PhilSci Archive

An Argument for 4D Blockworld from a Geometric Interpretation of Non-relativistic Quantum Mechanics

Silberstein, Michael and Stuckey, W.M. and Cifone, Michael (2007) An Argument for 4D Blockworld from a Geometric Interpretation of Non-relativistic Quantum Mechanics. UNSPECIFIED.

[img]
Preview
PDF
Download (155Kb) | Preview

    Abstract

    We use a new, distinctly “geometrical” interpretation of non-relativistic quantum mechanics (NRQM) to argue for the fundamentality of the 4D blockworld ontology. We argue for a geometrical interpretation whose fundamental ontology is one of spacetime relations as opposed to constructive entities whose time-dependent behavior is governed by dynamical laws. Our view rests on two formal results: Kaiser (1981 & 1990), Bohr & Ulfbeck (1995) and Anandan, (2003) showed independently that the Heisenberg commutation relations of NRQM follow from the relativity of simultaneity (RoS) per the Poincaré Lie algebra. And, Bohr, Ulfbeck & Mottelson (2004a & 2004b) showed that the density matrix for a particular NRQM experimental outcome may be obtained from the spacetime symmetry group of the experimental configuration. This shows how the blockworld view is not only consistent with NRQM, not only an implication of our geometrical interpretation of NRQM, but it is necessary in a non-trivial way for explaining quantum interference and “non-locality” from the spacetime perspective. Together the formal results imply that contrary to accepted wisdom, NRQM, the measurement problem and so-called quantum non-locality do not provide reasons to abandon the 4D blockworld implication of RoS. But rather, the deep non-commutative structure of the quantum and the deep structure of spacetime as given by the Minkowski interpretation of special relativity (STR) are deeply unified in a 4D spacetime regime that lies between Galilean spacetime (G4) and Minkowski spacetime (M4). Taken together the aforementioned formal results allow us to model NRQM phenomena such as interference without the need for realism about 3N Hilbert space, establishing that the world is really 4D and that configuration space is nothing more than a calculational device. Our new geometrical interpretation of NRQM provides a geometric account of quantum entanglement and so-called non-locality free of conflict with STR and free of interpretative mystery. In section 2 we discuss the various tensions between STR and NRQM with respect to the dimensionality of the world. Section 3 is devoted to an explication of the Kaiser et al. results and their philosophical implications. Likewise, the Bohr et al. results and their implications are the subject of section 4. In section 5, we present our geometric interpretation of quantum entanglement and “non-locality.”


    Export/Citation:EndNote | BibTeX | Dublin Core | ASCII/Text Citation (Chicago) | HTML Citation | OpenURL
    Social Networking:

    Item Type: Other
    Additional Information: forthcoming in "Relativity and the Dimensionality of the World", as part of Springer Verlag's "Fundamental Theories of Physics" series (volume ed. by Vesselin Petkov)
    Keywords: blockworld, special relativity, quantum mechanics, spacetime symmetry, non-locality, entanglement
    Subjects: Specific Sciences > Physics > Relativity Theory
    Specific Sciences > Physics > Quantum Mechanics
    Depositing User: Michael Cifone
    Date Deposited: 04 Mar 2007
    Last Modified: 07 Oct 2010 11:14
    Item ID: 3214
    URI: http://philsci-archive.pitt.edu/id/eprint/3214

    Actions (login required)

    View Item

    Document Downloads