On 03 Jul 2014, at 20:30, Richard Ruquist wrote:
On Thu, Jul 3, 2014 at 1:14 PM, Bruno Marchal <[email protected]>
wrote:
On 03 Jul 2014, at 06:51, Richard Ruquist wrote:
Quantum measure is the result of solving Schrodinger's Eq.
yielding a different probability for each quantum state
and a different measure for each different scenario
unlike the invariant measure of the reals.
Do you disagree?
Richard
The quantum measure is a measure on solutions of an equation, like
square normed functions or operators in a linear (Hilbert) space
(like in both QM and functional analysis). The measure on the reals
is a measure on real numbers. With comp, the measure is on the
relative states. It is really a measure on the transition <a I b>.
In quantum mechanics it is given by [<a I b>]^2, but with comp this
must be explained by a measure on all the computations going from a
mind state corresponding to observing 'a to a mind state of
observing 'b, taking into account the fact that an infinity of
universal numbers justifies those transitions (= makes them
belonging to a computation).
It seems that the measure of the reals and the quantum measure and
the comp measure are three different things.
Yes. They can be related though. For example you need a Lebesgue
measure on the real or complex to have nice measure on the square
normed functions, which in classical quantum theory can be related to
the position or impulsion bases. Math are quickly delicate, like with
the need of distributions instead of functions, due to that damned
Dirac "functions".
With comp, I handle the measure problem by isolating the possible
logic and semantics associated with the different machine's view (the
'arithmetical hypostases p, []p, []p & p, etc.), with p arithmetical
sigma_1 sentences.
Bruno
Richard
The protocol of the iterated WM-duplication is a very particular
case. The first person histories with computable sequence like
"WWWWWW...", or "WMWMWMWMWM... ", becomes the white rabbits event,
and the norm is high incompressibility (a very strong form of
randomness).
The ultimate protocol is the "logical" structure of the sigma_1
arithmetic. By the dovetailing on the reals, it mixes a random
oracle with the halting oracle so that we can expect a "non-machine"
for the first person truth. But it is already a non machine, from
the machine view, by simple incompleteness.
The interview of the löbian machine does not provide the measure
calculus (Plato-Plotinus 'bastard' calculus with the Plotinus
lexicon), but it provides the logic of the measure one, from which
the measure calculus + the arithmetical constraints) should be
derivable (and the measure one admits a quantization confirming
things go well there).
Bruno
On Thu, Jul 3, 2014 at 12:44 AM, Russell Standish <[email protected]
> wrote:
On Thu, Jul 03, 2014 at 12:23:35AM -0400, Richard Ruquist wrote:
> On Wed, Jul 2, 2014 at 10:34 PM, Russell Standish <[email protected]
>
> wrote:
>
> > On Tue, Jul 01, 2014 at 04:30:52PM -0400, Stephen Paul King
wrote:
> > > Hi Russell,
> > >
> > > Ah! I don't quite grok it completely, but thank you for this
example. We
> > > had to assume an already existing measure on the Reals. Where
does that
> > > come from?
> > >
> >
> > The standard measure on the reals is based on the observation
that we
> > expect the set of real numbers starting with 0.110... to have
the same
> > measure as those starting with 0.111... That would be a
reasonable
> > default assumption for most purposes.
>
>
> The measure obtained by compression of the reals in binary form
is close to
> the quantum mechanic measure, but not exact.
> In fact, the quantum measure varies with the scenario, whereas
the measure
> of the reals is invariant.
> Richard
>
What do you mean? What is this "quantum measure"?
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