Theory of local tmes
Theory of local times (http://arxiv.org/abs/astro-ph/9309051)
Theory of local times II (http://arxiv.org/abs/gr-qc/9403007)
A critique from a reader:
Hitoshi,
It appears to be a great paper. I followed little of the math as I seem to have lost the patience for that. But I love how you used the neutron experiment to prove your point. Bravo!
To me, your postulates are rather ugly. I believe we ought only postulate what is proven to be perfect experimentally. My approach is a lot simpler to me, starting only with t=h/e local time and t=x*c local time independance. Of course the devil is in the details.
My response:
It is not my responsibility that the axioms look ugly. It is the physics who is responsible. The physicists would be able to make the outlook beautiful, with letting some implicit assumption hidden behind. Mathematics has to state explicitly any implicit assumptions which physicists would take for granted.
Concretely speaking, in physics, the mutual independence of plural observers is implicitly assumed. But only after we are aware explicitly that observers are independent, it is possible that we recognize the importance and necessity of assuming the general principle of relativity among observers. Only after that we are aware that observers are independent, it is possible to introduce the local system and local time which is proper to each observer....
The ugliness you point out is in the above point, but only after making explicit those ugly assumptions, it is possible to formulate physics in the form that we are able to recognize the proper position of quantum mechanics and general theory of relativity in physics, and to understand that these two theories are on different planes (dimensions).
Only after recognizing that quantum mechanics and general theory of relativity are on different planes (dimensions), we can recognize that general theory of relativity and quantum mechanics are both correct and consistently united in orthogonal manner.
Only after knowing the independence of general theory of relativity and quantum mechanics as the ones in mutually orthogonal planes, one can explain the observed results which tell that the observed system also follows quantum mechanics when relativistic corrections are applied to the observed values.
These explain the failure of the current attempt of renormalization of quantum electrodynamics.