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Sub-Planck Symmetry?

  1. Feb 20, 2005 #1
    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

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

    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
  2. jcsd
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