From: maoh@phyast.nhn.uoknor.edu (Maureen O'Halloran)
Subject: Re: behavior and evolution
Organization: Engineering Computer Network, University of Oklahoma, Norman, OK, USA
Date: Sun, 16 Aug 1992 00:02:34 GMT

julian@fraser.sfu.ca (Julian Shillcock) writes:

> ... At least that we do no have any theory
>with the predictive power of the theories of physics. (By the by no one 
>responded to my question of how many theories in physics there are... 
>at my last count there are only five or six: General Relativity (including
>special as a "special" case), Relativistic quantum mechanics, Maxwell's
>equations and statistical mechanics. Although it is arguable whether QED
>and Maxwell's equations are derivable from RQM, anyway)

The number of theories that exist will depend on the definition of
what is a theory.  I guess you're talking about basic theories. First
you must define what the basic forces are: gravitational,
electro-magnetic and weak nuclear forces, strong nuclear force.
Maxwell's equations would be the "theory" of electromagnetic forces.
 To date the electromagnetic and weak nuclear forces have been
combined (by Weinberg and Salam) as the electro-weak force, much the
same way Maxwell showed that electric and magnetic forces are two
parts of the same thing. I believe this is what you would call QED, so
Maxwells equations are a simplification of part of QED. (Don't quote
me on this because I'm not an expert on QED)

Next are the theories that describe how you actually calculate things.
You would use General Relativity to calculate what happens during a
supernova explosion when gravity, electromagnetic and nuclear forces
are all acting between various particles.  You use Quantum Mechanics
to calculate what happens in atoms, plasmas, etc.  Last I heard
General Relativity and Quantum hadn't been "reconciled" which I think
means that no one knows what to do when both theories apply, as in
black holes.  

We also can't solve any problem analytically (ie, write down an exact
equation that is the solution) for more than two particles!  You may
have heard some one say that the "three-body problem" has not been
solved.  However given a big enough computer and enough time, we can
solve problems numerically to arbitrary accuracy.  Whether the three
body problem _can_ be solved is unknown, it may take invention of a new
kind of math, the way Newton invented calculus to solve problems in
classical mechanics.

When the number of particles in the system we're interested in gets
large, things become so complicated they get simple again.
Probabilities take over and statistical mechanics can be used to
describe the average macroscopic properties of the system while
ignoring microscopic motions of individual particles. If you use
statmech and quantum at the same time you call it Many Body Quantum
Theory. Thus the hardest problems to solve are "few-body problems",
where the number of particles is too large to solve on present day
computers, but too small for statistics to predict anything.
  
So the answer to "how many theories" depends on what you mean by a
theory. Is F=ma a theory and F= GMm/r^2 = gravitational force 
a separate theory?
Or do you include gravity in classical mechanics when calculating
trajectories and call them part of the same theory?

> .... Then in stat. mech. one makes massive  assumptions
>that allow predictions to be made but at the expense of knowing exactly what
>the system is doing.

Massive assumptions may be made in APPLYING stat mech, but the basic
theory has very few assumptions.  The only one I can think of off-hand
is that the probability of a certain macrostate is proportional to the
number of microstates.

>....  I do not see any problem
>in my asserting that there are things in the world that no theory, let alone
>evolution at its current stage, will be able to predict or explain.

Assert all you want, but as people are fond of remarking, you can't
prove a negative.  You could assert that there _may_be_ things no
theory can solve and until some one finds a theory that solves
everything you would be correct.

>It simply means therre are more things in the universe than we can know.
>(Not that this means we should give up trying, I love physics so I am
						^^^^^^^^^^^^^^
>not about to stop just because I will never know all the answers).

Good.

>BUT this leaves room for saying that there might be things in the universe
>that CANNOT be known by any scientific theory, viz God.
>The question is how can one find out?
>Ciao
>julian    


If you count theories that are approximations so are feable brains and
finite computers can calculate things then there are about a kazillion
theories of course.

--- Maureen O'Halloran
Newsgroups: talk.origins