There must be a way to construct a Lorentz invariant[and causally(adsbygoogle = window.adsbygoogle || []).push({});

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]

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# Sub-Planck Symmetry?

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