OSMU 2024 TALK 7 by Bernd Henschenmacher, 14th June 2024

OSMU 2024
14/06/24
Speaker: Bernd Henschenmacher
School: Aachen University of Technology
Title: Jordan algebras and Beyond: On attempts to generalize quantum theory from the 1920s to today
Abstract:
I will give a comprehensive summary of Pascual Jordan’s ideas and attempts to generalize the mathematical formalism of quantum theory and extend quantum theory. I will start with Jordan’s idea from 1925 that space and time need to be quantized, Jordan’s and Max Born’s suggestion to use a Time Operator in quantum theory in 1930 and briefly describe Jordan’s ideas on using Non-Hermitian Operators with a real spectrum as observables from the late 1920ies.
I will then describe the situation in particle physics in the 1930ies and Jordan’s introduction of Jordan algebras as an attempt to generalize quantum theory by using non-associative algebras. I will focus on Jordan’s ideas related to the octonions from the 1930ies and 1950ies, before describing his ideas to develop a non-linear extension of quantum theory based on Near Rings and Quasi Rings.
After describing Jordan’s ideas on nonlinear observables, I will describe his work on Noncommutative or Skew Lattices and their links to Non-Hermitian Linear Operators. Finally, I will describe Jordan’s work on Non-Power-Associative Algebras and their putative links to string theory and R-duality.
I will also cover ideas related to Jordan’s speculations put forward by Günther Ludwig (Generalized Observables in Banach spaces), Lawerence Biedenharn (Octonionic Quantum Theory) and David Finkelstein (The Space-Time Code).

[@Achrononmaster]

Total respect for Bernd working in the public sector and funding the time to do this super interesting research.✊🏽

[@Achrononmaster]

@9:00 this is where "quantum gravity" went down the proverbial garden path. There is a reason to quantize the EM field, (photons). There was no reason at all to quantize spacetime, there never has been. Today graviton detectors have been proposed that might someday work. If they detect gravitons and we see photoelectric type analogues with pure gravity, then.... no,... _even then_ there is no reason to quantize spacetime, because gravitons are gravity wave modes, it in not inconceivable they could be localized in wave packets, and even entangled due to ER=EPR topology, hence capable of forming Bell pairs. But this is a local effect, it does not require a gravitation path integral which presumes all the cosmos can be in a superposition.
The field (a continuum) is still the spacetime manifold. Gravity (even though it can be gauged) is qualitatively different to YM. If *_all of spacetime_* (the whole 4D thing) can be shown to exist in superposition or entangled with itself (all of 4D) *_then_* you can start worrying about quantizing gravity. But that experiment I venture will never be done. Nor will we need it.
I even doubt we will detect gravitons other than as soliton-like gravity waves. I'll bet anyone the graviton detectors will find gravity waves, but that's all they'll find. I know I could lose the bet, but I'd take the bet because I have an fairly nice plausible alternative (proto)theory that says gravity is already a quantum theory, you just need nontrivial topology (this is sufficient to get nonclassical GR).