56,197 research outputs found
Axiom System and Completeness Expression for Quantum Mechanics
The standard axiomatization of quantum mechanics (QM) is not fully explicit
about the role of the time-parameter. Especially, the time reference within the
probability algorithm (the Born Rule, BR) is unclear. Using a plausible
principle P1, about the role of probability in a physical theory, and a second
principle P2 affording a most natural way to make BR precise, a logical
conflict with the standard expression for the completeness of QM can be
derived. Rejecting P1 is implausible. Rejecting P2 leads to unphysical results
and to a conflict with a generalization of P2, a principle P3. It is thus made
plausible that the standard expression of QM completeness must be revised. An
absolutely explicit form of the axioms is provided, including a precise form of
the projection postulate. An appropriate expression for QM completeness,
reflecting the restrictions of the Gleason and Kochen-Specker theorems is
proposed.Comment: 20 pages, no figure
A generalization of Schur's theorem and its application to consecutive power residues
This article provides a proof of a generalization of Schur's theorem on the
partition regularity of the equation x+y=z, which involves a divisibility
condition. This generalization will be utilized to prove the existence of
'small' consecutive power residues modulo p, where p is a sufficiently large
prime.Comment: 5 page
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