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, 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 |

### 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]**

- Embedding Fundamental Aspects of the Relational Blockworld Interpretation in Geometric (or Clifford) Algebra. (deposited 05 Apr 2007)

### Commentary/Response Threads

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

- Kallfelz, WilliamEmbedding Fundamental Aspects of the Relational Blockworld Interpretation in Geometric (or Clifford) Algebra. (deposited 05 Apr 2007)

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