Behavior of the observed time showing simultaneous events compared to the proper time of a scene seen through an oscillating refractive index medium.

After previously highlighting time dilation and time reversal according to the refractive index value of the crossed medium, the temporal behavior at the observer place is studied when this refractive index varies as a function of time. Assuming a sinusoidal variation, two modes of progression with a stage of switching between these two modes are differentiated. The mode alternating time dilation and time reversal corresponds to the temporal variation with an alternating progression. The mode slowing down the proper time in the first step and accelerating it without reversing it in the second step corresponds to the temporal variation with a positive progression. The vision of an observer looking through a medium with a variable refractive index reveals directional variations of time and the simultaneity of several events in the scene. The determination of the number of simultaneous events as a function of observed time also indicates if the events are oriented to the future or to the past. Each orientation shows an acceleration zone, a deceleration zone, and a constant zone. These zones are determined by the value of the derivative of the observed time. The frozen time placed on the line of intersection between the future and the past corresponds to the derivative equal to zero. At that moment, the vision of an infinite number of events appears during a dot in observed time. This vision reveals a temporal singularity. The observed simultaneity can no longer be identified by an event number but by the duration of the proper time within the limits of frozen time. All the results obtained in this study were verified and validated, confirming the directional variations of the observed time and the simultaneity of events with the temporal singularity.