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 | ||||||
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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 |
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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 |
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Date: | April 2007 | ||||||
URI: | https://philsci-archive.pitt.edu/id/eprint/3278 |
Available Versions of this Item
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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
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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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