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/
Received on Tue Jun 07 2005 - 11:59:15 PDT