On 27 Feb 2015, at 07:09, Bruce Kellett wrote:
Jason Resch wrote:
On Thu, Feb 26, 2015 at 10:17 PM, Bruce Kellett <bhkell...@optusnet.com.au
<mailto:bhkell...@optusnet.com.au>> wrote:
Jason Resch wrote:
On Thu, Feb 26, 2015 at 9:51 PM, meekerdb
<meeke...@verizon.net
On 2/26/2015 7:10 PM, Jason Resch wrote:
So then the mystery of the Born rule is solved. I
don't see
why/how adding collapse solves anything.
I[t] adds that one of the probable states happens. MWI
fails
to add that.
Isn't it enough when one considers the FPI (which tells us you
will only experience one of the probable states)?
FPI has been around a long time. In the earlier literature on the
Anthropic Principle it was known as self-selection. The problem is
that any such principle applied to QM assumes what has yet to be
proved -- namely that anything that can be considered a "self" or
"1p" to be indeterminate about.
All it requires is denying there is magic involved in the first-
person view.
That assumes that the first person view exists -- which has yet to
be proved from within the theory.
That has been done.
It is simple intuitively with the mechanist (see the first step of the
UDA in the paper sane04).
It is subtle mathematically. The 3p-self can be defined by Gödel's
beweisbar predicate []p (beweisbar''p'). The 1p-self is then given by
the logic of []p & p. (the true justfied opinion of Theaetetus). It
can be shown that it obeys to the classical knowledge theory S4
(unlike the 3p-self). (indeed S4Grz).
If someone created a duplicate of you in Andromeda, there would be
no way for you here on Earth to know about that view because
there's no interaction between your brain on Earth and your Brain
in Andromeda. Similarly, there's no interaction between your brain
that's seen and formed memories of measuring the up-spin electron
and the one that's seen and formed memories of measuring the down-
spin electron. So unless you're operating according to a philosophy
of mind that allows it to violate physics and learn/know about the
other one, then there is no way to avoid the selection or
indeterminacy about which one you will later subjectively identify
with.
This is where the Born rule comes into play. You need some basis for
assuming that small off-diagonal terms in the density matrix
correspond to low probabilities.
The formalism merely says that an initial state evolves into a
superposition -- nothing is selected as a "person" in that
superposition that could self-select, or be an indeterminate
individual.
You seem to be ignoring/eliminating/denying the existence of the
first-person perspectives create by the brains that enter states of
superposition.
You assume that this happens. prove it!
It is intuitively obvious, assuming computationalism.
It is formally delicate: you need to understand that G* proves []p <->
[]p & p, and G does NOT prove that []p <-> []p & p.
This explains also why a subject feels like he is NOT a machine, and
why that feeling is correct from its first person point of view.
MWI does not lead to a useful notion of probability that can be
used, via the Born rule, to infer that interference terms are not
important.
I don't understand the above sentence. Could you clarify the
meaning in terms a non-physicist might understand?
As stated above, you need a notion of probability, and the Born rule
relating small terms to low probabilities, in order to get anywhere.
Attempts to derive the Born rule within the Everettian program have
proved to be either circular or incoherent. So the work remains to
be done.
My feeling is that Gleason theorem does answer this question, together
with comp and the FPI. The only work which remains to be done, and
which is huge: is that if we take comp seriously into account we have
to justify not just the collapse (Everett), but the SWE as well
(that's what UDA proves, and AUDA (the machine interview) confirms ...
until now.
Bruno
Bruce
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