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In physics given two physical system their composite is meant to be both systems regarded as a single system, but trivially so, without the two interacting.
In classical mechanics forming a composite in this sense amounts to taking the cartesian product of their phase spaces.
In quantum mechanics forming the composite amounts to taking the (non-cartesian) tensor product of the spaces of quantum states, hence their “multiplicative conjunction” in the language of linear logic/quantum logic. The non-cartesian nature of this tensor product is the source of the phenomenon of quantum entanglement and all that goes with this (cf. the EPR paradox and Bell's inequalities but also phenomena like quantum materials and topological order).
twisted generalized cohomology theory is conjecturally ∞-categorical semantics of linear homotopy type theory:
Early discussion of composite quantum systems and their quantum entanglement:
Last revised on November 12, 2022 at 15:20:50. See the history of this page for a list of all contributions to it.