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?
It makes me suspect indeed that comp is plausible, at least.
Actually that plausibility comes both for the 1-8 reasoning which forces
us to believe in some "many world", so the fact that some physicists
begin to think seriously about the possibility of many-things is by itself
a sort of confirmation. Interviewing the machines should give more
quantitative information about the "interference" between the possibilities.
Here too I want to say I got a confirmation, but, as I will try to explain,
I got something weaker than quantum logic, and I am afraid only the future
will decide. The problem is that 1) physicists propose not *one* quantum logic,
but a labyrinth of QL (to quote van Fraassen), and my interview gives rise
also to different sorts of QL. But forget all that, I will really try to give (new)
flavors of the mathematical confirmation of comp.
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.
We will see. Don't hesitate to tell me you don't understand, or that you are bored. Strictly speaking the math are much more simple than people imagine, at least for a passive understanding. But you should be frustated at the end, because we will arrive at my "incompetence point", that is, a set of open questions.
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?
Yes. The "flavor" is that eventually physics is equal to a sort of "integral on machine's self-ignorance", that is on machine's incompleteness. But today I still don't have, for example, a proof of something as simple as the violation of Bell's inequality, although I can argue it would be a miracle if they are not violated (in the comp physics I mean) due to the high non booleanity of the Arithmetical QL we obtain. Don't worry, I will try NOT to give a 120h course in mathematical logic which is just impossible without chalk & black board. But I will try to give some insights. I must think how to do it. It will help me, btw, to prepare my talk in Paris and Amsterdam so that any critics is welcome.