Tim May wrote:
> On Wednesday, September 4, 2002, at 10:08 AM, Hal Finney wrote:
> > There are a few objections which I am aware of which have been raised
> > against the MWI. The first is its lack of parsimony in terms of
> > creating a vast number of universes. We gain some simplification in
> > the QM formalism but at this seemingly huge expense. The second is its
> > untestability, although some people have claimed otherwise.
>
> The latter is the more important. If, for example, the plurality of
> worlds are out of communication with each other, forever and always,
> then it means nothing to assert that they "actually" exist.
Worlds are never absolutely out of touch. There is a small degree
of interference which is always present between worlds in the MWI.
Of course this is infinitisimal in practice and can't be observed between
macroscopically distinct worlds. But there is a continuum from totally
disjoint worlds down to worlds which differ only microscopically and
where interference is easily observed, such as an electron double-slit
experiment. As our technology improves, we will be able to detect smaller
and more subtle degrees of interference, corresponding to worlds which
are more and more macroscopically distinct. Assuming the MWI is in some
sense "correct", then eventually it will become increasingly difficult
to draw the line and say that, for example, small objects can be in
distinct superpositions, but large objects cannot.
> In weaker forms of the MWI, where it's the early state of the Big Bang
> (for example) which are splitting off into N universes, De Witt and
> others have speculated (as early as around 1970) that we may _possibly_
> see some evidence consistent with the EWG interpretation but NOT
> consistent with other interpretations.
I'm not familiar with the details of this. But I know that much of
the impetus for increased acceptance of MWI models comes from the
cosmologists.
> > And the
> > third is that it retains what we might call the problem of measure,
> > that is, explaining why we seem to occupy branches with a high measure
> > or amplitude, without just adding that as an extra assumption.
>
> What's the problem here? I find it utterly plausible that we would be
> in a universe where matter exists, where stars exist, where entropy
> gradients exist, etc., and NOT in a universe where the physical
> constants or structure of the universe makes life more difficult or
> impossible (or where the densities and entropy gradients mean that
> evolution of complex structures might take 100 billion years, or more,
> instead of the billion or so years it apparently took).
The problem is more formal, that if we abandon measurement as a special
feature of the physics, there is no longer an axiom that says that
probability is proportional to amplitude squared.
> > By the metrics we typically use for
> > universe complexity, basically the number of axioms or the size of a
> > program to specify the universe, the MWI is in fact simpler and
> > therefore
> > more probable than the traditional interpretation.
>
> This I'm not convinced of at all. I don't find the Copenhagen (aka
> "Shut up and calculate") Interpretation requires any more axioms. So
> long as we don't try to understand what is "really" happening, it's a
> very simple system.
The conventional formulation, as described for example at
http://www.wikipedia.com/wiki/Mathematical_formulation_of_quantum_mechanics,
has special axioms related to measurement. Systems evolve according to
the Schrodinger equation except when they are being measured, when we
get wave function collapse. MWI rejects the axioms related to observables
and collapse. In the page above we can eliminate axiom 3 and probably
axiom 2 as well. You are left with nothing but Hilbert space and the
Schrodinger equation. It's a simpler set of axioms.
> And, putting in a plug for modal/topos logic, the essence of nearly
> every interpretation, whether MWI or Copenhagen or even Newtonian, is
> that observers at time t are faced with unknowable and branching
> futures. (In classical systems, these arise from limited amounts of
> information available to observers and, importantly, in limited
> positional information. Even a perfectly classical billiard ball
> example is unpredictable beyond a few seconds or maybe tens of seconds,
> because the positions and sets of forces (turbulence in the air
> currents around the balls, even gravitational and static electricity
> effects, etc.) are only known to, say, 20 decimal places (if that, of
> course). Because the "actual" positions, masses, sphericities, static
> charges, etc. are perhaps defined by 40-digit or even 200-digit
> numbers, the Laplacian dream of a suffiicently powerful mind being able
> to know the future is dashed.
This is true in practice, but I think there is still a significant
difference between deterministic systems like classical physics or the
MWI, and inherently non-deterministic systems like the conventional
Copenhagen interpretation of QM. In the latter you have the difficult
philosophical problem of explaining where all the information comes from.
This is what led Schmidhuber to suggest that quantum randomness is
generated by a pseudo random number generator; otherwise you can't
simulate the universe on a computer because computers can't create
true random bits. The Copenhagen interpretation is fundamentally
non-computable.
Hal Finney
Received on Wed Sep 04 2002 - 14:45:59 PDT