From NetFlix:

John Maybury’s masterful thriller stars Adrien Brody as Jack Starks, a Persian Gulf War veteran who has lost his memories to amnesia. When Jack is accused of a heinous killing, he realizes he must find a way to prove his innocence. Desperate to unearth clues about his past, he seeks a controversial treatment that allows him to go back in time — which turns out to be a heart-wrenching decision when he realizes he’s destined for tragedy.

Take a tablespoon of time-travel, suspense, quasi-sadism, mix together to get “The Jacket”. If you are claustrophobic, you might feel a bit squeamish watching the sadistic (but excellent) Kris Kristofferson subject Adrien Brody to some horrific “treatment” (put into a straight jacket and stuck into a morgue body compartment). Jennifer Jason Leigh plays a sympathetic nurse who can only weakly object to this treatment. While he is so confined, Jack Starks (Brody) travels in time to help and fall in love with Keira Knightley.

Details of the mystery are not too hard to follow and were for me involving enough to hold my attention. With these four such good actors this film is not a complete waste of time.