Symmetries in the Mathematical and Physical Description of Nature

Symmetries play an essential role in nature. Symmetrical structures are generally perceived as beautiful. Mathematicians and also physicists even regard symmetries in the equations for the mathematical and physical description of the world as an indication of their correctness. The British mathematician Godfrey Harold Hardy [1.] writes: "The mathematician's patterns, like the painter's or the poet's must be beautiful; the ideas like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.“ A very interesting example of symmetries in physics has been provided by Emmy Noether, who found that certain system characteristics are preserved during changes (transformations). Emmy Noether derived the propositions of conservation of energy, momentum and angular momentum from the invariance (immutability) of the laws of nature during transformation of time, place and direction. These symmetries and their conservation laws form the foundation of physics. In this publication, further essential symmetries are to be investigated, which relate in particular to the symmetry of energy and information and their effects.