Psycho x Past: Bizarre Murder Undercover Investigation

Story:

Godai, the protagonist of the "psycho suspense" manga, is a police officer whose violent tactics led to his dismissal from the department's investigations unit. His new partner, Hidaka, calls himself a "paranormal police investigator" and asserts he can send Godai back in time to stop the terrible murders from happening. Is this conceivable, and if so, what are the repercussions?