In the movie Predestination (2014), does the ending imply that the temporal agent becomes the Fizzle Bomber and therefore a paradox?
Yes, it's a paradox.
The entire point of the film, as the title suggests, it to play with paradoxes and predestination. A very detailed description of the film can be found on its wiki, but perhaps of more interest is the short story (just ten pages) on which it was based: All You Zombies, by the ever-wonderful Robert A. Heinlein. If you read its wiki, you get the same breakdown as Predestination, but written far more verbosely. To quote from its wiki:
'—All You Zombies—'" chronicles a young man (later revealed to be intersex) taken back in time and tricked into impregnating his younger, female self (before he underwent a sex change); he thus turns out to be the offspring of that union, with the paradoxical result that he is his own mother and father. As the story unfolds, all the major characters are revealed to be the same person, at different stages of her/his life.
It was this series of paradoxes which inspired the film's creators:
FLICKS: How did you first encounter the short story?
PETER SPIERIG: I had just been reading a lot of short stories and All You Zombies by Robert A Heinlein was just one that really stuck with me. I remember reading it and thinking ‘Wow, that’s a real original’. I gave it to my brother to read and he reacted the same way. We both thought it would be great to make into a film one day. We didn’t know how we were gonna do it, but we both thought ‘Boy, this would make an interesting film!’ And then eventually we stopped saying ‘One day’ and we said ‘Okay, today we’re going to try and turn this into a screenplay.’ That’s kind of where it all came from.
Wow, insane film this was. Here's a timeline diagram to help explain the events of the movie, looks like yes, he does eventually become the Fizzle Bomber!
Timeline diagram source: Predestination (2014): Movie Plot Ending Explained. This is Barry
I think it's more philosophical than confusing.
1975, Temporal agent has face burnt whilst trying to stop the ‘Fizzle Bomber’ who then escapes. A faceless stranger appears and helps badly burnt agent activate his portable time machine.
1992, Agent travels forward in time to the Temporal Bureau, an organization founded in 1985 after the invention of time travel. There he has reconstructive facial surgery, and we find out the Fizzle Bomber killed 11,000 people in New York in 1975.
1970, Temporal agent goes back to New York posing as a bartender and seems keen to engage a man calling himself ‘Unmarried Mother’ in conversation. The man explains he was originally a girl called Jane who was left at an orphanage in 1945. In 1963 Jane fell in love with a mystery man, who then disappeared. Jane had a baby who 9 months later was stolen. She then had a sex change and became a writer called John.
The temporal agent says he suspects the mystery man was the Fizzle Bomber and offers John the chance to go back to 1963 and kill the man who who ruined his life. In return he insists John must then join the Temporal Bureau. They then travel back to 1963 together.
1963, John accidentally meets his younger, female self Jane, falls in love, and impregnates her with a child that eventually would grow up to be them. Meanwhile, the temporal agent travels 9 months into the future, takes Jane’s baby and drops her off at an orphanage in 1945. He then drops John off in 1985 to enlist in the Temporal Bureau.
1975, The temporal agent then retires to 1975 but he still retains the use of the time machine which fails to deactivate itself. The retired agent/John soon tracks down the Fizzle Bomber, who actually turns out to be him in the future. He seems to have become insane from using the non-deactivated time machine too often as he sought to travel in time and avert disasters from occurring. However, his actions actually caused thousands of other untold deaths to happen in the process, and so disgusted with his future self, the agent shoots and kills the Fizzle Bomber, thus ensuring he becomes him.
So essentially, The Fizzle Bomber and John, both are same, both are creation of an endless time loop. Whatever choices they made, they would be kept repeating themselves in the loop. The movie is called Predestination for a reason. It removes the many world interpretation by saying that everything, and everything is under a spatial time loop, stuck inside an original time loop. In the simplest term, Its like concentric circles upon circles. The circles being timeline. The bigger circles or timelines engulfing the other timelines. Whatever choices you make, you will be stuck in a loop and continue to do the same choices. If you choose to observe a different timeline, you would end up thinking you made a different choice, but choice has already had happened in a different timeline or circle.
It is implied that the main hero is the Fizzle bomber but I think he couldn't have done the big bombing in 1975. When he killed himself, it was before the bombing happened. He told his older self that "his next bomb is going to kill thousands of innocent lives" and that he couldn't allow it. And then he shot him, before the bomb was even there.
Am I getting it right? And if the main hero didn't plant the bomb in 1975, who did?
The message of the movie is that everything that happens is meant to happen, and there is nothing anyone can do to change it: hence the title "Predestination". We all have a predetermined destiny that cannot be altered.
Essentially there is nothing John/Jane/barkeep/fizzle bomber can do to prevent his creation or transformation into the fizzle bomber. His feelings and intentions, and his actions based off his feelings and intentions all have a predetermined outcome of which he has no control.