**Authors:** Fu Yuhua

In 1963, 1980 and 2008, the Nobel Prize for physics is related to symmetry principle, violation of symmetry, and broken symmetry respectively. These facts show the following viewpoint: In nature, not only symmetry principles exist, but also violations of symmetry and broken symmetries exist. While this paper presents the following viewpoint: There is no strict symmetry in nature, only approximate symmetry and partial and temporary symmetry can exixt; and for any symmetry, we can find the example of violation of symmetry or broken symmetry. For example, one case for violation of principle of general covariance is the fractal rule, because the fractal distribution is a straight line only in the double logarithmic coordinates. Theoretically, any equation in natural sciences and social sciences is corresponding to a symmetry and the related conserved quantity, and this conserved quantity can be equal to an arbitrary constant. The contradiction and incompatibility between symmetries are also discussed. For example, the incompatibility is existed between the symmetry for law of gravity and the symmetry for general relativity; and the law of conservation of energy generated by time translation symmetry is contradicted with the law of conservation of momentum generated by space translation symmetry and the law of conservation of angular momentum generated by space rotation symmetry. Although the symmetry for law of conservation of energy is only approximately correct, theoretically it could be considered as the unique symmetry in physics that is strictly correct. For other symmetries, they are correct only in the cases that they are not contradicted with this unique symmetry or they can be derived by this unique symmetry.

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[v1] 2015-05-02 09:08:56

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