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
