Fractal Relativity, Generalized Noether's Theorem and New Research on Space-Time
Yi-Fang Chang
We researched the fractal-dimensional and complex dimensional mathematics and the physics that may be represented thereby. From this the fractal relativity is discussed, which connects with self-similarity of the Universe and an extended quantum theory. The space dimension has been extended from real number to super-real and complex number. Combining the quaternion, etc., the high dimensional time ict -> ic1t1 + ic2t2 + ic3t3 is introduced. The arrow of time and irreversibility of processes are derived. Then the fractal dimensional time is obtained, and space and time possess completely symmetry. The higher dimensional, fractal, complex and super-complex space-time theory covering all might be constructed preliminarily. We propose a generalized Noether?s theorem, and irreversibility of time should correspond to non-conservation of a certain quantity. Possible reversibility of time and possible decrease of entropy are discussed. Finally, we obtain the quantitative relations between energy-mass and space-time, which is consistent with the space-time uncertainty relation in string theory.
