T-invariance violation of Neutrino oscillations*

We explored the probability of time reversal symmetry(laws of physics should be the same regardless of the direction of time) in neutrino oscillations. Neutrinos are nearly massless neutral particles that change identity or flavor while traveling or interacting with other particles. The phenomenon of neutrinos changing flavors as they travel is known as neutrino oscillation. We developed a two- step methodology: manually calculating the probability of two flavors neutrino oscillation in different environments(vacuum, constant matter, and time-dependent matter). We demonstrated that time invariance is preserved in all the environments in two flavors neutrinos. The fact that no violation was done brings up the question of how does matter potentially impacts neutrino oscillations. In the future, we will explore this question and study three flavor neutrinos.