TL;DR - Is Christine saying she doesn’t like the complex linear equations (ugh, finally!), or do we not need linear equations for a linear superposition?
The biggest roadblocks holding back the ensemble interpretation and related theories are people like Einstein who reject superposition and nonlocality. I am hypersensitive to coherent ideas, rejecting those postulates and letting ideas like MWI flourish.
I have not watched all the videos, but the material is cross-disciplinary and dense, which may limit the audience.
https://en.wikipedia.org/wiki/Curse_of_knowledge
Remember, a lot of people believe imaginary numbers in quantum physics represent other worlds, or whatever idea they want to stuff into them, instead of being just a piece of math. But to me, the specialness is linear/nonlinear.
On one slide, there are classical entropy, quantum, and the general relativity metric. You have my attention. The next slide shows that there is entropy with uncertainty, which aligns with information theory and my desire to remove complex analysis from quantum.
The uncertainty contains the standard deviations and the squared wavefunctions. It is a real probability distribution without needing the Born rule. And it is coupled to another observable and not allowed to evolve independently. As in, a measurement in one universe should change the coupled observables in this universe and in other universes, without needing to measure any observable in the child universe. That is not what is observed. But still they resist.
You show geometry is entropy. Using the symplectic to argue conservation in phase space?
I need a real basic example, analogy, or derivation to connect those two ideas, because I would love to have that connection. Still, it is not quite there yet in my mind as the fundamental basis for entropy. That is on me to figure out.
On the slide, "Nonlinear Representation of Quantum Mechanics." Christine says, "Some people argue there are physical representations of using linear equations in quantum mechanics."
I know I do that. Are you telling me there are others? I do see us using linear equations because they model linear superposition, and we cannot have superposition without them. A measurement is nonlinear due to an increase in entropy, which makes the wavefunction collapse to a single value, since I do not know how to convert a nonlinear solution into a linear superposition of solutions.
Although I do understand that macrostates, microstates, and multiplicity can change due to nonlinear effects, making some states more likely than others. But the reply is usually, "This is a Wendy's."
Quantum uses nonlinear ideas, which is why perturbation is a known torture method. But consider this. In Schrodinger's cat analogy, an atom's decay triggers the cat's death. Does observing the atom, instead of the cat, change the probability that the atom decays? Is there anything I can do besides x-ray spalation or relativistic effects that will change the atom’s half-life?
The nucleus has many protons and neutrons, each of which has three quarks, gluons with three self-interacting color charges. It is nonlinear, and lattice QCD is needed. However, the hydrogen atom wavefunctions involving a proton and an electron exhibit linear properties such as superposition and the Zeno effect. Nonlinear went linear.
The problem with combining GR is that it is fundamentally nonlinear. Two gravitational waves are not in a superposition; they influence each other. Gravity influences gravity because the gravitational field has energy, and we cannot solve many problems without a quantum computer. Instead, we start with the simplest cases and use perturbation theory.
When people talk about dark energy and dark matter, my first thought is that cosmologists make big claims with big error bars. They are the first to admit it. However, my second thought is that those big uncertainties are likely calculated by adding in quadrature. This is a linear method of error analysis.
The complex numbers are a mathematical convenience, but having a particle in multiple states simultaneously requires a linear superposition. Can we say they are in the same state with real numbers? If we can do superposition with real numbers, does that mean we give up causality and the arrow of time?
The trouble is, we need complex phase rotation for interference, which your phase space approach may handle elegantly. But I was thinking of showing that the observables with uncertainty are coupled oscillators rather than independent complex phase-space rotations.
I still have 2.5 hours to go on the first day. This is going to take me a while.
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