We cannot know if we have free will, and so maybe all science is broken
We cannot decide whether humans have free will because we experience time as monotonic. This fact, surprisingly, also undermines the credibility of scientific experiments.
If we argue that the human mind is like a computer, or a physical system in general, we will encounter the counter-argument of having free will. A physical system is considered predictable, mechanic, whose future states can in theory be predicted from its initial one. How could such a system have free will?
There are multiple different ways in which one can respond to this counter-argument.
First of all, humans are largely predictable: psychology, psychiatry and sociology describe and predict our behavior very effectively. So maybe we have less of a free will anyway than we imagine.
Secondly, physical systems are only completely predictable in classical physics, and even there only in theory. For example, predicting the movements of three celestial bodies (just three, without anything else in this simple universe) using classical physics is already so complicated numerically, that it can only be predicted inaccurately and with very great effort.
In quantum mechanics, some randomness is creeping into physical reality, which makes such predictions impossible even in theory. Indeed, some physicists, like Roger Penrose, find free will exactly here.
But on the most fundamental level, what would free will be? It would mean that a human, given some well-known conditions, can choose to act this way, or that way. To test whether the human indeed has this choice and is not simply at the mercy of the chemical processes in its brain, we would need to recreate the initial conditions exactly many-many times, and observe if the human behaves the same way all the time, or its mind can shake off the shackles of deterministic physics and somehow contradict it. This is the basis of all (scientific) knowledge: repeatable experiments.
But the truth is that we never are (or will be) able to recreate the initial conditions exactly. If nothing else, time has changed: in our world, time appears to be monotonic, moving forward all the time, and we can never jump back to a previous point to do a "what if" experiment. This means that we will never be able to determine if humans indeed possess free will or not.
Does this mean that all experiments are flawed? Yes, it does. But most systems that we experiment on are simple and robust enough, and they do not require a complete recreation of the initial conditions. If we release a cannon ball from the top of a tower, it will fall with roughly the same speed today, and tomorrow, if the sun shines, or if it rains. But free will precisely aims at determining whether there is any wiggle room in the laws of physics, and whether they can, somehow, be navigated or controlled. Such approximate experiments would not help us settle this question.
Some would argue though that time is not actually monotonic. There is space-time, and, under certain constraints, one can "move" in time similarly to moving in space. Therefore, it could be possible to recreate the initial state perfectly and test free will. It is indeed true that an almost forward flowing time is not inherent in most physical processes as they can happen forwards as well as backwards (with some extra conditions). Yet we do experience time as a separate, monotonic thing, and how this kind of time emerges is the subject of active research. As far as I understand, the current theory is that due to how universes evolve, certain processes (that usually go forward in time) are simply more probable than processes that go backwards.
Ultimately though we do not have the final answer about time, while understanding its exact nature would be crucial in understanding a scientific experiment, an initial state, a consequence, or something that goes against consequences: free will. In summary, we cannot decide at the moment if humans have free will, and if it turns out that time is indeed monotonic, the question itself is nonsensical.