What I liked about Roger Penrose is that he translated the math into ordinary English. Unfortunately I find the words much easier to cope with than the math; mainly because math-explanations are not always fully clarified in books.
Math is just another language; I suppose I could try and write it sometime.
Quote "Time: You seem to be defining time by how humans measure it. I would like to think that time has an existence that is not dependent on human measurement. That is why in another post I claim that time is defined by physical theory such as General Relativity. Does time exist for you if there are no humans to measure it? "
True, I am being consistent with how humans neasure "time". But it does not mean that its existence depends on humans. "time" is a self-referent reference-space; but in galaxies where there are no humans there is still "time".
Any structure, by virtue of being a structure, has the possibility of being looked at from differing perspectives which can be compared to give reference perspectives. "Time" occurs wherever there is a standing wave of stability, in a sea of change. Any relatively unchanging component of structure within a larger structure will give you "time", the potential to compare changes in structure with relatively unchanging portions.
Time is thus defined by relativity as you say; but exists in relativistic structures as a way one can view them.
Planck's constant apparantly represents the jump from one view of a set of permutations and combinations, to another view where the alternatives have changed due to the constraints imposed by the new view. It represents the quantum of action; the discontinuity. It, as I think Dick says, can be any size; in the theory it is a 2-D parameter, a jump, reflecting the nature of the measurement systems (clocks and rulers) in its dimensions, it seems. Change those rulers and you can change its value.
But I have to dig up a pattern-match explanation of blackbody radiation to derive its origin rigorously, I guess.
Quoting: "Regarding Schrodinger's equation in paragraph 30, most physicists seem to think that the wave functions derived from that equation do not have physical existence. They are just probabilities- not real. I tend to think they are fields and are the only things that exist. Does your analysis shed any light on the physical existence of wave functions? "
I agree that the wave functions are just about alternatives available to the system. But they are real possibilities in the context of limited knowledge of the system. What is real is that to exist is to have freedom. Just as the existence of a particular move in a Chess game involves a real freedom of opportunies related to that position.
Re; fields; I think existence and freedom are entangled. To exist is to have freedom. The light I might shed is that freedom exists; a "wave function" of opportunity asociated with a particular Chess move is a real field of freedom of available next-moves if you make that particular move.
Freedoms and constraints push each other along like electromagnetic waves; new constraints (moves in Chess) open up new freedoms but close down other options. This seems to tally with Chris Langan's CTMU ideas.
More work needed on precise derivation of Planck's constant.