Free will and quantum

There is rather interesting discussion about physics and free will in Hammock Physicist. I glue below my own comment which begins as objection against the strange claim that the experience of free will in some manner corresponds to inability to predict.

The basic flaw of argument claiming consistency of determinism of determinism and experience of free will is the identification of experience of free will with the inability to predict. I cannot calculate what will happen to me or the world tomorrow but I do not experience this inability as free will. Free will is something much more active. It involves selection between options and also intentionality, which is much more than a mere choice between a finite number of alternatives.

State function reduction is the obvious starting point when one tries to understand free will in terms of quantum theory or it generalization. The basic problems are well-known and the attempt to resolve them leads to the following big picture.

1. The non-determinism of state function reduction is inconsistent with the determinism of Schroedinger time evolution. This problem is resolved by replacing quantum states with counterparts of the entire time evolutions of Schroedinger equation. Also the geometric past changes in quantum jump: this conforms with the classical findings of Libet that conscious decision is preceded by neural activity.

2. One must replace state function reduction with quantum jump involving unitary process (something more general than unitary time evolution) followed by state function reduction. Unitary process would create superposition of worlds of quantum states and would be the genuinely creative aspect of free will. The first guess is that state function reduction chooses one state among the eigenstates of measured observables.

3. The chronon of subjective time is identifiable in terms of quantum jump but one has to understand the relationship of subjective time to the geometric time of physicist. These times are not same (irreversility of the subjecitve time contra reversibility of geometric time). This leads from the usual positive energy ontology to zero energy ontology (ZEO) in which quantum states are pairs of positive and negative energy states with opposite conserved quantum numbers assignable to the future and past boundaries of causal diamond CD (analog of Penrose diagram) defined as intersection of future and past directed light-cones.

   The identification conforms with the crossing symmetry of QFT but predicts deviations from positive energy ontology. In ZEO one can understand how the arrow of subjective time is mapped to that of geometric time and also the localization of the contents of contents of sensory mental images to a finite and rather short (about .1 seconds) time interval: memories are about the region of entire CD and means totally new view about how memories are realized. ZEO allows maximal free will since any zero energy state can in principle be achieved from given one by quantum jumps.

4. The natural variational principle for consciousness is what I call negentropy maximization principle (NMP). The fundamental observable would be density matrix characterizing the entanglement between system and its complement and characterized by entanglement entropy. NMP states that the reduction of entanglement entropy in state function reduction is maximal. This is consistent with standard quantum measurement theory but state function reduction would always lead to a state with vanishing entanglement negentropy in standard QM. Optimal situation would be no information at all. Something more is needed.

5. Skeptic can also argue that the outcome of state function reduction is random so that no genuine free will can be assigned it. I believe that this is the case in standard quantum theory. The existence of number theoretic variants of Shannon entropy making sense for rational and even algebraic entanglement probabilities saves the situation: the replacement of probabilities appearing as the arguments of logarithms in Shannon entropy with their p-adic norms for any prime p leads to a modification of Shannon entropy satisfying same defining conditions. The negentropy is maximal for a unique prime.

   This entropy can be negative and the interpretation is in terms of information carried by entanglement: the information is not about whether cat is dead or alive but tells that it is better to not open the bottle;-). In this framework the outcome is not anymore completely random and entangleed state can be stable against state function reduction. p-Adic physics is unavoidable outcome and has interpretation in terms of correlates of intention and cognition. p-Adic space-time regions would be the mind stuff of Descartes. The natural hypothesis is that life corresponds to negentropic entanglement possible in the rational intersection of real and p-adic worlds (matter and cognition).

   Second law generalizes: quantum jumps can create genuinely negentropic subsystems but the price paid is the creation of subsystems with compensating entropy: by looking around and seeing what we have done one becomes convinced about the plausibility of the generalization;-). Next Unitary process however means a moment of mercy cleaning all the dirt;-).

This is just the basic vision. Working out the details requires considerably more lines of text: see my homepage.