# Sub-Planck Symmetry?

1. Feb 20, 2005

### Russell E. Rierson

There must be a way to construct a Lorentz invariant[and causally
symmetric] theory that provides a detailed description of microscopic
quantum processes - including sub-Planck diameter violations of Lorentz
invariance that still becomes Lorentz invariant in the macroscopic
domain, via a statistical averaging of the ensemble of
multi-particulate microscopic wave functions. Thus the ensemble becomes
a causally connected sequence of space-like hypersurfaces, being
foliations that are themselves statistical[Gaussian] ensembles.

This would provide an accounting for a causally connected - evolving
configuration of macroscopic states. If it is entirely possible for
Lorentz invariance to be violated in the sub-microscopic Planck
lengths, then it could also be equally[symmetrically] possible for
Lorentz invariance to NOT be violated in the sub-microscopic lengths.
Thus, this bivalent symmetry of violation/non-violation is broken in
the multivariate statistical macroscopic ensemble. Thus macroscopic
Lorentz symmetry holds because another "higher energy" symmetry is
broken.

At the sub-Planck scales, all possibilities for existence must become
symmetrically equalized, due to the Heisenberg uncertainty DxDp >=
hbar/2.

A type of smoothed out infinite dimensional realm[Hilbert space?] of
isotropic and homogenous indistinguishability that somehow becomes
beholden to the specific macroscopic statistical averaging of
microscopic states. The uncertainty principle is merely a form of the
Cauchy Schwartz inequality, consequently becoming connected to the
"triangle inequality", which is a property of the N-dimensional
Riemannian metric.

Generalized Uncertainty:

http://www.people.fas.harvard.edu/~jreyes/math23/uncertainty.pdf [Broken]

Last edited by a moderator: May 1, 2017