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I think from a physics standpoint, strict free will is already an illusion and the only useful definitions of free will basically boil down to "choices can be made", perhaps as far as "Slight differences in initial conditions can lead to different choices" (but somehow excluding random processes). That kind of definition doesn't even require consciousness, and is compatible with a deterministic universe like ours seems mostly to be. Would also be compatible with the time traveler unwittingly doing everything as must happen, but still via individual choices.
Choice is one of the slight differences that can lead to different outcomes. A rock falling down a hill will always fall downhill because of gravity. An animal can choose to slow itself or even work against gravity to move uphill. Instead of gravity, there are a ton of prior experiences that will influence that choice, but choice is still a distinct part of the process.
Exactly. That's why I think the only useful definitions of free will are those that are weak enough to distinguish between the animal and the rock in a situation like that.
Are you saying that even without time travel, free will is an illusion? Surely there has to be a time travel scenario, like going back 1 second in time and shaking hands, where all information is known to both travelers, and the future self would know what was done previously, and can choose to take a different action.
I can think of a couple ways around that, the easiest is that I actually think time travel is impossible. (Like this for example)
If it's not impossible, then single-timeline travel probably is, and all (backwards) travel would start a new timeline.
Short of that, maybe something ridiculous would have happened when the traveler "first" went back, like one of them tripping or whatever, and the handshake they agreed to try didn't go as planned, and then "still" didn't the traveler's second time. Basically this.