Re: subjective reality

From: scerir <scerir.domain.name.hidden>
Date: Wed, 24 Aug 2005 23:38:05 +0200

Godfrey:
'MWI + Projection postulates should reproduce
regular Copenhagenian QM since MWI is basically
QM - Projection Postulates!'



Imagine a superposition like this

|'spin_z' +1> |'detector' +1> +
|'spin_z' -1> |'detector' -1>

It describes a superposition of spin up/down
states, and the entagled (or relative) states of a
detector.

Now imagine a second - whatever, human? - device,
to measure a specific observable of the above
superposition.

Let this observable be such that the ray generated by
the above superposition state is an eigenspace of this
observable, corresponding to a definite eigenvalue,
the eigenvalue 'yes'. Since neither component of
the above superposition state lies in the eigenspace
of this observable, this observable fails to commute
with the 'spin_z' observable, and fails to commute
with the 'detector' observable.

We can write (canonically) ...
|'z-spin' +1> |'detector' +1> |yes> +
|'z-spin' -1> |'detector' -1> |yes>

In a MWI, a world should instantiate an eigenvalue
for an observable if the superposition term associated
with that world is an eigenstate of the observable
corresponding to that eigenvalue.

So, after the (second) measurement, what would
an Everettista write?

This one?

|'z-spin' +1> |'detector' +1> |?> <=> world A
|'z-spin' -1> |'detector' -1> |?> <=> world B

(Since, in each world, the observable measured by
the second - whatever, human? - device does not
commute with the 'spin_z' observable, so it has no
predeterminate value, that is to say that the outcome
of the (second) measurement must occur by chance.)

Or this one?

|'z-spin' +1> |'detector' +1> |yes> <=> world A
|'z-spin' -1> |'detector' -1> |yes> <=> world B

(In this case the fact that the second device would later
record the state |yes> seems to be fixed ... in advance
of the measurement itself. And this is magic. White Rabbit?
What else?)

Godfrey:
'I believe that YD is incompatible with
the whole formalism of QM which I don't quite
think is simply reducible to Unitary Evolution
plus Collapse, by the way.'

Maybe.

s.

[It is too late here, I cannot write more, and I cannot
check the above :-)]
Received on Thu Aug 25 2005 - 13:32:29 PDT