[FOM] proofs by contradiction in (classical?) Physics

mlink at math.bu.edu mlink at math.bu.edu
Sat Sep 24 14:14:41 EDT 2011

> Is there some intrinsical problem in proving a
> physical fact assuming its contrary? Is it "formally" correct, in the
> system we use to build physical models? Is the "tertium non datur" true
> in classical or quantum Physics?

See above.  What we can say about physics is as much a question about 
language as it is about physics.  LEM can be falsified in one logical 
framework that embeds naturally in another that validates it.


A somewhat related example comes from Goedel [1949], in which
Goedel solves Einstein's cosmological equations in a model of the
universe that is homogeneous and isotropic but does not rotate,
thereby showing that (at least one version of) Mach's principle
(rejecting that space is absolute) is independent of general
relativity theory.  The Goedel universe is geodesically complete,
while the actual universe is not.  Penrose and Hawking in their
1960s work on singularities make essential use of Raychaudhuri's
fundamental equation (Raychaudhuri [1955]).  Raychaudhuri cites
and discusses Goedel's work, rotation being the specific property
that leads to his fundamental equation of gravitational
attraction.  In a model of the universe that does not rotate,
singularities cannot be eliminated even under the absence of
homogeneity and isotropy.  Basically the Raychaudhuri equation is
a negation of the situation that holds in the Goedel universe.
Hawking [1967] then formalized cosmic time to be exactly that
which is excluded from Goedel's universe.  But I am no expert on
this topic:  Ellis [1996] gives a nice account.

Montgomery Link

Ellis, G.F.R.  [1996].  Contributions of K. Goedel to relativity
and cosmology.  

Hawking, S.V.  [1967].  The occurrence of singularites in

Raychaudhuri, A.  [1955].  Relativistic cosmology.  I.

Full references available upon request.

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