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]
> 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.
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.
[Computationalist Aparte
And with Digital Mechanism, the mind-body problem is reduced with the
problem of justifying the wave-matrix itself from an apparently larger
one: all halting computations (equivalently, all true sigma_1
arithmetical sentences).
For this we can define "bet on p = 1" by []p & p, with p sigma_, with
two slight but important variants ([]p & <>p, []p & <>p & p).
The three of them gives rise to a quantization obeying quantum logic,
with semantics in term of differentiating neighborhood, or (at the G*
level) a more complicated limiting proximity structure. The key
advantage is that such logics appears at the G* level (in case you
have read one of my papers) and this help to understand the (giant)
difference between the qualia and the quanta, by the difference
between G and G* (inherited by the variants above, except []p & p, a
very interesting fact actually, but I will stop here on this for now).]
Hmm..., It looks like on this list, it is the same people who see
spooky actions at a distance in the universal wave or matrix
(multiverse) and who have a problem with the digital Mechanist first
person indeterminacy.
Precisely when you say
M1|psi> = (M1(+)|+>|-> - M1(-)|->|+>)/sqrt(2).
If Alice's result is M1(+), but no projection on to the
corresponding eigenvector takes place, then a subsequent measurement
of particle 1 by Alice would be represented by:
M1*M1|psi> = M1(+)*(M1(+)|+>|-> - M1(-)|->|+>)/sqrt(2).
You don't let the resulting Alice to repeat her measurement in the
relative state she found herself after the first, that violates what I
described above. The subsequent measurement is given by the evolution
of the independent terms. You just cannot factor out Alice (M1(+))
once she has made her measurement. She got herself entangled
irreversibly from her point of view, and can cohere again only by
getting amnesic of here (+) result (cleaning any trace possible of it
in here environment (something making no sense in Copenhagen, btw).
Bruno
http://iridia.ulb.ac.be/~marchal/
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