 Feb 2023

www.youtube.com www.youtube.com

 physics/mathematics  Classical Physics  Quantum Mechanics <br /> <br />  State Space  fields satisfying equations of laws<br> the state is given by a point in the space  vector in a complex vector space with a Hermitian inner product (wavefunctions) <br />  Observables  functions of fields<br> usually differential equations with realvalued solutions  selfadjoint linear operators on the state space<br> some confusion may result when operators don't commute; there are usually no simple (realvalued) numerical solutions 

One of the problems in approaching quantum gravity is the choice for how to best represent it mathematically. Most of quantum mechanics is algebraic in nature but gravity has a geometry component which is important. (restatement)
This is similar to the early 20th century problem of how to best represent quantum mechanics: as differential equations or using group theory/Lie algebras?
This prompts the question: what other potential representations might also work?
Could it be better understood/represented using Algebraic geometry or algebraic topology as perspectives?
[handwritten notes from 20230202]
Tags
 differential equations
 classical physics vs. quantum mechanics
 mathematical physics
 complex vector spaces
 quantum gravity
 commutativity
 state spaces
 algebraic topology
 algebraic geometry
 fields
 selfadjoint operators
 Hermitian inner products
 gruppenpest
 observables
 quantum mechanics
 quantum observables
 open questions
Annotators
URL


royalsocietypublishing.org royalsocietypublishing.org

Bell’s theorem is aboutcorrelations (joint probabilities) of stochastic real variables and therefore doesnot apply to quantum theory, which neither describes stochastic motion nor usesrealvalued observables
strong statement, what do people think about this? is it accepted by anyone or dismissed?



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.

 Nov 2022


Diseases don’t have to follow rules.
Reminds me of something Carl Sagen said  I think it was Sagen though might have been Feynman  in the context of quantum physics, that the universe is under no obligation to observe our rules, or something like that.

 Nov 2021

thenewpress.com thenewpress.com

“Because physicists started out with the imaginary, unstable cube as their model instead of the realworld stable tetrahedron, they got into all these imaginary numbers and other complicated and completely unnecessary mathematics. It would be so much simpler if they started out with the tetrahedron, which is nature’s best structure, the simplest structural system in Universe.
(Just as an aside, to remember later when you’re studying physics in school, I want to point out that the tetrahedron is also equivalent to the quantum unit of physics, and to the electron.)”

 Oct 2021

timeenergyresources.com timeenergyresources.com

If the Bauhaus existed today, what would it look like?
What would the Bauhaus do differently, learning from the mistakes of the past and how modernism was coopted by neoliberal capitalism.

 Apr 2021
 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.

 Jul 2019

en.wikipedia.org en.wikipedia.org

unitary operator is a surjective bounded operator
Why must unitary operator only be surjective? Why not bijective?
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Annotators
URL

 Mar 2018

www.tcm.phy.cam.ac.uk www.tcm.phy.cam.ac.uk

A new theory of the relationship of mind and matter, David Bohm

 Oct 2015


the strongest evidence yet to support the most fundamental claims of the theory of quantum mechanics about the existence of an odd world formed by a fabric of subatomic particles, where matter does not take form until it is observed and time runs backward as well as forward.
