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Embedding Fundamental Aspects of the Relational Blockworld Interpretation in Geometric (or Clifford) Algebra

Kallfelz, William (2007) Embedding Fundamental Aspects of the Relational Blockworld Interpretation in Geometric (or Clifford) Algebra. [Preprint]

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    Abstract

    I summarize Silberstein, et. al’s (2006) discussion of the derivation of the Heisenberg commutators, whose work is based on Kaiser (1981, 1990) and Bohr, et. al. (1995, 2004a,b). I argue that Bohr and Kaiser’s treatment is not geometric enough, as it still relies on some unexplained residual notions concerning the unitary representation of transformations in a Hilbert space. This calls for a more consistent characterization of the role of i than standard QM can offer. I summarize David Hestenes’ (1985,1986) major claims concerning the essential role Clifford algebras play in such a fundamental characterization of i, and I present a Clifford- algebraic derivation of the Heisenberg commutation relations (taken from Finkelstein, et. al. (2001)). I argue that their derivation exhibits a more fundamentally geometrical approach, which unifies geometric and ontological content. I also point out how some of Finkelstein’s ontological notions of “chronon dynamics” can give a plausible explanatory account of RBW’s “geometric relations.”


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    Item Type: Preprint
    Commentary on: Silberstein, Michaeland Stuckey, W.M. and Cifone, Michael (2006) Relational Blockworld: Radically Archimedean Physics. UNSPECIFIED.
    Additional Information: I show how Silberstein et. al.'s derivation of the Heisenberg algebra can be characterized in a more fundamentally geometric manner, using geometric (Clifford) algebra, based on the work of Finkelstein et. al. (2001).
    Keywords: Relational Blockworld, Clifford algebraic derivation of Heisenberg algebra, Clifford algebraic characterization of quantum spacetiem
    Subjects: Specific Sciences > Physics > Relativity Theory
    Specific Sciences > Physics > Quantum Mechanics
    Depositing User: Dr. William Kallfelz
    Date Deposited: 05 Apr 2007
    Last Modified: 07 Oct 2010 11:15
    Item ID: 3278
    URI: http://philsci-archive.pitt.edu/id/eprint/3278

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