He discovered a general mechanism by which violations of Einstein’s theory of relativity could occur without violating basic principles, leading to observable effects from the unification of gravity with quantum physics. Together with his colleagues, he demonstrated the existence of anisotropy in string theory models and considered the possible violations of space-time symmetry, specifically those underlying Einstein’s theory of relativity. Large contributions in this field came from Kostelecky. Tests on the special relativity in cosmic rays and neutrino physics were proposed to investigate the LLI breakdown in the framework of the standard model. Starting from the theoretical ground, experimental tests were also proposed, some of them to be performed in the space. Theoretical studies on the LLI breaking, together with the consequent validity of special relativity, can be found in the literature. This parameter can also measure different anisotropic contributions from the different interactions. In the case of speed of light, the deviations from a constant value of the light speed in vacuo, usually assumed as constant and equal to the value “c,” are measured by a kinematical violation parameter defined as follows : At any rate, the validity of LLI at the Planck scale is queried, due to the quantum fluctuations. It is an old debate whether the LLI holds at any distance and any energy. In this condition, the Einstein special relativity is valid. The LLI holds in absence of local gravitational interaction. The local Lorentz invariance (LLI), on the contrary, imposes an isotropic and flat space-time in any 4-dimension (4D) variety (Minkowski space-time) tangent to a possibly curved (Riemann) space-time, as assumed by the Einstein general relativity. The Lorentz invariance together with the invariance for space and time translations establishes the Poincare symmetry, which is strictly valid only in flat space-time. As common directions of asymmetry are found in these three cases, a fundamental asymmetry of the interactions is suggested which can also shed new light on the question of symmetry breaking in the history of the Universe.
The asymmetry of the two experiments is related to the asymmetry of the Cosmic Microwave Background Radiation (CMBR). A difference in electric potential in a static conductor inside a static magnetic field and an anisotropic and asymmetric distribution of neutrons emitted in nuclear reactions induced by ultrasound are assumed as marks of local Lorentz invariance (LLI) violation.
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