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
