Le 07-juin-05, à 12:28, Russell Standish a écrit :

On Tue, Jun 07, 2005 at 10:37:10AM +0200, Bruno Marchal wrote:OK. it seems to me that (equation 14 at http://parallel.hpc.unsw.edu.au/rks/docs/occam/node4.html ) ?In LaTeX, this equation is \frac {d\psi}{d t}={\cal H}(\psi) It supposes time, but not space (TIME postulate). Moreover, it supposes continuous time,

`Yes but that is a lot of assumptions. Why a linear time capable of`

`being represented by the very special line with the usual topology of`

`the reals? I can imagine many topology on the reals.`

but I do suggest in the paper how it might be generalised to other possible timescales.

`yes but if you pretend to derive your equation, I don't understand what`

`you mean by generalizing your conclusion (if only by: I have not derive`

`it and it remains some work to do).`

Perhaps it also supposes continuity in time for \psi, although this probably flows from assuming continuity of time.

`Why should a function be continuous just because it is defined on a`

`topological space (which is what I assume you are saying when you say`

`continuity of time).`

I do not think time is necessarily continuous - I think it is interesting to explore alternative QMs without this assumption.

`Sure. But again how to talk on derivation then. I mean if someone`

`pretend to derive B from A, then if someone else derive something mùore`

`general than B from A, it is a critic of the assertion that B has been`

`derived from A. If from facts I can derive the murderer is among John`

`and Charles, I am not so interested in knowing the derivation can be`

`generalized into leading that the murderer is among John, Charles, Lee,`

`Bruno and Nicole!`

The question is whether this is the most general evolution equation for continuous time, or whether there is some more general equation.

Absolutely.

Remember, we do have already that \psi is a member of a Hilbert space, so we can write things like:

`OK, but you assume Set theory (that by itself is huge in our context).`

`I show only that you have a preHilbetian space (why should "cauchy`

`sequence of vectors converges).`

\psi(t')-\psi(t) = ... What do you mean by derivability notion for H, and topological notion?

`Topological notion are needed for talking of continuity (a continuous`

`function is just a function from topological space into a topological`

`space such that the inverse image of open set is an open set).. You`

`"assume" the familiar topology of reals, complex number, etc.`

`Derivability is a stronger requirement (although some algebraist would`

`introduce many nuances). Someday I will show you make also assumption`

`on consciousness, but that is more subtle, and then all physicist if`

`not almost scientist are doing them when they pretend to solve the`

`consciousness problem like Dennett, or when they put it under the rug`

`(a little bit like Lee in his last posts, I would say).`

`Look Russell, as I said I appreciate your attempt, it is just that, as`

`Hal and Paddy mentionned, there remains quite a lot of work to make it`

`thoroughly communicable. You should really put more clearly your`

`assumptions. You assume a vast part of mathematics, and I would say of`

`physics, mainly with your time postulate and your equation. Compare`

`your work with those I have mentionned (I will give the reference for`

`those you don't have yet). Don't compare it to quickly to mine where`

`the assumptions are made still at a much more basic (logical and`

`arithmetical) level. I assume less than Peano arithmetic. I know I`

`could seem a little bit presomptuous, but nuance would make the post`

`more long and more boring. Hope you don't mind, (actually I would be`

`glad someone criticize the most severely possible my work),`

Bruno http://iridia.ulb.ac.be/~marchal/