Math 4 Wisdom. "Mathematics for Wisdom" by Andrius Kulikauskas.

Quantum Foundations

By the Spectrum theorem, self-adjoint operators are averages of projections. Thus they can be thought of as manifesting continuity of the Unconscious and physical reality of observables. Similar, neural networks that express weight vectors must be self-adjoint operators. Whereas entropy manifests the discreteness of the Conscious. And with discreteness there is the problem of whether or not there is reversibility, whether information can be forgotten or lost.

Sean Carroll. Quanta and Fields. https://amzn.to/3R7ahLp

Seth Lloyd. Computing universe.

Energy (where mass is the rest energy of a particle) as a fifth dimension where mass indicates the energy required for the particle to come into being. Thus a particle can be like a sphere where the mass indicates the minimum radius when the particle is manifest in this world. In this way, a particle does not behave as a point but rather as a sphere.

Todd Trimble: You may know that Wolfgang Pauli was in analysis with a Jungian psychologist, in the early 1930's (with Jung keeping a close watch over the case); he was in some mental distress before the analysis and may have thought he was going insane. It's probably not as well known that the analysis of Pauli's dreams, which Pauli worked very hard on with his analyst, became essentially part II of Jung's Psychology and Alchemy. The course of the analysis more or less concluded with a spontaneous vision (or perhaps it was a very vivid dream) Pauli had, of a kind of 4-dimensional "World Clock", which Pauli in his conscious reflections subsequently experienced as a kind of healing synthesis or culmination of the analysis. I imagine that for Pauli, this was connected in some way with quaternions and Pauli matrices and so forth and so on.

The quantum world receives a question and its answer given does not change, thus remeasurement does not yield a new answer. The language is degenerate. Meaning is given to the language by the answer. A basis is thereby chosen.

Six postulates of quantum mechanics

Quantum mechanical system is completely specified by the wave function, and integrating the square of the wave function yields the probability of being in the delimited state.
To every observable in classical mechanics there corresponds a linear Hermitian operator in quantum mechanics
The only values ever observed are the eigenvalues of the operator
The formula for the average value of an observable
The wavefunction or state function of a system evolves in time according to the time-dependent Schroedinger equation
The total wavefunction must be antisymmetric with respect to the interchange of all coordinates of one fermion with those of another. Electronic spin must be included in this set of coordinates.

Bohm Pilot Wave, Thomas Spencer

Rovelli, Carlo. “Relational Quantum Mechanics.” International Journal of Theoretical Physics 35, no. 8 (August 1996): 1637–78. https://doi.org/10.1007/BF02302261. References in this text/chapter and quotes are from this paper, if not otherwise noted.

Relational quantum mechanics

In what sense is a particle's location in space and time smeared out in both space and time?

Leonard Susskind. Dear Qubitzers, GR=QM. Gravity and quantum mechanic. Susskind sphere.

Think of a series of low energy pits. Consider quantum tunneling as an outcome of Heisenberg's uncertainty principle, that because of this uncertainty, there is a definite probability of a particle appearing in another pit. Also, think about what Heisenberg's uncertainty principle means for the particle itself, as with regard to itself, it is completely definite. What does that imply?

Light can go backwards in time. Double "time slit" experiment. How to interpret this? What would it mean if all of time consisted of such time slits? (By analogy with Feynman's explanation of all of space as made of slits, as the basis of quantum field theory.)

How does conversation of energy, momentum, angular momentum require and ground continuity? Where exactly is that enforced in quantum mechanics? Study Noether's theorem.

There is a gap between the quantum ether (the quantum foam) and the waves that propagate through it. Particles don't exist, particles are the medium. Waves exist in the medium.

In the book on interpretations of quantum mechanics, there is the question of what is real. For example, in electromagnetism, the gauge can be adjusted by adding any gradient. This can change whether the change is transmitted by the speed of light or whether that speed is infinite and it happens instantaneously. But these two scenarios also raise the question of the reality of the "wiggle". What is real is a moral choice. Is the medium real? Or is the wiggling real? The wiggling creates the wave that moves across the medium. The medium is made of particles and anti-particles that appear from the foam.

https://researchsemin The many-worlds interpretation of quantum mechanics and the Born rule Lev Vaidman (Tel Aviv University) ( view ) Mon May 22, 19:00-20:30 (7 days from now) Abstract: I will argue that the many-worlds interpretation is the best interpretation of quantum mechanics and discuss the status of the probability assignments in this deterministic theory.ars.org/seminar/AlgebraParticlesFoundations

Physics 283b: Spacetime and Quantum Mechanics, Total Positivity & Motives

N. Arkani-Hamed, Lecture #1, Spacetime & Quantum Mechanics, Total Positivity & Motives - 09/03/2019
Is Monty Hall problem related to quantum probability?

Bose statistics - can't assign labels. Fermi statistics - can assign labels to particles.

{$\phi(x,t)=\int\frac{d^4k}{(2\pi)^4}[\tilde{\phi}_{(k)}^+a^+(k)e^{ikx}+\tilde{\phi}_{(k)}^-a^-(k)e^{-ikx}]$}

Thought forms as radiation have frequency which is time, and the form is spatial, in space. Also, colors (frequencies) are perceived as on a color wheel, thus in a circle.

Higgs boson flips chirality of fermions, which yields their mass. Just like frequency yields energy. So they are flipping between universes. Neutrinos do not flip in this way. They are stuck in our universe.

Think of matter anti-matter cancellation, creating energy, as a driver for culling? Yielding an imbalance? as anti-matter moves away? by randomness?

John Baez. Getting to the Bottom of Noether's Theorem.

https://researchseminars.org/seminar/AlgebraParticlesFoundations