Hi Jochen,
Thank you for your very thorough and well-thought-out comments. It is a compliment and honor to receive such attention.
First, let me address the Heisenberg Uncertainty Principle. Even though this is not what the essay is about, my characterization of it was very intentional. I very strongly disagree with you that uncertainty is caused by QM algebra or wave mechanics. As I addressed in Footnote 4, this characterization of HUP (e.g., ¤âx ¤âp ÔëÑ ÔäÅ/2) is merely a mathematical tautology that follows from the assumption that an object is fully described by a wave and that the momentum wave packet of a particular quantum state is equal to the Fourier transform of the position wave packet for the same state. Heisenberg was attempting to give some realistic explanation for WHY the commutator [X,P] is nonzero (and hence why the order of measurement matters). You can certainly argue that his explanation was wrong. However, HUP, like any principle in physics, is an empirical question that is always subject to falsification (and in fact only a handful of empirical verifications have been performed, beginning in the 1960s). HUP cannot be proven or derived from the underlying assumptions that form the foundation of wave mechanics... instead, empirical verification of HUP can lend further credence to those assumptions.
The reason I went out of my way to explain this is because the goal of the paper is to introduce a new interpretation of QM that may contribute to our understanding of measurement, superposition, and predictability, and it would be very easy for someone to summarily dismiss it on the basis that it doesn't follow from the QM formalism. And I agree - it doesn't. But it is important to underscore the fact that QM itself is based on two very big assumptions (that a system can be described by a superposition of waves and that momentum is quantized by p=k), and that the purpose of those assumptions and resulting QM formalism is to make predictions. However, there are clearly problems with QM, leading many of the smartest physicists and philosophers, over the past century, to develop and defend over a dozen distinct interpretations, and none of them provides any a priori explanation for QM. It's quite possible that QM itself is an emergent phenomenon, in which case the assumptions and equations of QM follow from the underlying ontology.
An interpretation or model of physics that makes the same predictions as QM (e.g., interference, the photoelectric effect, etc.) cannot be disproven by the mathematical formalism of QM. And that was the point I was trying (but perhaps failed) to make in my discussion of HUP. By not realizing that HUP is an empirical question, and that Heisenberg was trying to make physical sense of an abstract QM commutator relation, it is easy to forget that physics is always about experiment, falsifiable hypothesis, and prediction. Math is its servant, not master. (Actually, Sabine Hossenfelder makes an interesting and related case in her essay.)
I knew it was a risk to discuss HUP. I fully expect many readers to glance at my paper and dismiss it. "This guy doesn't understand uncertainty and I can easily disprove his interpretation with the following equations..." If there is a fundamental problem with QM, we won't find the solution by starting with QM equations. Instead, we will have to do what Heisenberg did and try to figure out, on a physical level, what might be happening that could give rise to those QM equations. He might have been wrong, but if so, it's not because he was "disproven by math," but rather that there is some underlying physical reason why position and momentum (for example) cannot be measured simultaneously.
Very quickly on your other points. Yes, the Lagrangian formalism is written ostensibly in configuration space, but it also assumes the timed rate of change of each generalized coordinate... e.g., each object has a position and velocity. OK so maybe that's not phase space, but it allows classical predictability. This isn't true in QM (except in Bohmian mechanics... see my footnote 6.)
Thank you for bringing up Consistent Histories. Part of my motivation in submitting this essay was to hear comments on how my interpretation might relate to others. I'm well versed in most QM interpretations, but for some reason CH continues to elude me conceptually. There's little discussion of it in the philosophy of science literature. Can you recommend a resource? Your characterization of my interpretation as "anything not expressly forbidden by the facts is mandatory" isn't quite what I was saying, as nothing is mandatory.
I recently printed out your essay and very much look forward to reading it. I have already read the first two pages and enjoyed it... clearly we have something in common if we are both discussing QM from the point of view of information! (My footnote 16.) Also the topic you address and your means of addressing it are clearly important and competent.
Best of luck to you in this contest!
Andrew