Jacques Mallah wrote:
>
> --- Russell Standish <R.Standish.domain.name.hidden> wrote:
> > Jacques Mallah wrote:
> > > resulting in M(y) = y <y|x> / (y <y|y>) = <y|x>
> > > which is still the wrong formula since M(y) should
>
> > >be p(y) = |<y|x>|^2. Your paper seemed, from what
> I
> > > could tell, to have the same problem and thus give
> > > a wrong prediction.
> >
> > OK, I've been hoisted by my own petard. The basic
> > axioms of probability require the state space to be
> > a Hilbert space, which implies the L_2 norm should> > be used, ie the modulus squared of the above
> > property. I skipped over this portion of it in
> > my paper, so it is not suprising I made a mistake. I
> > also haven't opened a QM textbook in 15 years.
>
> Well I doubt your approach to deriving the
> probabilities is legitimate, and this certainly
> doesn't help convince me otherwise. So I suggest you
> try to fix up your paper.
It is the answer to the question "What is the function over a complex vector
space consistent with the axioms of probability?". If there were more
than one such argument, then I would be in trouble. However, I seem to
remember from when I was studying statistics and probability, that
only one such answer is possible. Of course, one can ask the question
"Why a vector space (or equivalently, why linearity?". I do ask this
question, and give in my opinion, a vague and somewhat unsatisfactory
reason for this, but hey we must start somewhere. One can also ask the
question "Why these axioms for probability?". Well, I'm going to duck
that one!
I will expand that part of the paper, as it is now clear that this is
less widely understood than I thought. But this may take a while,
given current commitments.
>
> > > > A quantum history is a set of observed outcomes
> > > > (linked by time), governed by a quantum process
> > > > (ie Schroedinger equation).
> > >
> > > First, explain what you mean by "linked".
> > > Second, the SE governs a physical system, not
> > > a "set of observed outcomes".
> >
> > Linked in the sense that points of a trajectory are
> > linked. Not a difficult concept.
>
> So you seem to be saying that there is some
> variable U(t) which varies continuously, and that U
> takes on "observed outcome" values. If so, be *much*
> more specific about what is involved, and I might
> start understanding what you have in mind. (Which, in
> turn, might help me learn you some stuff.)
>
U(t) need not be a continuous function. t, however, is drawn from a
continuous set. U(t) is also observer dependent, but unique for every
observer (which I identify as a particular history).
> > In the Multiverse view, there are _no_ physical
> > systems. The SE governs evolution of the individual
> > histories (or worlds if you like) of the Multiverse.
>
> Why isn't the multiverse a physical system then?
>
This is probably a question of definitions. I suspect that most people
would not think of the Hilbert space on which the SE is defined as a
physical system. Trajectories through that Hilbert space, is more
commonly identified with a physical system. In order to have a
trajectory, one must add some initial conditions.
I don't know about you, but my impression of what the Multiverse is
that it is the whole Hilbert space of possibilities.
> =====
> - - - - - - -
> Jacques Mallah (jackmallah.domain.name.hidden)
> Physicist / Many Worlder / Devil's Advocate
> "I know what no one else knows" - 'Runaway Train', Soul Asylum
> My URL: http://hammer.prohosting.com/~mathmind/
>
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>
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Dr. Russell Standish Director
High Performance Computing Support Unit, Phone 9385 6967
UNSW SYDNEY 2052 Fax 9385 6965
Australia R.Standish.domain.name.hidden
Room 2075, Red Centre
http://parallel.hpc.unsw.edu.au/rks
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Received on Tue May 16 2000 - 20:30:48 PDT