On 25 Dec 2017, at 21:41, agrayson2...@gmail.com wrote:
On Monday, December 25, 2017 at 8:28:30 PM UTC, Russell Standish
wrote:
On Sun, Dec 24, 2017 at 07:11:25PM -0800, agrays...@gmail.com wrote:
>
> *OK. I was thinking of the time evolution operator, denoted by U,
which I
> believe is linear in t. AG*
Yes, it is linear and unitary. Unitary operators are linear, but
linear operators are not necessarily unitary. That is what I meant
when I said "unitary is not linear". They are not synonyms.
>
>
> > Projection operators are linear.
>
>
>
>
>
> *IIUC, projection operators model the "collapse" of the
superposition of
> states to a single state within the superposition. Since the
measurement
> process is believed to be non linear, how can the projection
operator be
> linear?
I've never heard of a nonlinear measurement process. Who believes
that? The only person who's done any work researching nonlinear QM was
Weinberg IIRC.
Spin measurements are irreversible in principle, not simply FAPP.
Bruce
showed that on Avoid2 IIRC. I think this means the measurement
process,
at least in this case, must be non-linear. If that's true, then how
can a linear
process such as decoherence, model measurements? AG
von Neumann's proposal was to use projection operators, which are
linear, but non-unitary. Being non-unitary is a problem, given unitary
evolution is one of the foundational axioms of QM.
Unitary evolution does not extend to the measurement process;
In the theory which assumes a physical collapse. Without collapse, the
projection is a first person indexical explainable by Mechanism.
only
evolution of the wf prior to measurement. AG
Which leads to a dualist (and unknown, controversial) theory of mind.
That is the main motivation for Everett: it solves the measurement
problem, just by eliminating the collapse of the wave, and showing how
the recover the appearance of collapse in the mind (or in the personal
diaries) of the observers.
The extension of that idea to arithmetic seems promising to explain
how the wave itself get selected in the mind of most universal beings.
Bruno
> This raises a question about decoherence. If the myriad of
> individual processes are linear, which I believe is what the model
affirms,
> how can any measurement be non linear as it presumably is for spin
> measurements. AG*
>
Indeed that would be a problem. A sum of unitary operators need not be
unitary, though.
--
----------------------------------------------------------------------------
Dr Russell Standish Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Senior Research Fellow hpc...@hpcoders.com.au
Economics, Kingston University http://www.hpcoders.com.au
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