“Presentiment” means an emotional or stress response before any knowledge or known physics could have informed about the exciting or dangerous future situation (“anomalous retroactive influence on affect”). “The Science of Precognition” argues that “presentiment” studies can be proper science and that presentiment would be strongly selected for and thus would arise at some point during evolution. The big problem: presentiment seems to require an influence from the future, and that is impossible in classical physics.
However, quantum physics may allow retroactive causation, which was somewhat discussed also in “Future Influence: Quantum Physics of Precognition”. Let us not repeat the arguments in those articles, but add to them here.
1) Quantum Parallelism and Empirical Probability in Many Worlds Models
In classical physics, the future does not yet exist, so it cannot have any effect, period. However, any future situation is just another world that observes to be further along in cosmic time (the cosmos has cooled and expanded further). Quantum mechanics allows or perhaps even cosmologically requires those parallel worlds to be in quantum superposition with the one you observe now.
1.1) Presentiment versus Psychokinesis
The trigger of presentiment in the present would be indeed in the present and thus not from the future. Even if the sentiment were traced back to some quantum physical ongoing in certain evolved neural circuits, you could claim that since these happen in the present, they influence the future rather than the future being their cause.
This is similar to claiming that the presence of an effect in the present makes the term “precognition” or “future influence” not applicable by definition. Here it is a more physical argument: rather than being influenced by the future, the future was shaped by the presentiment. Since it is still paranormal, one speaks of “psychokinetic” effects. Studies try to differentiate between these by using pseudo random number generators (PRNG) instead of hardware random number generators (HRNG) which tap quantum randomness. The problem with PRNG: presentiment becomes clairvoyance/remote viewing of the already present information.
All these ‘mechanistic’ hypotheses, i.e. presentiment by signal like future influence, naïve psychokinesis, or remote viewing, are extremely suspect. There is nothing evolved* in humans that could pick up on or influence anything inside a computer and its random number generator. There is no conceivable way in which the brain has anything evolved that can make use of entangled particles to look inside a computer or kick the electrons in the HRNG. The problem is not the physics per se. There is no overlap between what humans are evolved for to perceive and the internal representations of information in a computer.
(* Evolutionary conceivability inside a causal description where “past” is a self-consistent record rather than a dynamical origin seems sufficient and less suspect given the very topic here.)
There is only one way that conceivably works, and this way is relevant also for those who argue about issues of terminology, because there may be no signal, no trigger from the future in the present at all, yet nevertheless there could be effectively presentiment.
1.2) Empirical probability in Many World Interpretations
Probability is the frequency found in records (memory/laboratory log). In a many world interpretation (MWI) with so called branch counting, it is sufficient if there are more future worlds remembering having felt the correct presentiment. The past worlds are equal in number, half feeling that heads will come up, half anticipating tails. No trigger or "effect" may be found in the past worlds. Nevertheless, you may find yourself with higher probability in a world where the laboratory log shows significant effects.
The MWI has shortcomings when it comes to normalizations of probabilities, but these models are used successfully in cosmology and they resolve the Einstein Podolsky Rosen (EPR) paradox. Violation of the Bell inequality in quantum mechanics can be modeled by MWI in precisely the way just described: While the world branches, it may branch according to classical probabilities, but “after” the classical branching, the branches re-combine and branch/multiply further. After many subsequent experiments, in most future worlds, the recorded outcomes imply the quantum probabilities, not the classical ones.
Presentiment could turn out correct in most of the future worlds. In that case, nothing goes back into the past, no signal, yet nevertheless it seems as if the future informed the past.
Big problem: Why would correct presentiment multiply the number of parallel branches? This I will come back to the next time. In short: quantum physical probability is well known to be increased by mere consistency, by the constructive interference of consistent histories, while inconsistent histories destroy each other via quantum interference. Belief adds consistency. But does this not lead to contradictions? Do I not find myself in worlds where others with different beliefs are also present? Is this all semi-religious pseudo-scientific drivel?
Just one promise: Sheer crazy like Henry P. Stapp’s “choices made by nature stem from sufficient reasons, and that two such reasons are to promote the positive and to curtail the negative experiences of observers”  will have no place in my considerations. How the hell does nature care about what Henry feels is “positive” to then destroy the inconsistent pasts? The guy has gone certifiably bananas.
 Henry P. Stapp: “Retrocausal Effects As A Consequence of Orthodox Quantum Mechanics Refined To Accommodate The Principle Of Sufficient Reason.” (2011), on the preprint archive, don’t waste your time.