Authors: Carl Brannen
Carlo Rovelli's ``relational interpretation'' of quantum mechanics tells us that our understanding of quantum states is limited to their interactions with other quantum states. This implies that we have no understanding of the symmetry properties of a state vector except when considered in relation to at least one other state vector. The SU(3)xSU(2)xU(1) symmetry of the Standard Model is derived from their interactions and therefore cannot necessarily be applied to a single state vector. Steven Weinberg showed that mixed density matrices can have symmetries that are not available to state vectors. We explore the symmetry properties of finite symmetry groups for mixed density matrices. Just as mixed density matrices can define mixed states that require multiple state vectors, we find that the symmetries of mixed density matrices define ``mixed symmetries'' that are similar in structure to the symmetry of the Standard Model. We explore the point group symmetries and show one that gives the Standard Model symmetry. With this symmetry, we can generalize the Pauli spin matrices to a set that has irreducible representations matching the Standard Model plus a dark matter candidate.
Comments: 18 Pages. To be submitted to Foundations of Physics
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[v1] 2021-05-24 06:58:31
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