causal set theory booksreviewed by T. Nelson
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