Sunday, January 13, 2008
Lets analyze for a moment shall we the idea of physics as geometry. Now most successful physical theories have at their heart been geometries. For instance Newtonian mechanics was based deeply on euclidean geometry and the deep success of Newtonian mechanics is at least related to how well it sits with Euclidean geometry. Electromagnetics is an area where the connection is less strong but because the laws are so well described by fields the theory has become very much a geometric one though in its inception it was not necessarily so. General relativity is entirely dependent on geometry not only for its success but also for its explanation. Rather the reverse phenomenon occurred in the others where the geometry was a side effect of the explanation but with general relativity the geometry was the explanation. Quantum mechanics however is less than strictly geometrical because although we use geometry to describe the wave function of a quantum mechanical object the theory itself is not a geometrical object we merely use geometry as a useful means of calculating transitions. The wave function is only a probabilistic guide to reality any actual event requires a collapse of the wave function which makes the idea of viewing the wave function as the geometry of the real physical situation at the very least quite difficult. It may seem an odd sort of thing to require of the world but I like to think of the world as being a place that can be described by a static geometry. The uncertainty and indeterminism of quantum mechanics are such that this sort of description makes the description of our world by a static geometry impossible if you keep to the usual tenets of such representations. I think that it is possible that one could describe the world using a static geometric reperesentation if one is willing to accept the parallel universes postulate which is I think a very good argument for it.