Here's my comment on David Wallace's 2005 paper, "Quantum Probability from
Subjective Likelihood:
improving on Deutsch's proof of the probability rule" available at
http://philsci-archive.pitt.edu/archive/00002302/. I think this is probably
one of the main works referred to in the New Scientist article.
The main assumption Wallace uses for his derivation of the Born rule is
"equivalence", which means that any rational agent must regard
equally-weighted events to be equally probable. In my view, the biggest
problem with this assumption is, what if the two events have equal weights
but different phases? Wallace handles the question in a couple of sentences
on page 18:
As for phase, this can be incorporated
by allowing phase changes in the erasure process: if |'erased(i)',
rewardi> is a
valid erasure state, so is exp(i theta) |'erased(i)', rewardi>. More
directly, it can be
incorporated by observing that a phase transformation of an entire branch is
completely unobservable, so an agent should be indifferent to it.
(end quote)
I'd answer that an event being unobservable is not sufficient reason for an
agent to be indifferent to it. If it were, then we would all be indifferent
to events that will only occur after our death (such as the disposition of
our estates) but we clearly are not. Another way to see this is that the
phrase "phase change" in the above argument can be replaced with "quantum
suicide" and the argument goes through with the same force of logic (or lack
thereof).
Instead of saying any rational agent must follow the Born rule, I'd
reinterpret Wallace's derivation as saying that for any rational agent, if
he doesn't care about phase, then he should follow the Born rule. Similarly,
for any rational agent who really cares only about what he will observe, he
should be indifferent to virtually everything since he can always make the
observations come out the way he wants by using quantum suicide.
--------------------------------------------------
From: ""Hal Finney"" <hal.domain.name.hidden>
Sent: Monday, September 24, 2007 9:39 AM
To: <everything-list.domain.name.hidden>
Subject: New Scientist: Parallel universes make quantum sense
>
> New Scientist has an article on parallel universes:
>
>> David Deutsch at the University of Oxford and colleagues have shown
>> that key equations of quantum mechanics arise from the mathematics of
>> parallel universes. "This work will go down as one of the most important
>> developments in the history of science," says Andy Albrecht, a physicist
>> at the University of California at Davis. In one parallel universe,
>> at least, it will - whether it does in our one remains to be seen.
>
> It is behind a paywall at
> http://space.newscientist.com/article/mg19526223.700-parallel-universes-make-quantum-sense.html
> but I found a copy on Google Groups:
> http://groups.google.com/group/alt.kq.p/browse_thread/thread/9631b2e37ba5e7a2/fb3202c9c5b71228?lnk=st&q=%22new+scientist%22+deutsch+albrecht&rnum=1#fb3202c9c5b71228
>
> It has a great quote from Tegmark: "The critique of many worlds is
> shifting from 'it makes no sense and I hate it' to simply 'I hate it'."
>
> The thrust of the article is about recent work to fix the two perceived
> problems in the MWI: non-uniqueness of basis (the universe splits in all
> different ways) and recovering the Born rule. The basis problem is now
> considered (by supporters) to be resolved via improved understanding
> of decoherence. This work (which was not particularly focused on the
> MWI) generally seems to lead to a unique basis for measurement-like
> interactions, hence there is no ambiguity in terms of which way the
> universe splits.
>
> As for the Born rule, the article points to the effort begun by Deutsch in
> 1999 to base things on decision theory. The idea is that we fundamentally
> care about probability insofar as it influences the decisions and choices
> we make, so if we can recover a sensible decision theory in the MWI, we
> have basically explained probability. I've seen a number of critiques of
> Deutsch's paper but according to this article, subsequent work by David
> Wallace and Simon Saunders has extended it to the point where things
> are pretty solid.
>
> Hence the two traditional objections to the MWI are now at least arguably
> dealt with, and given its advantage in terms of formal simplicity (fewer
> axioms), supporters argue that it should be considered the leading
> model for QM. This is where we get claims about it being among the most
> important discoveries in the history of mankind, etc.
>
> It's interesting to see the resistance of the physics community to
> multiverse concepts. It all comes back to the tradition of experimental
> verification I suppose, which is still pretty much impossible. Really
> it is more a question of philosophy than of physics as we currently
> understand these disciplines.
>
> We see the same thing happening all over again in string theory. I
> don't know if you guys are following this at all. String theory is
> going through a crisis as it has turned out in the past few years that
> it does not predict a single universe, rather a multiverse where there
> is a "landscape" of possible sets of parameters, each of which would
> correspond to a universe. The big problem is that there is no natural
> or accepted measure (unlike with QM where everyone knew all along that
> the measure had to be the Born rule and it was just a matter of how
> many hoops you had to jump through to pull it out of your model). As a
> result it looks like it might be impossible to get even probabilistic
> predictions out of the string theory landscape.
>
> AFAIK no one within the community has followed our path and looked
> at algorithmic complexity as a source of measure (i.e. the Universal
> Distribution, which says that the simplest theories have higher measure).
> Granted, even if that direction were pursued it would probably be
> computationally intractable so they still would not be able to pull much
> out in the way of predictions. Neverthless physicists are skilled at the
> use of approximation and assumptions to get plausible predictions out of
> even rather opaque mathematics so it's possible they might get somewhere.
>
> But at this point it looks like the resistance is too strong. Rather
> than string theory making the multiverse respectable as we might hope,
> it seems likely that the multiverse will kill string theory.
>
> Hal Finney
>
> >
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Received on Mon Sep 24 2007 - 16:36:19 PDT