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Superluminal Computing

So today an interesting article on the wonderful Arxiv Blog that caught my eye.
It’s a report on a piece of theoretical physics which suggests something that I’ve long suspected that current theories implied. Namely, that if the universe is smooth, that you should be able to perform computational miracles.

The way I tend to describe this idea is as follows:
How do you tell if the universe is smooth or discrete? You can’t build an apparatus directly to test for smoothness, because whatever apparatus you build, there will always be some level of detail that it fails to examine. Thus, it might be that the universe is discrete, but simply made of granular events at some scale that you haven’t yet measured.

Thus the only way that you can determine whether you’re in a smooth universe or not is by doing something that would be computationally impossible in a universe that contained a finite amount of information. In other words, can you beat Turing’s Halting Problem, or Godel’s Incompleteness Theorem? If you can, then you can go to bed at night comfortably certain that the Calculus enthusiasts are right. The universe can do impossible things, and therefore physical theories that depend on continuous variable are just fine. On the other hand, of course, if you can’t beat Godel’s theorem, then you have to consider the ghastly possibility that the application of calculus to physics is only a handy approximation, as it is in every other field where it’s applied, rather than an absolute truth.

The Arxiv article is the first time I’ve seen people in the theoretical physics community come to these conclusions on their own. What’s wonderful about it is that it points the way toward a falsifiable experiment some time in the future that might actually settle the question. It hinges on the fact that a superluminal computer should be able to pack an infinite number of calculations into a finite period of time–something that digital physics forbids. Thus, if we can build an optical computer and an electron bath, neither of which seem impossible, then we can feed our computer a theorem-checking program and a nice list of Godel sentences. Then we go grab a bite of lunch and when we come back, the answer to one of the most contentious questions in physics has been answered for us. Hoorah!

It perhaps doesn’t come as a surprise that I’m skeptical of the idea of hyper-computers. Nevertheless, it’d wonderful to be wrong. A universe capable of miracles might be a fun place to live. Roll on optical computing technology. Your first grand application awaits!

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