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 Aug 2023

royalsocietypublishing.org royalsocietypublishing.org
 Feb 2023


Principle (The Born rule). Given an observable O and two unitnorm statesψ1〉 and ψ2〉 that are eigenvectors of O with distinct eigenvalues λ1 and λ2Oψ1〉 = λ1ψ1〉, Oψ2〉 = λ2ψ2〉the complex linear combination statec1ψ1〉 + c2ψ2〉will not have a welldefined value for the observable O. If one attempts tomeasure this observable, one will get either λ1 or λ2, with probabilitiesc21c21 + c22and c22c21 + c22respectively.

Weyl’s insight that quantization of a classical system crucially involves understanding the Lie groups that act on the classical phase space and the unitary representations of these groups

 Jan 2023

inferencereview.com inferencereview.com


Woit, Peter. Quantum Theory, Groups and Representations: An Introduction. Revised and Expanded version [2022]. Springer, 2017. https://www.math.columbia.edu/~woit/QM/qmbook.pdf.

 Jul 2021


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]]
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 Oct 2020

www.quantamagazine.org www.quantamagazine.org

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.

 Aug 2018

www.wesjones.com www.wesjones.com

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.
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