16 Matching Annotations
  1. Oct 2023
    1. If you look at George Ellis’s Google Scholar, it’s clear that he has gone down the deep end a while ago. What is it with these cosmologists? (Ahem, Penrose). Suddenly they discover quantum physics and it’s the solution to consciousness. Or gravity makes wavefunctions collapse.

      quote from Christoph Adami at https://twitter.com/ChristophAdami/status/1711583362647814485

      Re: George Ellis https://www.nature.com/articles/d41586-023-03061-y

      Physicists and quantum mechanics as solution to consciousness.

      See also: Physics in Mind: A Quantum View of the Brain by Werner R. Loewenstein

  2. Feb 2023
    1. | 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 real-valued solutions | self-adjoint linear operators on the state space<br>- some confusion may result when operators don't commute; there are usually no simple (real-valued) numerical solutions |

    2. 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 2023-02-02]

    1. Bell’s theorem is aboutcorrelations (joint probabilities) of stochastic real variables and therefore doesnot apply to quantum theory, which neither describes stochastic motion nor usesreal-valued observables

      strong statement, what do people think about this? is it accepted by anyone or dismissed?

    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. Nov 2022
    1. 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.

  5. Nov 2021
    1. “Because physicists started out with the imaginary, unstable cube as their model instead of the real-world 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.)”

  6. Oct 2021
  7. Apr 2021
  8. 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.
  9. Jul 2019
    1. unitary operator is a surjective bounded operator

      Why must unitary operator only be surjective? Why not bijective?

  10. Mar 2018
  11. Oct 2015
    1. 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.