Extremely High Energy and Violation of Lorentz Invariance

Extremely high-energy(EHE) cosmic rays might provide a chance to check a violation of the Lorentz symmetry of spacetime. Some theoretical consideration is described about why the Lorentz symmetry might breakdown in EHE phenomena in this universe. Some models which introduce the violation of the Lorentz symmetry will be discussed. 1 Violation of Symmetry in Actual Universe Great achievement of the 20-century Physics was discoveries of various symmetry hidden deep in the diversity of peripheral phenomena: we can count many symmetries such as rotational and boost symmetry of 3-space, past-future symmetry in mechanics, duality symmetry between electroand magneto-fields, Lorentz symmetry of spacetime, discrete symmetry in atomic structure of solid, particle-antiparticle symmetry, isospin symmetry of nuclear force, chiral symmetry, ”eight-fold symmetry”, super-symmetry, colour symmetry and so on. Particularly, in the middle of 1970’s, the pursuit to find a theory on fundamental interactions of elementary particle focused into the unified-gauge-theory based on internal or local symmetry hidden in electro-weak and strong interactions among quarks and leptons. This unification of the fundamental interaction was accomplished, however, by an additional idea called ”spontaneous symmetry breakdown(SSB)”, which is schematically written as [observed law] = [symmetric law]x[SSB]. To be published in Proc. of the International Workshop: Space Factory on JEM/ISS held on June, 1999 [email protected]