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.