NewScientist (30 June 2018, paywall) wants to tell me how to think about black holes, the icons of Einstein’s Theory of Relativity. Among the observations is this:
Black holes are cast-iron predictions of general relativity, Einstein’s peerless theory of gravity, and yet they stretch it to breaking point. Its equations fail catastrophically at a black hole’s centre, known as its singularity, where the warping of space-time simply goes off the scale. “Everything you calculate goes to infinity,” says Ferreira. “It has no meaning.”
Even Einstein thought that black holes were too absurd to be real. They emit no light, so we cannot see them. Yet we infer their presence from their influence on nearby matter as they suck in gas and dust and stars, the contortions of which produce awesome light shows. In 2015, when we detected gravitational waves for the first time, the observed ripples in space-time matched the predicted signal from two black holes spiralling into one another and merging.
Which makes me think of systems which are too interesting. That is, Kurt Gödel, a mathematician of Einstein’s vintage, proved that systems of sufficient power were inevitably incomplete, meaning there were certain statements about such systems which were not provably true nor false.
It’s not hard to see black holes as analogous to the unprovable statements of Gödel’s work. In fact, they might even prove to be a more direct representative of the concept, in two different concepts of the underlying nature of our Universe.
The first is Mathematical Universe Hypothesis, which asserts that the Universe is the physical manifestation of a mathematical equation, or system. If this proves true in the latter sense, then the black holes may be the representation of the various unprovable statements of the system of which the Universe is representative, instabilities, one might say, of the system. Even insanities, if we go so far as to admit an author is necessary for the mathematical system to exist in the first place.
The second is the scenario in which the Universe, and all of us inside it, is a computer simulation. What, then, do the black holes represent? Since matter and even information seems to simply disappear into them, perhaps they might be considered the input/output ports of the computer system. Perhaps black holes are simple samplers of the state of the system for whoever authored our postulated computer simulation. True, black holes do come in different sizes, as we know from observation, but rather than reflect the matter gathered directly, it may reflect the processing which takes place on the sample so gathered.
This may all sound quite silly, but I do know that sampling the interior states of computer programs can be quite challenging, even in the relatively simple projects on which I work. How much harder is it for sophisticated simulators, especially something that scales from sub-atomic all the way to stars and galaxies? I’m not sure.
And it’s a lovely, lazy thought for a Sunday afternoon.
