Based on parity violation in the weak interaction and evidences from neutrino oscillation, a natural choice is that neutrinos may be superluminal particles with tiny mass. To keep causality for Superluminal particles, a kinematic time under a non-standard form of the Lorentz transformation is introduced. A Dirac-type equation for Superluminal neutrinos is further investigated, and its solution is briefly discussed. This equation can be written in two spinor equations coupled together via tiny mass while respecting maximum parity violation. As a consequence, parity violation implies that the principle of relativity is violated in the weak interaction.
The arrow of time is one of the most difficult questions in modern physics. In this paper, a damping vibration equation is discussed, which shows that this equation reflects the arrow of time. We have further discussed that the concept of "the arrow of time" in this equation is quite different from the thermodynamic arrow.
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