On 4/14/2022 2:00 PM, George Kahrimanis wrote:
On Wednesday, April 13, 2022 at 8:55:48 PM UTC+3 meeke...@gmail.com
(Brent) wrote:
Decoherence has gone part way in solving the when/where/what basis
questions, but only part way.
As I wrote at the end of my first reply to your message, I share your
concern about decoherence but I see the glass as half-full; that is,
with a little more subtlety I hope that the matter can be formulated
in clear terms.
Surely collapse is easier to handle as a general concept (except, on
the other hand, that it requires new dynamics). I forgot to mention
that *my argument for deriving the Born Rule works with collapse, too*
-- so it is an alternative to Gleason's theorem.
Here I define colapse as an irreversible process, violating unitarity
of course, and I keep it separate from randomisation. The latter means
that each outcome is somehow randomised -- an assumption we can do
without.
*Collapse can also be described in a many-world formulation!* It
differs from the no-collapse MWI only in being irreversible.
If you can throw away low probability branches, what's to stop you from
throwing away all but one? You've already broken unitary evolution. If
you read Hardy's axiomatization of QM you see that the difference
between QM and classical mechanics turns on a single word in Axiom 5
Continuity: There exists a *continuous *reversible transformation on a
system between any two pure states of that system.
My argument in outline is
1. assessment that MWI-with-collapse is workable;
2. therefore, outcomes of small enough measure can be neglected in
practice;
Yes, I've wondered if a smallest non-zero probability could be defined
consistent with the data.
3. now Everett's argument can proceed, concluding that the Born Rule
is a practically safe assumption (to put it briefly).
So I have replaced two assumptions of Gleason's theorem, randomisation
and non-contextuality, by the assessment of workability only.
If you don't feel comfortable yet with formulating collapse in a
many-world setting, let us also assume randomisation (God plays dice),
for the sake of the argument, in a single-world formulation. That is,
we ASSUME the existence of probability; then the previous argument
just guarantees that this probability follows the Born Rule.
Assume? Randomness is well motivated by evidence. And it's more random
than just not knowing some inherent variable, because in the EPR
experiment a randomized hidden variable can on explain the QM result if
it's non-local.
Of course I favour the first version of the argument, using the
many-world formulation of collapse, to avoid the "God plays dice"
nightmare.
Why this fear of true randomness? We have all kinds of classical
randomness we just attributed to "historical accident". Would it really
make any difference it were due to inherent quantum randomness? Albrect
and Phillips have made an argument that there is quantum randomness even
nominally classical dynamics. https://arxiv.org/abs/1212.0953v3
Brent
Thanks for the comments so far, because they stirred my thinking and
motivated fresh ideas, some of which I hope will prove helpful and
worth discussing, if and when they mature.
George K.
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