Re: Gravity Solves Paradox raised by Einstein's Theory
Posted by Uncle Al on Sep 26, 2003 at 14:06
(68.5.243.16)Re: Gravity Solves Paradox raised by Einstein's Theory (Pasti)
Nobody knows what a good (compatible with quantum mechanics) gravitation theory might look like. As you say, there is a huge accumulation of beautiful math. We are lost.
Euclid was the gold standard of deductive reasoning into the 19th century. Euclidean plane geometry is bullet-proof. Euclid is internally sound without any possiblity of argument. However...
...Euclid's postulates (e.g., there exists one and only one external line parallel to a given line) are arbitrary. One can trivially erect hyperbolic (infinite lines parallel to a given line) or elliptic (no lines parallel to a given line) geometries with the same rigor and internal validity. The Earth is not flat. If you wish to navigate, you abandon Euclid or you fail to find your destination.
Positive, zero, negative curvature. We're done! No, we aren't. Thurston brought the total to eight simply-connected geometric 3-manifolds with compact quotients: E3, S3, H3, S2xR, H2xR, SL2, Nil, and Sol.
Go to 4-space and things get complicated! It could be 16 fundamental geometries a la Thurston. We need something observationally simple as pruning shears, not a theoretically complex rat's nest of possiblities.
M-theory has infinite (one of the big infinities, not merely the countable number of integers) solutions, most of them non-physical in this universe. Attempts to whittle that down by applying anthropic principles (any good theory has to allow what we see, and us) still leaves an infinite - or at least an embarassingly exponentially huge - number of mathematially valid solutions.
M-theory is useless unless it cleans up its act.
We have oceans of mathematical theory. What we lack is empirical constraints to discard mathematically valid but non-physical theory. That would put a huge hot air industry out of work (or at least into productive venues).
Metric spacetime curvature demands the Equivalence Principle (all bodies fall identically in vacuum) and is parity even. Affine spacetime torsion ignores the Equivalence Principle and can be parity odd. The two vastly different approaches have absolutely identical physical predictions except for a vary narrow disjoint set. Spacetime torsion is slightly richer in phenomena than spacetime curvature.
Only an idiot's idiot would try to tell the difference between the two by looking where they agree. You look where they differ and see which one is empirically correct. GR cannot swallow odd parity any more than Euclid can accept three independent parallel lines. An outstanding challenge to GR is then a quantitative odd-parity test. Now, go convince physics of the obvious.
("Bob suddenly realized that the black horse was a full hand taller than the white one and that they could never again be confused.")
--
Uncle Al
http://www.mazepath.com/uncleal/eotvos.htm
(Do something naughty to physics)