At 06:46 AM 4/26/04, Bruno Marchal wrote:
The important point is that once we keep up comp through the eight points, we see that the laws of physics, whatever they are, must be given by the invariant in the comp-accessible worlds.
I'm pretty sure I now understand points 1-8, but let me confirm something: the conclusion of points 1-8 is *not* that "comp is true". The conclusion is that *if* comp is true, then the invariant predicted by that model will ultimately match the "laws of physics" that we have discovered empirically. One could accept points 1-8, but still remain agnostic about whether or not the invariant actually does match the empirical laws of physics - that is, agnostic about whether or not comp is actually true. Correct?
The task of point 9 is to start showing mathematically what the invariant actually looks like. You make the tantalizing claim that the invariant actually looks like quantum physics, but for the moment I have to remain agnostic, because I don't know enough about the mathematics of provability, nor do I know enough about quantum physics. From your perspective, are your results strong enough to make you suspect that comp is true?
That would make a great part of quantum physics into physical laws in the sense of comp. It would be a pleasure to explain this with more details. Are you willing to hear a little bit about Godel's theorem and some of its generalisation by Lob and Solovay?
I am certainly willing to hear about it - I know more about Godel's Theorem and the theory of computation than I do about quantum physics - but I doubt I know enough to make much sense of your explanations, so it might be a waste of your time. Perhaps all I can pick up right now is the flavor of your results. For instance, does your position entail that the "weirdness" of quantum physics is deeply connected to the "weirdness" of provability theory?