# Re: PhD-thesis on Observational Selection Effects

From: Jacques Mallah <jackmallah.domain.name.hidden>
Date: Thu, 06 Jul 2000 20:24:52 EDT

>From: Brent Meeker <meekerdb.domain.name.hidden>
Jacques Mallah wrote:
> > The whole point is that right now, we don't have such a theory! And
>what my analysis seems to point to is that there isn't one.
>
>What analysis is that?

My analysis example in the anthropic principle page.

>The hypothesis that every mathematically consistent universe exists may
>admit infinitely many in which there are no free parameters and in which
>there are sentient beings.

Of course it does. Although, the term "free parameter" then just becomes
a matter of arbritrary definition, since the ensemble has no free
parameters.

> > If, on the other hand, we had a theory that exactly specified (up to
>many decimal places) each physical constant, and it predicted the values we
>see, then that theory would have a huge probability advantage over #2
>(which only constrains the values to a range, albeit a narrow one).
>
>I assume you say this because, although p(o|2)=p(o|4)=1, you assign a lower
>prior probability to 4 so that p(4)>>p(2).

Nope. I was assuming equal prior probabilities.
I never said p(o|2)=1. I just said it was "large". Suppose in the case
of one physical parameter (p) some model, i, leads to a uniform Bayesian
probability distribution for what value would be observed for p within a
range of width w, and no chance for outside that range. Then if the
observation, o, falls within that range, the probability _density_ p(o|i) =
1/w. (And p(o|i) = 0 if o is outside that range.)
If w = 0, and the predicted value for p is correct, p(o|i) ~ inf.
In practice there is the experimental uncertainty (e.g. of width u, so
p(o|i) would ~ 1/u).
#2 beats #1 by having a much smaller a-priori w, larger 1/w.

> > The advantage will always belong to *some* type of ensemble theory,
>erasing the anthropic "coincidence". [...]
> > But important to point it out now, lest physicists should come up
>with a unique consistent set of physical constants, and then try to use
>that as evidence against the MWI way of thinking about physical laws! It
>wouldn't be.)
>
>It would not disprove an ensemble theory, but it would make it irrelevant.

Hardly. On the contrary, since #1 is so unlikely, such a development
(eliminating #2) would make AUH more important than ever.

>Imagine Ptolemy saying to Newton, "That all possible epicycles exist is the
>simplest hypothesis. Your elliptic orbits and theory of gravity are not
>evidence against it."

Where's the similarity? In the P-N case, p(o|P) << p(o|N). P and N
could still argue about the priors p(P) and p(N), but there Occam's razor
also favors N.

> > You still don't seem to understand what the MWI says. In both 1) and
>2) you seem to assume branching is some special physical process beyond
>normal Shrodinger evolution. You probably have seen a lot of books
>characterize the MWI that way.
>
>Apparently I don't. I was relying on David Deutsch's description of an
>experiment to distinguish Everett's MWI from the other interpretaitons
>[Quantum Concepts in Space and Time, Penrose & Isham, pp 219]. "...At this
>point an outside observer could measure O(T) but the result would be to
>transfer the split to himself..." Deutsch seems to think a split has
>occured in the quantum process, which is a parallel computation, and if it
>is observed the observer will split. Is it your interpretation that these
>splits don't occur or that they are not physical processes or they are just
>part of the unitary evolution?

I wouldn't advise relying on Deutsch. He has his own school of thought
about the MWI. (OK, we all do.) I'm sure few Copenhagenists would accept
that thought experiment as a valid way to distinguish them experimentally.
But I'm sure he is also just using split as a figure of speech, or else he
means a divergence in train of thought.

> > As I said, in both my version of the MWI and Everett's, "branching"
>is just a manner of speaking about the typical behavior in Shrodinger
>evolution where decoherence occurs.
>
>I understand decoherence is just part of the unitary evolution and hence to
>get from the *almost* diagonal density matrix to a definite classical value
>still takes a step.

Yup.

> >A theory of mind is needed by *any* theory to generate *any* prediction
>about observations. I attempt to formulate one in
> > my CWIA.
>
>In Deutsch's paper [ibid] he requires a 'mind' for his crucial experiment;
>but the mind seems a very simple one. The hard part about the experiment
>is keeping all the interactions reversible.

What's your point? BTW, even a rare Copenhagenist who might be inclined
to allow an interference experiment as an experimental test of 'collapse'
would insist on using a human brain if experiments on simpler systems failed
to show collapse. Others would simply hold fast to their operationalist
doctrine and mumble something about different information being available to
different people.

> > Finally, it's obvious to me that a stochastic theory, which says that
>the Kolmogorov complexity of the physical world increases with every event,
>continuously violates Occam's razor.
>
>It certainly leads to an increase in information - but not number of
>hypotheses.

Hypotheses, in this context, mean a description of the world. The most
precise form of Occam's razor we have (albeit, still imprecise) is to take
the prior probability of a model to be exp(-l), where l is the length of the
shortest description, ie the K complexity. Note that adding an extra
statement of fixed length thus decreases the prior by a factor independent
of the length of the rest, as should obviously be the case if that statement
is unrelated to the rest. (Compare the model with the extra, vs. the one
otherwise the same but without it.)

>In any case Occam's razor is a rule-of-thumb; you're trying to
>promote it to a law of physics.

Not a law of physics, but the basis upon which physicists work.

- - - - - - -
Jacques Mallah (jackmallah.domain.name.hidden)
Physicist / Many Worlder / Devil's Advocate
"I know what no one else knows" - 'Runaway Train', Soul Asylum
My URL: http://hammer.prohosting.com/~mathmind/

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Received on Thu Jul 06 2000 - 17:32:12 PDT

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