Traditionally philosophical literature recognizes a distinction between fatalism and causal determinism. Causal determinists don't say that human actions and thoughts don't or can't affect the future, just that those actions and thoughts are themselves causally dependent on prior conditions and the laws of nature. Fatalism is generally defined as something like "no matter what you think or do the future cannot be altered. It's Oedipus killing his father despite doing everything he can to avoid it.
The psychological and physical answers above sound to me like what it would be like if fatalism were true than if hard determinism were true. I mean, hard determinists think we don't have free will; it would be odd if they thought not having free will involved novel psychological or physical experiences.
Anyway, I think the only kind of free will that makes sense is compatiblist free will. So when it comes to what it would be like not to have free will I'm concerned with what it would be like if my decisions weren't made according to my wishes and reasons.
I would expect to have a very hard time predicting my behavior or explaining it after the fact with any kind of rational model. If I did have reasons and preferences to back up my decisions they would probably be invented after the decision had been made. Post-facto rationalizations instead of genuine reflection about the decision. Also, I would probably feel like I had a lot of reasons and preferences that contradicted each other and would often find myself doing x even though I wanted to want to not do x.
Rest assured, I have never experienced any of that.
Fatalism is generally defined as something like "no matter what you think or do the future cannot be altered. It's Oedipus killing his father despite doing everything he can to avoid it.
Interestingly, fatalism in that sense is compatible with free will as I would understand it: Oedipus can make any choice he likes, it's just that some specific future event is guaranteed to happen (the particular way in which it happens depending on the choice he makes).
Perhaps one could distinguish between "local" and "global" free will, or -- ...
Given the spike in free-will debates on LW recently (blame Scott Aaronson), and the usual potentially answerable meta-question "Why do we think we have free will?", I am intrigued by a sub-question, "what would it feel like to have/not have free will?". The positive version of this question is not very interesting, almost everyone feels they have free will most all the time. The negative version is more interesting and I expect the answers to be more diverse. Here are a few off the top of my head, not necessarily mutually exclusive:
Epistemic:
Psychological:
Physical:
For me personally some of these are close to the feeling of "no free will" than others, but I am not sure if any single one crosses the boundary.
I am sure that there are different takes on the answers and on how to categorize them. I think it would be useful to collect some perspectives and maybe have a poll or several after.