Fractal Relativity, Generalized Noether Theorem and New Research of Space-Time

TL;DR

This paper develops a fractal and complex extension of space-time, proposing a generalized Noether theorem, and explores implications for irreversibility, entropy, and energy-mass relations within a unified fractal relativity framework.

Contribution

It introduces a novel fractal and complex dimensional space-time theory, extending traditional physics and proposing a generalized Noether theorem linking irreversibility to non-conservation.

Findings

Fractal dimensional space-time unifies space and time symmetry.

Generalized Noether theorem relates irreversibility to non-conservation.

Derived energy-mass and space-time relations consistent with string theory.

Abstract

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.