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Algebra of Physical Space, Dirac equation, geometric algebra, interpretation of quantum mechanics, special relativity, spin entanglement
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Entangled states are often given as one of the most bizarre examples of “weirdness” described as inherent to quantum mechanics. The present work reinterprets entanglement as not being a property of states at all, but rather as a relationship between the reference frames in which the states reside, which proposes to reduce “weirdness” of interpretation. Using the geometric Algebra of Physical Space, it has been shown that a classical form of the Dirac equation can be satisfied by any eigenspinor, which is a Lorentz transformation operator describing the relative velocity and relative orientation of the rest frame of a system as seen from a particular lab frame from which it is described. The real linear nature of the Dirac equation means any real linear superposition of such eigenspinors are also solutions. Thus, with entanglement modelled as an operator consisting of a linear superposition of rotation operators describing the possible relative orientations of a particular particle frame and the frame from which it is observed, it too can satisfy a bipartite form of the Dirac equation. To investigate this model, the present work applies relativistic boost transformations to the entangling operator in various ways, including as an identical boost of both parts in the same direction, and also as equal and oppositely-directed boosts. The resulting “entangling eigenspinors” are then analyzed in various ways, including the application to specific spin states — only to discover that doing this results in a reduction of the information, which can be interpreted as a reduction in the amount of entanglement. By comparing this to the treatment of the Dirac equation in APS, it may be concluded that the application of the entangling eigenspinor to a state — which models the typical approach of simply boosting an entangled state — gives an incomplete account of what is happening. The full information is thus contained within the entangling eigenspinor, justifying the interpretation of the entanglement in terms of geometric information relating the reference frames, rather than as a property of the state.
McKenzie, Crystal-Ann, "An Interpretation of Relativistic Spin Entanglement Using Geometric Algebra" (2015). Electronic Theses and Dissertations. 5652.