This Week’s Science News from SWTG

A Quantum Threat & Hype For Hypergraphs

Theory of Everything Predicts New Physics For Supermassive Black Holes

Image: Gorard, arXiv:2402.0233

A month ago, I told you about Stephen Wolfram’s attempt to develop a theory of everything based on hypergraphs. And just the other day, I learned from New Scientist that if he is right, it would imply a characteristic change in the emission of supermassive black holes that could be observable. That would be very interesting if true, so let’s have a look.

In my recent video about Wolfram’s hypergraphs, I mentioned that most of the recent work on this seems to have been done by a young mathematician by the name of Jonathan Gorard. I didn’t know, though, that two seem to not be on the best of terms. Gorard mentioned on X/Twitter that “Spending the last 5 years watching Stephen take sole credit for ideas, insights, developments, and discoveries that were the products of our collaboration has been a uniquely exhausting experience.”

This new work also comes from Jonathan Gorard and is based on hypergraphs, but it doesn’t seem to directly involve Stephen Wolfram. As a brief recap, a hypergraph is a set of graphs or networks that describe space-time. Not just space, but space-time.

They have a finite resolution that on the one hand can reproduce Einstein’s theories to good accuracy - on the other hand, it can avoid the troubles that Einstein’s theories have on the shortest distance scales, where singularities can form. This way they might one day also help to combine General Relativity with Quantum Physics.

Discretizing space-time has, of course, been tried before, but most attempts have run into conflict with observations quickly. This is because in Einstein’s theory, you just cannot have discrete chunks of a fixed volume of space. This is because of length contraction: something that is very big for one observer will be very small for another one, and volumes of space change. So the idea of having discrete space is itself incompatible with Einstein’s theories.

Hypergraphs circumvent this problem because they are treating space and time together as one entity and have deviations at small volumes of space-time. Not volumes of space, but space-time. If length contracts, then time dilates, but the product remains the same. So this doesn’t result in any obvious problems with the symmetries of Einstein’s theories.

Gorard now used these hypergraphs to describe what happens if a black hole accretes matter. The matter will spiral into the hole and heat up dramatically along the way, releasing a lot of radiation. We can observe this radiation from many supermassive black holes in the middle of big galaxies.

In a paper from February, Gorard uses fluid dynamics to describe the accretion of matter and says that the amount of energy that is emitted depends on how dense the hypergraphs are. The less dense the graph, the higher the deviations from Einstein’s theory. In the paper, he doesn’t quantify it, but just somewhat vaguely says that “These results provide tentative evidence that there may exist astrophysically observable effects of the underlying discreteness of spacetime arising within certain quantum gravity models.”

Then, a few weeks ago he leaked on Twitter some preliminary results according to which “Preliminary simulations suggest that this could result in a boost in jet luminosity (assuming approximately Planck-scale discreteness) of around 2-3x over the predictions of classical GR.”

Big if true, as they say, because that could mean we might be much closer to finding evidence for the quantization of gravity than we thought.