[...]
> There are many other consequences to the association of a force with a
> space symmetry group. For example, if you can show that the
> gravitational field itself has an intrinsic space symmetry group
> associated with it, then it may be possible to relieve Biology of much
> of its burden to account for the symmetry of the bodies of living
> things. At the moment, biological studies can not really account for
> the ubiquity of radial and bi-lateral symmetries in many different
> organisms. And biological studies almost never take into account that
> their subjects have evolved in a gravitational field. Just about
[...]
Something else to consider -- gravity certainly has an effect on evolution and morphology, but simply as a body force -- you needn't appeal to any property specific to gravity at some fundamental, uh, trans-Newtonian level. You can call it a generic force and leave it at that.
While I'm quite certain that molecular-scale arrangements overwhelm gravity in the matter of symmetrical crystal structure, I don't mean to dismiss the notion that subtle effects can occur across scales. Favored chirality (handedness) comes up in odd places, and the effects can reach where you might not expect them. For example, almost all tornados rotate in a cyclonic direction (counterclockwise in the Northern Hemisphere, like hurricanes), which suggests that coriolis is a significant force in their dynamics. But they're too fast and small for that to be the case (the same for toilet bowls!), moreover the rare anticyclonic tornados would be outright impossible. The fact that tornados favor cyclonic rotation suggests that some larger, slower upstream process tends to set them off in that direction.
-- Andy