[extropy-chat] Role of MWI and Time Travel

[scerir]

> Is that what is meant by Conway and the others?
> That past causes cannot determine some event in
> order for it to be "free"? That is too strange.

Difficult question (at least for me). And I'm not
sure I understand your (deep) question properly.
Anyway I try to write what I can :-)

As W.Pauli said 'In the case of undefiniteness 
of a property of a system for a certain arrangement 
(with certain state of the system) any attempt 
to measure that specific property destroys
(at least partially) the influence of earlier knowledge
of the system on (possibly statistical) statements
about later possible measurement results.'

Difficult? It is (at least for me). Let us try 
to say some more, i.e. about that 'undefiniteness'.

Imagine a pure state describing a 1/2-spin particle
prepared as
    (1)  psi = 1/sqrt2 [S(+)_z + S(-)_z]
Imagine we wish to know if that 1/2-spin particle
has, *before* we measure it, a *definite* *value* 
of the spin, on the z projection, i.e. +1/sqrt2 S(+)_z 
*or* -1/sqrt2 S(-)_z .

We can write that [S(+)_z + S(-)_z] =
= 1/sqrt2 [(S(+)_x + S(-)_x) + (S(+)_x - S(-)_x)] =
= 1/sqrt2 (2 S(+)_x) = sqrt2 S(+)_x 
Then, psi = 1/sqrt2 [S(+)_z + S(-)_z] => S(+)_x
where S(+)_x is a state for which the spin, on the
x projection, is +1/2 .
This means that if you have a certain number of
particles described by equation (1)
and you send them through a Stern & Gerlach,
with a field along the x axis, *all* particles 
take the *same* path, qualified by the state 
S(+)_x .

On the contrary, if you have the same number
of particles described by 
(1) psi = 1/sqrt2 [S(+)_z + S(-)_z]
and you pretend to say that, *before* the measurement, 
each particle must not be in the superposition state 
1/sqrt2 [(S(+)_x + S(-)_x) + (S(+)_x - S(-)_x)],
but it is in the state 
S(+)_z = 1/sqrt2 [(S(+)_x + S(-)_x)]
*or* in the state
S(-)_z = 1/sqrt2 [(S(+)_x - S(-)_x)]
well, passing these particles through the 
Stern & Gerlach you will find that 50% of them 
take one path, and 50% of them take the opposite 
path.

All the above just means that if you have a
simple state like psi = 1/sqrt2 [S(+)_z + S(-)_z] =
= 1/sqrt2 [(S(+)_x + S(-)_x) + (S(+)_x - S(-)_x)],
you cannot attach to this state, *before* the
measurement is performed, any *definite* property,
i.e. 1/sqrt2 [(S(+)_x + S(-)_x)], 
or 1/sqrt2 [(S(+)_x - S(-)_x)]. 

But we find there are different kinds of
'undefiniteness'. 

John Bell, i.e., writes in 1966 that "It was tacitly
assumed that measurement of an observable must yield
the same value independently of what other [compatible]
measurements may be made simultaneously [....] There
is no apriori reason to believe that the results
should be the same. The result of an observation
may reasonably depend not only on the state of the 
system (including hidden variables) but also on
the complete disposition of the apparatus [...]".

It is easy to realize that the above has much to
do with some famous koan by Bohr, such as "the 
impossibility of any sharp distinction between the
behaviour of atomic objects and the interaction
with the measuring instruments which serve to define
the conditions under which the phenomena appear."

It is easy to realize that Bohr's "complementarity"
has much to do with Bell's and Kochen-Specker
"contextuality". What John Bell (in 1966) and 
Kochen-Specker (1967) showed is that any deterministic
theory (and any hidden variable deterministic theory)
which would attribute a *definite* result to a
quantum measurement, still reproducing the statistical
properties of the indeterministic QM, must be
"contextual".

http://koantum.blogspot.com/2006_04_01_koantum_archive.html
http://koantum.blogspot.com/2006/04/koantum-end-game.html

What John Bell (in another more famous theorem), 
and Ghirardi, and Eberhard, etc. showed, is that
any deterministic theory (and any hidden variable 
deterministic theory) which would attribute 
a *definite* result to a quantum measurement, 
still reproducing the statistical properties of 
the indeterministic QM, must be "superluminal".

>From the above "undefiniteness", "contextuality",
supposed "superluminality", you can get an idea,
at least 'in nuce', of what it is possible to say
about the so called particle's "free will". 
And if one is as brilliant as Conway and Kochen 
(they wrote many papers about quantum "contextuality") 
you can even try to *prove* something, under strict 
conditions, about "free will" in general! 
     
[I'll write about the rest later, or tomorrow]

> Especially---moreover---if it is also added that
> future 'causes' are forbidden. The latter I can
> only interpret to mean as the event may not leave
> an unambiguous record, so that the event may be
> (backwards) determined.

> As for overpopulation, I would simply suppose
> that the version of me who saw the photon go
> up would smoothly merge into the version of me
> who saw it go straight; if we branch into 
> separate versions going forward in time, wouldn't
> it be very natural to merge into a single version
> going backwards?