Dear Yutaka Shikano:
I am an old physician and I don't know nothing of mathematics and almost nothing of physics,
But maybe you would be interested in my essay over a subject which after the common people, physic discipline is the one that uses more than any other, the so called "time".
I am sending you a practical summary, so you can easy decide if you read or not my essay "The deep nature of reality".
I am convince you would be interested in reading it. ( most people don't understand it, and is not just because of my bad English).
Hawking in "A brief history of time" where he said , "Which is the nature of time?" yes he don't know what time is, and also continue saying............Some day this answer could seem to us "obvious", as much than that the earth rotate around the sun....." In fact the answer is "obvious", but how he could say that, if he didn't know what's time? In fact he is predicting that is going to be an answer, and that this one will be "obvious", I think that with this adjective, he is implying: simple and easy to understand. Maybe he felt it and couldn't explain it with words. We have anthropologic proves that man measure "time" since more than 30.000 years ago, much, much later came science, mathematics and physics that learn to measure "time" from primitive men, adopted the idea and the systems of measurement, but also acquired the incognita of the experimental "time" meaning. Out of common use physics is the science that needs and use more the measurement of what everybody calls "time" and the discipline came to believe it as their own. I always said that to understand the "time" experimental meaning there is not need to know mathematics or physics, as the "time" creators and users didn't. Instead of my opinion I would give Einstein's "Ideas and Opinions" pg. 354 "Space, time, and event, are free creations of human intelligence, tools of thought" he use to call them pre-scientific concepts from which mankind forgot its meanings, he never wrote a whole page about "time" he also use to evade the use of the word, in general relativity when he refer how gravitational force and speed affect "time", he does not use the word "time" instead he would say, speed and gravitational force slows clock movement or "motion", instead of saying that slows "time". FQXi member Andreas Albrecht said that. When asked the question, "What is time?", Einstein gave a pragmatic response: "Time," he said, "is what clocks measure and nothing more." He knew that "time" was a man creation, but he didn't know what man is measuring with the clock.
I insist, that for "measuring motion" we should always and only use a unique: "constant" or "uniform" "motion" to measure "no constant motions" "which integrates and form part of every change and transformation in every physical thing. Why? because is the only kind of "motion" whose characteristics allow it, to be divided in equal parts as Egyptians and Sumerians did it, giving born to "motion fractions", which I call "motion units" as hours, minutes and seconds. "Motion" which is the real thing, was always hide behind time, and covert by its shadow, it was hide in front everybody eyes, during at least two millenniums at hand of almost everybody. Which is the difference in physics between using the so-called time or using "motion"?, time just has been used to measure the "duration" of different phenomena, why only for that? Because it was impossible for physicists to relate a mysterious time with the rest of the physical elements of known characteristics, without knowing what time is and which its physical characteristics were. On the other hand "motion" is not something mysterious, it is a quality or physical property of all things, and can be related with all of them, this is a huge difference especially for theoretical physics I believe. I as a physician with this find I was able to do quite a few things. I imagine a physicist with this can make marvelous things.
With my best whishes