Re: many worlds (was RE: Einstein)

From: Mitchell Porter (
Date: Tue May 27 2003 - 01:59:02 MDT

A much-delayed reply to these posts... I've been discussing another
(John Cramer's "transactional interpretation") elsewhere, and have come to
conclusion that to make any progress on this question (the truth about QM),
has to think about all the various interpretations (hidden variables, many
time-symmetric, spontaneous collapse) at once, because they have all sorts
unexpected connections... and that this is going to be slow hard work,
two things have to be done:

(i) Get the technicalities of each interpretation right.
(ii) Get them to 'talk to each other' - establish a common frame of

I will spare you all my current thoughts about those connections, since they
are a work in progress, but interested parties might want to look at the
preprints hep-th/0302111 (which I think is pointing the way towards an
Everett-derived "one-history" interpretation) and quant-ph/0305089.

D. Goel said

> > Well, the coefficients of "mismatch states" like |x=1>|you=2> should
> > become very small, compared to those of "veridical states" like
> > |x=1>|you=1>. But I don't see how that addresses the basis problem.
>The mismatch state's coefficient was 0 in the first place. I had
>added and subtracted a term like that to both sides.

I was describing an effect of decoherence (mismatch coefficients become
small). In your argument (see,
you are basically taking this effect for granted and setting those numbers
equal to zero. Which is OK as an approximation, precisely *because* of
decoherence, but there should in actuality be an infinitesimal (but still
nonzero) amplitude for cross-terms in your equation (3).

In any case, I think the crucial step is this:

>Again, note that (2) can be put into (4) in many many ways. But the
>issue is to put the time-dependent equation (3) into form
>(4)----viz. we want an "interpretation" that is "stable" with time.

Who says? Where does this condition come from? This looks to me
like an "extra postulate".

Amongst the experts, I think the most popular way to pick the many
worlds out of the wavefunction is via 'decoherent coarse-grained
histories'. Each history is specified by a time series of projection
and it's required that each history decoheres from each other history,
where this is calculated using a 'decoherence functional' constructed
from the Hamiltonian. There is a brief exposition of this in the second
paper above, by Hartle. But an important point is that there is no
canonical set of decoherent histories associated with a particular
wavefunction, not even a canonical 'maximal set' (no extra histories
or finer graining of operators possible). So it's the basis problem again,
at a more sophisticated level.

Lee Corbin said

>I suggest that you post your question to
>the Fabric of Reality list, where Deutsch himself often answers

I tried posting there years ago, a question about Deutsch's "shadow
photons". Early in his book he says that the double-slit diffraction
pattern can be explained by the effect on photons in our world of
"shadow photons" in the worlds next door. My question was along
the lines: Can you mathematically describe this in terms of interactions
between individual shadow photons and individual photons in this
world? I don't think he could, in which case this way of speaking is
misleading. As I recall, I posted my question, it never showed up,
the moderator hadn't seen it, and I just lost patience and stopped
trying. I'll probably have another go eventually, but first I want to
work through my own version of many-worlds, in the context of
step (ii), back at the start of this post.

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