分形相对论、广义Noether定理与时空新研究
Fractal Relativity, Generalized Noether Theorem and New Research of Space-Time
摘要：
首先，设分形维数D=n（整数）+d（小数），从而将分形维数矩阵表示为一个普通矩阵加上一个特殊的小数行（列）。研究了数学如分维线性代数、物理学等可以向分形发展，以及由分形延伸出的复维数。由此讨论了分形相对论与自相似宇宙和广义量子理论的联系。空间维数从实数扩展到超实数和复数。结合四元数等，引入了高维时间。由此导出了时间的矢量和不可逆性。从而得到时间的分形维数，空间和时间具有完全对称性。可以初步设想，高维、分形、复、超复时空理论涵盖了一切。我们提出了一个推广的Noether定理，时间的不可逆性应该对应于某个量的不守恒。讨论了时间的恢复可逆性和熵的可能减少。最后，我们得到了能量-质量与时空的定量关系，这与弦论中的时空测不准关系是一致的。
英文摘要：
First, let the fractal dimension D=n(integer)+d(decimal), so the fractal dimensional matrix was represented by a usual matrix adds a special decimal row (column). We researched that mathematics, for example, the fractal dimensional linear algebra, and physics may be developed to fractal and the complex dimension extended from fractal. From this the fractal relativity is discussed, which connects with self-similarity Universe and the extensive quantum theory. The space dimension has been extended from real number to superreal and complex number. Combining the quaternion, etc., the high dimensional time is introduced. Such the vector and irreversibility of time are derived. Then the fractal dimensional time is obtained, and space and time possess completely symmetry. It may be constructed preliminarily that the higher dimensional, fractal, complex and supercomplex space-time theory covers all. We propose a generalized Noether theorem, and irreversibility of time should correspond to non-conservation of a certain quantity. Resumed 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.
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