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.
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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.”
| Keywords: | Relational Blockworld, Clifford algebraic derivation of Heisenberg algebra, Clifford algebraic characterization of quantum spacetiem |
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| Subjects: | Specific Sciences: Physics: Relativity Theory Specific Sciences: Physics: Quantum Mechanics |
| ID Code: | 3278 |
| Deposited By: | Kallfelz, William |
| Deposited On: | 05 April 2007 |
| 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). |
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