From: Mitchell Porter (mitchtemporarily@hotmail.com)
Date: Fri Aug 01 2003 - 19:40:55 MDT
>Here's the paper cited by the article:
>
>http://doc.cern.ch//archive/electronic/other/ext/ext-2003-045.pdf
Thumbs down from me. The basic idea is just Zeno's Arrow: it's not moving
at any instant in time, so it's never moving. Zeno was trying to prove that
motion is an illusion. Lynds, conversely, believes motion is real and that
therefore "there is not a precise static instant in time underlying a
dynamical
physical process", and also no "precisely determined" instantaneous values
of physical magnitudes. I find it peculiar that he does not simply propose
this
as the genesis of the uncertainty principle. The argument is that you can't
simultaneously have an exact position and a velocity; which at least
*resembles*
the uncertainty principle; but instead he says explicitly, they're not the
same
thing. Lynds's uncertainty is something extra.
In any case, the original argument goes nowhere as far as I'm concerned.
It's like an argument that there is no such thing as length, because
individual
points have no length, and adding zeroes just gives you zero. Well, in the
continuum model of space, any line interval of nonzero length is already a
little continuum; and there are infinitely many smaller continuum-intervals
within it; but none of that gets in the way of the individual points having
exact coordinates. An analogous view of continuous time would say that
change exists in any nonzero interval of time, and an instant of time is
just
the limit in which change is zero because the starting point and the
endpoint
are the same moment. This does imply that "process" or "becoming" is
something which involves more than one moment of time, but that should
not surprise anyone.
Julian Barbour's view, which Eliezer mentioned, is a response to the
technical "problem of time" in quantum cosmology. In ordinary quantum
mechanics, Schrodinger's equation takes the form
H psi (is proportional to) dpsi/dt
"H" is the Hamiltonian operator, which specifies the dynamics of "psi",
the wavefunction. The problem in quantum gravity is that you also know
that "H psi=0". This implies that the wavefunction of the universe does not
evolve in time. Barbour's theory is a many-worlds theory without time;
he says that the various spatial configurations to which psi assigns a
probability all exist, without evolving in time, and the perception of time
is just an illusion. I believe that Kant, having formulated the notion that
time was an "a priori form of intuition", had a similar idea - what if each
of "my experiences" is happening to a separate, static monad, rather
than to the one "changing" self?
Personally, I think we do have knowledge of change on a deeper level
than just the use of memory to confirm that "this moment differs from
my memory of the previous moment". If that sort of comparison was the
only way that we derived a sense of time's passage, then I think the
Kant/Barbour idea would be "phenomenologically viable", that is, it would
be an idea about fundamental reality which is at least consistent with
perceived reality. But in fact, it seems to me that perceived reality is
already a process at an unreflective level, and that "moments of experience"
are an artefact of reflection, and that the idea of trying to prove the
reality of time by comparing one moment with another is basically doomed,
precisely because you've already adopted a mode of perception in which
you are filtering out the dynamic aspect of things.
Anyway, apart from the philosophy, I may have a more formal problem with
Barbour's theory. How do you judge the plausibility of a multiverse theory,
given that by definition you are stuck in just one world? First of all,
there
simply has to be *something* in the postulated multiverse corresponding
to what you see; your world must be somewhere in the ensemble.
Second, yours should be an average sort of world, modulo anthropic
considerations. In Barbour's case, this means arguing that his (deluded)
observer-moments, with their (fake) memories, should characteristically
remember a past (which never happened) in which the statistics of events
conformed to ordinary quantum theory - since this is what we see in our
world. In making that argument, does Barbour need to use the probabilities
associated with each world by psi? Because if he does, I think it's fair to
ask what those probabilities actually mean.
Suppose someone said, "In my theory of the multiverse, complex systems
cannot form in most universes." You might object that this would make
our world unusual, violating the second principle above. Now suppose
that the multiverse theorist, instead of arguing anthropically, said, "Yes,
the complex-systems worlds are greatly outnumbered by the boring
ones; but the complex-systems worlds are *more probable*, and that
makes up for it." This way of talking makes no sense. The probability
in question cannot be "probability of existing", since by hypothesis all
these worlds exist equally. So what does it mean?
The only way out which I can see is via the concept of a "measure".
In calculus, a measure tells you how to sum over continua, by assigning
a size to each subset. Any set which consists of a countable number
of points has measure zero and can be ignored (unless there are
delta-functions involved, but let's not go there). If the wavefunction
of the universe can be interpreted as a measure - as the thing which
tells you *how* to count the many worlds - then the "probabilities" are
legitimate, and describe the actual universal prior for that multiverse.
Otherwise, the probabilities are just a nonsensical fudge factor added
to Bayes's formula without justification. (I think this is a familiar
consideration in many-worlds philosophy, but I've never seen it stated
this directly.)
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