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Kaj_Sotala comments on Causal Universes - Less Wrong
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Mainstream status:
I haven't yet particularly seen anyone else point out that there is in fact a way to finitely Turing-compute a discrete universe with self-consistent Time-Turners in it. (In fact I hadn't yet thought of how to do it at the time I wrote Harry's panic attack in Ch. 14 of HPMOR, though a primary literary goal of that scene was to promise my readers that Harry would not turn out to be living in a computer simulation. I think there might have been an LW comment somewhere that put me on that track or maybe even outright suggested it, but I'm not sure.)
The requisite behavior of the Time Turner is known as Stable Time Loops on the wiki that will ruin your life, and known as the Novikov self-consistency principle to physicists discussing "closed timelike curve" solutions to General Relativity. Scott Aaronson showed that time loop logic collapses PSPACE to polynomial time.
I haven't yet seen anyone else point out that space and time look like a simple generalization of discrete causal graphs to continuous metrics of relatedness and determination, with c being the generalization of locality. This strikes me as important, so any precedent for it or pointer to related work would be much appreciated.
The relationship between continuous causal diagrams and the modern laws of physics that you described was fascinating. What's the mainstream status of that?
Odd, the last paragraph of the above seems to have gotten chopped. Restored. No, I haven't particularly heard anyone else point that out but wouldn't be surprised to find someone had. It's an important point and I would also like to know if anyone has developed it further.
I found that idea so intriguing I made an account.
Have you considered that such a causal graph can be rearranged while preserving the arrows? I'm inclined to say, for example, that by moving your node E to be on the same level - simultaneous with - B and C, and squishing D into the middle, you've done something akin to taking a Lorentz transform?
I would go further to say that the act of choosing a "cut" of a discrete causal graph - and we assume that B, C, and D share some common ancestor to prevent completely arranging things - corresponds to the act of the choosing a reference frame in Minkowski space. Which makes me wonder if max-flow algorithms have a continuous generalization.
edit: in fact, max-flows might be related to Lagrangians. See this.
Showed up in Penrose's "The Fabric of Reality." Curvature of spacetime is determined by infinitesimal light cones at each point. You can get a uniquely determined surface from a connection as well as a connection from a surface.
Obviously physicists totally know about causality being restricted to the light cone! And "curvature of space = light cones at each point" isn't Penrose, it's standard General Relativity.
Not claiming it's his own idea, just that it showed up in the book, I assume it's standard.
David Deutsch, not Roger Penrose. Or wrong title.
Page number?