Dear Philip, Jonathan Vos Post, Christine,
I enjoyed reading your essay. The introduction gives a good overview of the issues with current physics. I believe that these issues cannot be resolved without adopting a fundamentally different perspective. The incompatibility of Quantum Theory and General Relativity (GR), at very small scales, is an indication that either both have issues, or ne of them is fundamentally wrong. According to MOND, GR is also not valid at galactic scales and beyond. Hardly anyone is seriously considering the possibility that GR could be invalid and inhibits unification. Obviously, current phenomena that are supposedly validate (not falsify) GR should then be rationalized in a different fashion. In the past, some people have provided alternative explanations, but they have not stuck.
From my perspective, since the early 1900s, the development of physics has taken the opposite path from where it should it should have gone. This highly formal approach has resulted in all kinds of supposedly existing non-observed interaction particles like gravitons, gluons, and weak bosons. This 'discrete' approach does not provide a good foundation for development of a truly unified theory of physics.
The alternative 'continuous' approach is to appreciate the observed existence of four fundamental interactions and develop a reality-based theory based on this. This results in an interaction theory which shows the real existence of only massive particles and photons (no virtual particles). In this theory, space and time are discrete and dynamically emerging, which addresses some of the issues you discuss on page 5 of your essay wrt time intervals. It turns out that discreteness of space and time are extremely important elements to enable unification of quantum behavior and relativity. Time follows from a kind of periodic clock behavior of an oscillation quantum beat process, much in line with the original ideas of Louis de Broglie. A very short overview of the theory that covers this can be found in my essay (which admittedly includes some shortcuts, but all results are rationalized in the references). In this essay, I also provide some critical remarks about incompatibility of GR and quantum behavior. I would also like to point you to a slide deck on my website for another perspective. I don't expect many people to agree with this style of physics, because it goes against the current thinking of trying to solve unification by formalization.
I agree with many of Barbour's thoughts on time. However, where I fundamentally disagree is his idea that time does not exist. The non-existence is, in my opinion, based on formal manipulation of formulas without appreciating the physical origin of those formulas.
On page 6 you describe that the Schrodinger equation has unwelcome consequences for thermodynamic reversibility. Strictly, Schrodinger's equation holds for a free single massive particle (electron) and possibly also for a collection of free bound particles. The fact that Schrodinger's equation is time symmetric is a mathematical artifact, because it ignores the irreversibility of time at a more fundamental level (see QFM-II report on my website).
Thanks again for your essay.
Ben Baten