A relativity principle in quantum mechanics

Yi‐Fang Chang

From quantum mechanics and relativity,the basic principles are summed up:symmetrical principle(including the generalized conservation principle and violation of symmetry) and statistical principle.Further,a development of the Noether's theorem is researched.Moreover,the relativity principle(including extensive equivalence principle),the limit value principle and approximate principle,etc.,are discussed.

Luis Grave de Peralta, Maricela Fernández Lozada, Hira Farooq +3 more

Eijiro Sakai

We propose six principles as the fundamental principles of quantum mechanics: principle of space and time, Galilean principle of relativity, Hamilton's principle, wave principle, probability principle, and principle of indestructibility and increatiblity of particles. We deductively develop the formalism of quantum mechanics on the basis of them: we determine the form of the Lagrangian that satisfies requirements of these principles, and obtain the Schroedinger equation from the Lagrangian. We also derive the canonical commutation relations. Then we adopt the following four guide lines. First, we do not premise the relations between dynamical variables in classical mechanics. Second, we define energy, momentum, and angular momentum as the constants of motion that are derived from homogeneity and isotropy in space and time on the basis of principle of space and time. Since energy and momentum are quantitatively defined in classical mechanics, we define them in quantum mechanics so that the corresponding conservation laws are satisfied in a coupling system of a quantum particle and a classical particle. Third, we define Planck's constant and the mass of a particle as proportionality constants between energy and frequency due to one of Einstein-de Broglie formulas and between momentum and velocity, respectively. We shall obtain the canonical commutation relations and the Schroedinger equation for a particle in an external field in the definitive form. We shall also prove that relations between dynamical variables in quantum mechanics have the same forms for those in classical mechanics.

Wenwen LYU, Feng Wang

This paper introduces the development of the principle of relativity from Galileo's principle of relativity to special relativity and then to general relativity. Inspired by this, we explored the transformation form of quantum mechanics to meet Galileo's principle of relativity. Firstly, from the point that unitary transformation can keep the physical laws of quantum mechanics unchanged, we correspond the momentum translation unitary transformation in quantum mechanics to the Galileo transformation in classical mechanics, and reveal that the transformation form of quantum mechanics that meets the Galileo principle of relativity can be realized through the momentum translation unitary transformation. This inquiry is conducive to students' in-depth thinking about the corresponding relationship between quantum mechanics and classical physics, can help beginners reduce the conflict between quantum physics and classical physics, and help students build a bridge from classical to quantum thinking.

Tirupattur Srinivasan Natarajan