book reviews

### causal set theory books

reviewed by T. Nelson

### Causal Space-Time: Emergent Physics From Causality Richard D Bateson

Cassini, 2010, 74 pages

y now I guess everybody's gotten bored with superstring theory, with only 10500 possible solutions, and with loop quantum gravity, which is so easy. So we're all asking: what else ya got? Maybe something with a really dull-sounding name, perhaps?

Well, ask no more. There's a new theory called causal set (or causet) theory, based on Hans Reichenbach's old ideas. Reichenbach is remembered for talking a lot about time, but he also said that if there are no causal violations, then causality must determine the topology of space. Physicists are now asking whether the idea of causal nets could be employed to create a model of spacetime.

It's not so new: Einstein talked about it back in 1916. Physicists like Rafael Sorkin, who has a chapter in Foundations of Space and Time (reviewed here), and others are now using it to model quantum gravity. In this model, space is a bunch of nodes connected together by cause and effect. It's closely related to causal dynamical triangulation and also loop quantum gravity. These theories propose a discretization of the causal structure of continuum Lorentzian manifolds; one goal is to preserve GR in the larger-scale approximation. Bateson describes the idea in words (mostly) and concludes that, yes indeed, causal nets can explain most phenomena in quantum mechanics, solve the so-called measurement problem, and account for fermions.

The network itself consists of a lattice of nodes arranged in a triangular shape, rather like a spinfoam structure. The connections between nodes are probabilities and they must sum to 1. The sign of the square root of the probability amplitude corresponds to the spin state of the fermion. Thus every possible event on the net represents something that could be observed about a particle. For example, Bateson says the scaling of the triangles defines the mass of a particle.

But that's not all! If you call right now and if you add randomness to the net, you also get quantum indeterminacy! In the two-slit experiment, to calculate the result you have to consider every possible path the photon could take; in the causal net model, this is corresponds to the conservation of probability.

This is a very clever idea. Bateson compares the network to a bunch of electric wires containing waves of electrical current. In a sense making a measurement is like getting an electric shock when you touch a live wire: even though the electricity is everywhere it's possible for it to go, the shock happens only at a specific point. Whether that's really how quantum wavefunction collapse works or not, it might be a good way of thinking about it.

I'll probably get burned at the stake for suggesting this, but I think this is also a great way of conceptualizing all quantum phenomena. Particles only need to be quantized when they interact. Philosophers tell us we're not individual beings except in relation to others. Maybe that's true in physics as well: the only time a particle is a discrete quantum is when it interacts with something else.

There's one big question remaining: what the heck are these causal nodey things? How could ‘causation’ be the essence of spacetime? I don't think the theory has gotten far enough to answer that question, but if you're interested in radical ideas about how spacetime might work, but don't need the math, this 74-page book is nontechnical enough and witty enough to be worth checking.

Part of this book also is available on Arxiv.

jul 10, 2017

### Discrete Causal Theory:Emergent Spacetime and the Causal Metric Hypothesis Benjamin F. Dribus

Springer, 2017, 558 pages

t's not every day when an author tells you not to read his whole book. But Benjamin Dribus is not an ordinary physicist, and for readers of this 500-page book on causal set theory it's good advice. In fact, it's not necessary: your instinct for self-preservation will ensure it.

The Causal Metric Hypothesis, or CMH, is a competitor to loop quantum gravity, so the reader will naturally be asking what it brings to the party. The answer, Dribus says [p.30], is not much yet. The advantage of visualizing spacetime as a network of causal nodes (note: not once does he ever call it a causal nexus) is that it's easier to see particles as disturbances on those nodes than on a continuum model, because the continuum requires additional phenomena such as fields for the particles to exist on.

The big cheese in this field is Rafael Sorkin. The original idea came from Hawking and Malament. And it's a clever one. There are no compactified extra dimensions and no wonky four-dimensional triangles. Just nodes connected by lines that represent potential cause-and-effect relationships.

The causal metric hypothesis is also very simple: The properties of the physical universe are manifestations of causal structure. In other words, the CMH says that information about cause and effect describes everything there is to know about relativistic spacetime geometry, except for a conformal factor, i.e. scale [p.91].

Dribus says this enables perfect background independence by eliminating any tension between matter and spacetime. But what exactly is a “causal structure”? He defines it as “the aggregate of actual causes and effects.” Well, you asked.

To clarify what he means, Dribus considers a Cauchy surface. A Cauchy surface is a subset of a relativistic spacetime in which every inextensible causal curve intersects the subset exactly once. This means these causal nexuses . . . er, nodes . . . are really representations of time: events in space can go in either direction, but events in time can't. This makes sense, because it's impossible for one object to affect another at the same instant; it can only do so at a future time.

He also spends a lot of time discussing closed timelike curves, which would create paradoxes. They are impossible in the causal metric hypothesis.

Actually he spends a lot of time on many of these topics—the book is quite repetitive and could have been shortened quite a bit without losing much. And maybe then we could have gotten more discussion to convince us about what these nodes are in physical terms, since even after 500 pages they're never really sensibly defined. There's a tremendous amount of work to be done to make this theory palatable. But it's fascinating stuff, and it could become a major competitor to loop quantum gravity.

There are few equations, but don't kid yourself: this book is still rather complicated. I always say ideas start out simple, then they get more and more complex until they're understood, at which point they become simple again. Causal metric theory is just entering the complicated stage. Better learn it now before Rafael Sorkin's book comes out.

jul 29, 2017