Relative State Quantum Logic
- URL: http://arxiv.org/abs/2203.06695v1
- Date: Sun, 13 Mar 2022 16:08:53 GMT
- Title: Relative State Quantum Logic
- Authors: Martin Paul Vaughan
- Abstract summary: It is shown that the Birkhoff and von Neumann approach to quantum logic is unable to deal with such conjunctions.
It is argued that the probabilities associated with projections be mapped to an orthocomplemented ternary logic.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: A projective quantum logic in terms of relative states is developed,
emphasizing the importance of information transfer between a system under study
and its environment. The need for accounting for the historical evolution of
system is highlighted and it is found that the conjunction of observations
involving conjugate variables can be consistently defined but is found to be
non-commutative. It is shown that the Birkhoff and von Neumann approach to
quantum logic is unable to deal with such conjunctions. It is found that whilst
the proposed scheme is still not distributive in general, the discrepancy is
directly related to interference effects that may disappear when information is
transferred from the system to its environment. It is argued that the
probabilities associated with projections be mapped to an orthocomplemented
ternary logic, in which it is shown that the law of the excluded middle still
holds.
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