Massimo,
Isn’t the real question here whether consciousness is a factor in the course of events, or simply an observer?
Consider my point about time, that energy is “conserved,” because it is the present state and its changing configuration is the effect of time, though it’s the events that move through the present, future to past.
As such, causation is due to the energy. The bat hitting the ball causes it to fly away.
Now consider that consciousness is also present, going past to future, while the forms and effects it manifests, perceptions, thoughts, emotions, even individual lives go future to past.
As such, it would seem that consciousness functions as an energy. It is causal. Of thought, of emotions, desires and all those other impulses of sentience. Which then are transmitted to the environment along these sentient beings.
Science has tended to dismiss consciousness as epiphenomenal to information processing and maybe admit some element to other expressions of life, but it can’t be observed or measured, other than how it is expressed. In fact, it is assumed by many that if something imitates sentient behavior sufficiently, it amounts to consciousness. Such as expressed by the Turing test.
Yet science has also tended to be a bit dismissive of energy as well. Other than how it can be measured, quantified and qualified. In fact, the measurement has been taken as more fundamental than what is being measured, such as with time, where it is supposedly symmetric, because there is no direction to the unit of duration, so the apparent asymmetry only emerges with entropy.
Though what is measured is action and action is inertial. The earth only turns one direction.
So yes, causation yields determination and consciousness is causal.
Aka, will.