How can we investigate to determine what causal relations lie behind the patterns of correlated events we observe? Scientific experiments are a powerful procedure for investigating causal relations. To experimentally determine if event B causes event C, the key requirement is that we be able to freely generate event B. If event C occurs each time we generate B, but does not occur when we don't generate B, we can be confident that B indeed causes C. If instead we observe occurrences of C only after spontaneous occurrences of B but never after the occurrences of B that we freely generate, then we can be confident that C is not caused by B, but instead caused by some prior A that also causes B in a parallel chain.
Note the complementary relation between free will and causation revealed by examining the experimental method. Often free will and causation are held to be in conflict: if events arise due to causation from prior events, then how can human actors freely perform actions? But now we see that in fact causation is meaningless without free will; without free will, causation cannot be distinguished from correlation. And conversely, without causation free will would also be meaningless; without causation, free will could not engage the world, the chain of events trigger by free action would be abruptly terminated and action would be utterly ineffective.
Curiously the scientific description of the world does not include the free will of the scientific experimenter, even though that free will is an essential requirement for the generation of that description. It's a bit like the blind spot in the visual field caused by the connection of the optic nerve to the retina. The optic nerve is an essential requirement for the effective functioning of the retina, yet the retina is blind just at that point.
Experimental procedures can attempt to avoid relying on free will. There is indeed a danger that the occurrence or non-occurrence of some event A will influence the decision of the experimenter to generate event B or not. If A also in parallel causes C, then the experimenter will observe that C occurs just when B is generated and so conclude that B causes C. But this conclusion is fallacious, because the generation of B was not in fact free, but caused by A through a causal chain of events that include the experimenter's decision to generate B.
In order to avoid such errors, experimenters often rely on some sort of mechanical randomized process to govern the decision of whether to generate B or not in any particular repetition of the experiment. For example, a coin toss might determine when a particular patient is given a new test drug or a placebo. In order to prevent the experimenter's observations from being distorted by expectations driven by the outcome of this decision process, the experimenter can be kept ignorant of the outcome. This is the widely used "double blind" procedure.
While double blind procedures are doubtless effective at reducing the distortion of experimental results due to biases of the experimenters, the procedure still relies on an essential element of free will. The experimental procedure requires that a link be established between some random process such as a coin toss, and the generation or non-generation of some event in the experiment. One could interpret "heads" to mean "give the placebo", or alternative one could interpret "heads" to mean "give the test drug". For the experimental results to validly indicate whether casual relations exist or not, the choice between these interpretations must be freely made.
Thus we see that free will is an essential requirement for discovering the causal relations in the world. But the descriptions that are constructed as a result of these discoveries do not include free will. Free will is an inevitable blind spot in any scientific explanation of how the world works.