Time travel book from the 50's

Question

I'm looking for a time travel book that my parents and I have both read. My father thinks he got it in the 50's.

Plot: A man is murdered while conducting an experiment and wakes up in a different body. It turns out that he time traveled into the future and took someone else's body. Every time he dies, it happens again. At one point, there is a group of people who tries to stop people like him, because he, and others, apparently, are killing people through time. He escapes from them. It turns out that time is cyclical or something and he loops back around to when he started, in a different body, and kills the person who killed him, before the murder happens. Then he (she, now, lol) is going to be executed and is wondering if he's going to time travel again when he is executed.

Answer 1

It sounds like Charles Eric Maine's Timeliner (1955).

Timeliner is a time travel story. A scientist working with "dimensional quadrature" is flung forward in time, to a period where his consciousness ousts that of another man. When that man dies, the protagonist leaps forward again, and so on. In each case, the personality he replaces belongs to a person who is close to a woman who resembles his wife.

Also, the story was originally a BBC radio play The Einstein Highway and first broadcast in 1954.

One detail mentioned by the OP, not mentioned in Wikipedia, is that a time barrier is erected in the future to prevent time travellers returning to their own eras. The time traveller is given a choice between imprisonment, I think, on the Moon or going to the disintegration chamber. When he discovers there is a theory that the disintegrated can return to their own era, he accepts the disintegration chamber. He succeeds in returning to his original era only to find he is now his own murderer on trial for murdering himself.

Charles Eric Maine employed the same form of time travel in his 1960 novel Calculated Risk where two citizens of a harsh dystopian future escape to the past the world of the 1960s. Their minds take over the bodies of twentieth century people. It doesn't end well.

Answer 2

This is something of a long shot, as my answer is second-hand like your question, but the main plot device sounds similar to Star Kings by Edmond Hamilton. It was published in 1949, so the timeline fits. If correct, credit for the find goes to user Odmin, whose answer to a previous question here is what I thought of when reading this.

The goodreads.com summary provides some names that might jog your father's memory:

Flung across space and time by the sorcery of super-science, John Gordon exchanges bodies with Zarth Arn, Prince of the Mid-Galactic Empire 2000 centuries in the future! Suddenly John is thrust into a last-ditch battle between the democratic Empire World and the tyranny of the Black Cloud regime. Only one weapon—the terrifying Disruptor— can win the struggle for the Empire Forces. But it is so powerful that unless John uses it correctly it could destroy not only the enemy but the cosmos.

Could his 20th Century mind cope with the technology of 200,000 years from now?

If that sounds promising at all, further verification can be had by checking out the first seven chapters online via Baen ebooks. It's old enough that it may be out of copyright, and it appears that several sites offer it as a free text or ebook.