’t work, with the main problem being the generation of infinities in the expressions. A more sophisticated model, that of loop quantum gravity, has created finite outcomes, but (if my understanding is right) it works by encoding the spacetime of relativity directly into a quantum geometry. The complexity which comes from including the quantum states of all the geometric degrees of freedom in the model has made it difficult to get the dynamical four-dimensional spacetime back out again. [UPDATE (29 Sept.): See a few additional notes on LQG below in the comments.]

So, now, the idea is to take the BI approach even deeper and construct a quantum “pre-spacetime” theory. Looking at these approaches, Smolin also concludes they must include causality as a fundamental feature. In relativity, the light-cones implement a causal structure: you can tell which events precede or succeed others from a given reference frame. While we usually might think in terms of spacetime imposing the causal structure, Smolin says you could turn this around and say that causality determines the spacetime geometry. In this spirit, many researchers in quantum gravity now think causality is fundamental, and must feature in the construction of a pre-spacetime theory.

Here is Smolin’s summary of his meta-thoughts on quantum gravity theories:

“The most successful approaches to quantum gravity to date combine these three basic ideas: that space is emergent, that the more fundamental description is discrete, and that this description involves causality in a fundamental way. (emphasis original)”

Note he doesn’t say time is emergent. If causality is fundamental, then some notion of time is fundamental. However, it wouldn’t be a global time dimension we’re talking about: time would be localized at the level of the building blocks.

The chapter includes a survey of a number of approaches, however, the two newer ideas which Smolin seemed most enthusiastic about were a model called Causal Dynamic Triangulations and a new take on Quantum Causal Histories which utilizes an idea from quantum information processing to make spacetime emerge from a pre-spacetime reality. I will follow up with an attempt to look a bit more closely at these models.


Clark Goble said...

Is there a good text to get into LQG? I know there are several so-so ones for String theory.

As I understand it the approach developed out of some of the more mathematically interesting approaches to QM or GR using spinors. I'm really intrigued.

BTW - the whole Leibnizean space as emergent is quite interesting however I'm really interested in how mathematically they get GR curved spacetime if time is fundamental and quantized.

I'll admit that LQG interests me more simply because it seems closer to the GR approach rather than String theory that seems to adopt a more traditional substantial spacetime. (Something as I recall Bell thought would have to happen way back when)

Anyway, I've read several of the popularizations, including Smolin's own Three Roads to Quantum Gravity. But I firmly believe you don't really understand physics until you understand the math. There just doesn't seem to be a nice middle ground for people with a background in physics who simply didn't go the fundamental physics route in grad school.

Steve said...

First, I agree with your comment about the difficulty or impossibility of understanding these theories if you can’t follow the formalisms. While I can probably handle more than what is included in most books targeting laypeople, I clearly can’t come close to keeping up with the actual research papers. There doesn’t seem to be a lot of middle ground.

For learning more about LQG, I don’t know of a text: the main internet sources I know of are courtesy of John Baez (see this page). I just noticed the publication of this paper: “Loop and Spin Foam Quantum Gravity: A Brief Guide for Beginners”, but I haven’t read it yet.

In terms of LQG, it is a direct quantization of GR, seeking to define quantum states of the spacetime geometry. “Loops” I take it came from early work using mathematical expressions like the ones used to describe quantized loops of electromagnetic fieldlines. Then, Smolin and Rovelli made progress by deriving a formulation where the loops were arranged in graphs called spin networks, which had been invented by Penrose in the 1960’s (constructed from “spinors”, I guess, which is a sort of vector?). I take it that the spin network was the simplest possible structure which did the job (connecting the quantum and classical geometry), and it enabled the theory to calculate a number of meaningful results.

At this point, it was a static picture, though, not a dynamical one like GR itself. Trying to put spin networks in motion – evolve them (using a path integral approach like that of a Feynman diagram) – leads to the “spin foam” models. The issue with these has been that 4D spacetime doesn’t come back out easily. The two models mentioned at the end of the post evidently show some promise on this front - I’ve read the papers and am going to post some summary comments: of course it remains the case that the math is beyond me! I just hope some of the concepts leach into my brain.

Alejandro said...

The most easily accessible textbook (beyond popular science level) on LQG is Rovelli's Quantum Gravity. It contains all the essentials and also many fascinating conceptual discussions, for example on the meaning of background independence in GR and on his preferred "relational" interpretation of QM.

Steve said...

Thank you Alejandro. I remember now when the draft was on his website. That sounds like the one to read.

Steve said...

I need to clarify something: I linked in my first comment above to a web page with resources on quantum gravity and gave the impression that it was a page created by John Baez; it included a collection of relevant entries from Baez' proto-blog "This Week's Finds in Mathematical Physics", but has many more good links; this excellent page is the work of J. Daniel Christensen. My apologies for the confusion.

Clark Goble said...

Thanks for the book suggestion. I confess that, like Smolin, the background independence issue makes me think LQG is the way to go. But of course with a bias like that it is kind of meaningless. It's just the Leibnizean in me I guess.