[extropy-chat] still no biscuit!

[Hal Finney]

At 03:24 PM 1/19/2005 -0500, Eliezer wrote:
>the hypothesis of conservation of momentum is not that momentum is 
>conserved 90% of the time or even 99.9999% of the time.  The hypothesis of 
>conservation of momentum is that momentum is conserved 100.00000% of the 
>time.  We may be uncertain, but the hypothesis of "conservation of 
>momentum" hypothesizes a state of affairs in which reality is *not* 
>uncertain; a reality in which it is *absolutely certain* that momentum 
>will be conserved on each and every occasion.

This is true, but if it should turn out that this law is broken, it is
likely that in fact it will turn out that momentum is conserved 99.9999%
of the time (or to a 99.9999% degree of accuracy).  That's how it has
gone in the past.  We used to believe in conservation of mass, but then
it was found out that mass can change very slightly when energy changes.
We used to believe in CP symmetry, but then it was found that a tiny
percentage of very rare particle reactions violate CP symmetry.

Today the standard model predicts CPT symmetry, but there are plenty
of authors who are searching for models that would allow the symmetry
to be broken.  And if it is, it will be broken to a very slight degree.
(And I think that this may indeed imply breaking conservation of momentum,
although I'm not sure).

I am attracted to the Schmidhuber model that says that all universes
exist, but that they have different "measures" which somehow represent
the degree of likelihood that we could experience them.  The measure of a
universe is based on the size of the information content used to describe
it (equivalently, the size of a computer program that could simulate it).
Simpler universes would have greater measure and therefore we are likely
to be living in a universe which is among the simplest possible that
can allow the creation of intelligent life.

This model can, with a bit of hand waving, explain why the physical laws
we observe are relatively simple, and predicts that conservation law
will more likely hold 100% of the time than 99.999% of the time, because
the latter case demands the complexity of specifying the exceptions.
OTOH without CP violation, matter and antimatter would balance and there
would be essentially no residual matter in the universe to form stars and
planets.  So we need a little bit of CP violation for planets to exist.
And of course we need conversion of mass to energy for stars to exist.
But if we had too much of a violation of these conservation laws, there
would presumably be other problems.  So we predict that physical laws
are complex enough to allow for life, but not more so.

We can explain things in this qualitative sense, "just so stories" which
may or may not be convincing.  It tries to provide some justification
for Occam's Razor.  The problem is that there is a loophole in the
explanation: more complex universes will have lower measure, but there
are correspondingly more of them.  It turns out that in the specific
Schmidhuber model these factors balance out.  We are reasonably likely
to be living in a universe which is basically lawful but has extremely
rare, bizarre exceptions to physical laws.  As long as these exceptions
could not have anthropic consequences, i.e. intelligent life would still
evolve, there is no strong reason for exceptions not to be present.

It is true that the classical conception of physical laws is that they
hold 100% of the time.  But even apart from these rather ideosyncratic
anthropic/multiverse views, I think many physicists see today's laws as
mere approximations to a deeper truth.  The mismatch between QM and GR
is a blatant reminder that we are far from a convincing and universal
physical model.  I would not be surprised if physicists working in these
frontiers agreed that conservation of momentum was more likely to hold
to a 99.9999% degree than with 100% universality.

Hal