On 4/05/2016 3:41 am, Bruno Marchal wrote:
On 03 May 2016, at 00:32, Bruce Kellett wrote:
On 3/05/2016 1:49 am, Bruno Marchal wrote:
On 02 May 2016, at 07:54, Bruce Kellett wrote:
On 2/05/2016 3:15 pm, Jesse Mazer wrote:
On Mon, May 2, 2016 at 12:13 AM, Bruce Kellett
<[email protected] <mailto:[email protected]>> wrote:
No, I disagree. The setting *b* has no effect on what happens
at a remote location is sufficiently precise to encapsulate
exactly what physicists mean by locality. In quantum field
theory, this is generalized to the notion of local causality,
which is the statement that the commutators of all spacelike
separate variables vanish -- as you mention below.
And if you used full quantum description of the measuring
apparatus and experimenter, and didn't assume any collapse on
measurement, then there would in general be no single "setting b"
in the region of spacetime where one experimenter was choosing a
setting, but rather a superposition of different settings. Do you
think your preferred definition can be meaningfully applied to
this case, and if so how?
I do not know what you here mean by "collapse on measurement"? It
seems that you might be confusing a collapse to a single world
after measurement with the projection postulate of standard quantum
theory. The projection postulate is essential if one is to get
stable physical results -- repeated openings of the box in
Schrödinger's cat experiments would result in oscillations between
dead and alive cats.
The projection postulate is replaced by the FPI in Everett, and as I
explained yesterday, it is just self-entanglement, or what I call
often the contagion of superposition:
Alice * (up + down) = Alice * up + Alice * down.
If Alice look, as many times as she want at the up/down state of the
particle, she will find up (and always up) *and* down and always
down. The reason is that once she find up, Alice becomes Alice-up,
and that state does no more factor out the particle state (unless
memory erasure).
That is just the projection postulate, it cannot be replaced if you
want to agree with observation.
Well OK. If that is the projection postulate, then it is a theorem in
QM-without collapse, through the direct use of the First Person
Indeterminacy.
As I thought, you have confused this with the collapse of the wave
function to a single world.
That is the confusion of the Copenhagen people, who believe
(correctly) that a measurement select one world among many, but
believe (incorrectly) that the other worlds, or wave suterms, have
mysteriously disappear.
With Everett analysis of measurement, we have:
Alice * (up + down) = Alice * up + Alice * down. (linearity of tensor
product),
and it becomes:
Alice-seeing-up * up + Alice-seeing-down * down (linearity of time
evolution)
With the copenhagen collapse of the wave, we have:
Alice * (up + down) = Alice * up + Alice * down. (linearity of tensor
product),
and it becomes
Alice-seeing-up * up (non-linearity of time evolution)
or
Alice-seeing-down * down (again with a non-linearity of time evolution)
The proportion of worlds, or the probability of results being given by
the (square-root of 1/2)^2 (= 1/2), square root hidden above for
reason of readability.
When it is boiled down, this is nothing more than a matter of taste. By
concentrating on the individual worlds, so that
A(|+>|-> - |->|+>) --> A(+)|+>|-> OR A(-)|->|+>
where A(+) means "Alice sees + as her result", and so on, the
conventional understanding simply implements the insights coming from
decoherence and wider entanglement with the environment, leading to the
emergence of disjoint worlds: the original pure state reduces to a mixed
state (represented by the use of 'OR' in the above equation) as a result
of the partial trace over environmental degrees of freedom. The
alternative formulation (where 'OR' is replaced by '+') simply retains
the original pure state and does not represent the formation of disjoint
worlds following environmental decoherence.
This is sometimes referred to (following Tegmark) as the difference
between the 'frog' and 'bird' views. Nothing substantial hangs on this
-- it is just a difference of perspective which adds nothing to the
state. The 'frog' view is what you would call a result of FPI: I see it
as a result of the formation of actual disjoint worlds that continue to
evolve separately, never to influence one another again. The 'bird' view
is an abstraction that never actually influences anyone or anything.
Unless you sort out this confusion you will never understand quantum
mechanics.
You see a confusion, because sometimes I talk about the projection
postulate in the copenhagen frame, where it is associated with the
collapse during the corresponding measurement, and sometimes I talk
about the projection postulate in the frame of the non-collapse
formulation of QM (Everett), in which case there is no collapse
associated of course, but the differentiating or bifurcating
realities/computations (relative terms of the linear wave).
See Price for the analysis of the singlet state in those terms. Or
Tipler, that you interpreted incorrectly apparently by avoiding the
first person indeterminacy.
I did not misinterpret either Price or Tipler -- they both make the same
elementary mistake, and neither sees that they have, in fact, built
non-locality into their analyses. You need to make good your claim that
my analysis is a misinterpretation.
Bruce
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