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
Creators:	Creators Email ORCID Kallfelz, William
Commentary on:	Silberstein, Michael and 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 15:15
Item ID:	3278
Subjects:	Specific Sciences > Physics > Relativity Theory Specific Sciences > Physics > Quantum Mechanics
Date:	April 2007
URI:	https://philsci-archive.pitt.edu/id/eprint/3278

Available Versions of this Item

• Embedding Fundamental Aspects of the Relational Blockworld Interpretation in Geometric (or Clifford) Algebra. (deposited 06 Apr 2007)
  • Embedding Fundamental Aspects of the Relational Blockworld Interpretation in Geometric (or Clifford) Algebra. (deposited 05 Apr 2007) [Currently Displayed]

Commentary/Response Threads

• Silberstein, Michael and Stuckey, W.M. and Cifone, Michael Relational Blockworld: Radically Archimedean Physics. (deposited 31 May 2008)
  • Kallfelz, William Embedding Fundamental Aspects of the Relational Blockworld Interpretation in Geometric (or Clifford) Algebra. (deposited 05 Apr 2007) [Currently Displayed]

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