On Wednesday, April 20, 2022 at 6:14:31 PM UTC-6 Alan Grayson wrote:
On Wednesday, April 20, 2022 at 5:21:47 PM UTC-6 Alan Grayson
wrote:
On Friday, April 15, 2022 at 12:41:03 PM UTC-6
meeke...@gmail.com wrote:
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
The authors regard quantum fluctuations as fundamental.
How are they defined? AG
I think I get it. Whereas before QM we could attribute
single, unpredictABLE outcomes to ignorance of initial
conditions, and but with QM our understanding is augmented;
now we can attribute it to ... nothing? AG
Is that because, if we could attribute a single, unpredictable
outccome to ignorance, that would be, defacto, a hidden variable
theory? AG
