8 Matching Annotations
  1. Aug 2023
  2. Feb 2023
    1. Principle (The Born rule). Given an observable O and two unit-norm states|ψ1〉 and |ψ2〉 that are eigenvectors of O with distinct eigenvalues λ1 and λ2O|ψ1〉 = λ1|ψ1〉, O|ψ2〉 = λ2|ψ2〉the complex linear combination statec1|ψ1〉 + c2|ψ2〉will not have a well-defined value for the observable O. If one attempts tomeasure this observable, one will get either λ1 or λ2, with probabilities|c21||c21| + |c22|and |c22||c21| + |c22|respectively.
    2. Weyl’s insight that quantization of a classical system crucially involves un-derstanding the Lie groups that act on the classical phase space and the uni-tary representations of these groups
  3. Jan 2023
  4. Jul 2021
  5. arxiv.org arxiv.org
    1. a basic ingredient of quantum theory: the category Hilb whose objects are Hilbert spaces, usedto describe physicalsystems, and whose morphisms are linear operators, used to describephysicalprocesses

      [[hilb]] == [[hilbert spaces]] + [[linear operators]]

  6. Oct 2020
    1. The notion that counting more shapes in the sky will reveal more details of the Big Bang is implied in a central principle of quantum physics known as “unitarity.” Unitarity dictates that the probabilities of all possible quantum states of the universe must add up to one, now and forever; thus, information, which is stored in quantum states, can never be lost — only scrambled. This means that all information about the birth of the cosmos remains encoded in its present state, and the more precisely cosmologists know the latter, the more they can learn about the former.
  7. Aug 2018
    1. Hegel believed that history culminated in an absolute moment - a moment in which a final, rational form of society and state became victorious.

      and probably not a bad outcome in an earlier era that thought of things in terms of clockwork and lacked the ideas of quantum theory and its attendant uncertainties.