 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 

https://www.youtube.com/watch?v=5qGRPOzMWnA
Watched the first 46:39 on 20230202. His personal communication style is a bit offputting, but remedied slightly by watching at 1.25 or 1.5x speed. He's broadly covering pieces directly from his text which seems much more compact and elegant. Questions from the viewers in real time is a bit muddy with respect to understanding what they're saying.
I gave up on the video due to streaming issues.

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
 quantum observables
 open questions
 mathematical physics
 quantum gravity
 watch
 state spaces
 complex vector spaces
 selfadjoint operators
 fields
 algebraic geometry
 classical physics vs. quantum mechanics
 Peter Woit
 observables
 differential equations
 gruppenpest
 quantum mechanics
 commutativity
 algebraic topology
 Hermitian inner products
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Instead of trying to resolve in general this problem of how macroscopic classical physics behavior emerges in a measurement process, one can adopt thefollowing two principles as providing a phenomenological description of whatwill happen, and these allow one to make precise statistical predictions usingquantum theory
To resolve the measurement problem from quantum mechanics into the classical realm, one can use the observables principle and the Born rule.

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.

Axiom (States). The state of a quantum mechanical system is given by a nonzero vector in a complex vector space H with Hermitian inner product 〈·, ·〉.

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.

 Sep 2022

www.youtube.com www.youtube.com

TLDR Hyperion is a moon orbiting Saturn and has chaotic motion about its CoM. This chaos is modeled correctly with classical mechanics but incorrectly with quantum mechanics. The catch being that if the average of all wavefunction collapses due to decoherence with interactions particles+photons is included then the prediction is correct. However, averaging is a nonphysical process and, furthermore, collapsing a wavefunction requires instantaneous transfer of information which is nonphysical.
 Saturn's moon, Hyperion, has chaotic motion due to the orientation of the moon about the orbit. Due to chaos, we can't predict orientation due to chaotic tumbling.
 This can be described classicly with relativity.
 Quantum Mechancis has been falsified because it fails to recreate or predict chaotic behaviors of the moon after 20 years.
 Due to the linear nature of the eigenvector in Schrodinger's equation, it can not contain chaos.
 By applying the correspondence principle, we only see chaos for up to the Ehrenfest time upon having the time function applied.
 Physicists explain this incongruence in theories because the Schrodinger equation isn't including the entangled interactions of light/dust. These effects result in decoherence.
 By averaging over the predictions we achieve the same solution as classical mechanics. Howevering averaging isn't a physical process. (e.g. rolling a 6 sided dice many times gives an average of 3.5 which is nonphysical)
For a model to be real, we require that each individual prediction is true not the average. One solution is that Hyperion interacts and is having it's wavefunction updated nonlinearly resulting in decoherence. * Collapse of a wavefunction is said to not be physical due to instantaneous transfer of information being impossible. However, this wavefunction collapse due to interactions is required for the chaos of Hyperion to be modeled correctly. This is the issue.
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 Jul 2022

docdrop.org docdrop.org

i just wanted to interject that uh could i come at this point carlo i would like to insist a bit on this because i'm i'm not quite clear 01:07:22 on whether you are agreeing or not on the question of the mind um thank you this is also i wanted to ask him the same question mario uh so by just raise the question 01:07:40 specifically all right so let me okay since we're talking about nagarjuna now i would also like to uh read some simple verses that he has and get from both from barry and you what do you 01:07:53 think so this is from chapter three examination of the sentences seeing hearing smelling tasting touching and mind are the six sense faculties their 01:08:04 spheres are the visible objects etc like the scene the herd the smell that tasted and the touched the hair sound etc and consciousness should be understood so actually i'm confused from both of 01:08:18 you first of all barry is the mind anything special in buddhist philosophy or is it just like seeing and hearing and carlo are you saying there is anything 01:08:31 special about them right
Mario interjects in the conversation to clarify Barry's question to Carlo, which is concerning the subjective aspect of experience and how it fits into science as the observer. It comes down the the question of existence of reality and the obrserver's role in that, epitomized in the question: If a tree falls in the forest, does anybody hear?

 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.

 Jan 2019

www.quantamagazine.org www.quantamagazine.org

The new experiment shows that, in a quantum world, two people can end up disagreeing about a seemingly irrefutable result, such as the outcome of a coin toss, suggesting something is amiss with the assumptions we make about quantum reality.

Frauchiger and Renner came up with their thought experiment, which is an extension of something the physicist Eugene Wigner first dreamed up in the 1960s.
