On direct testing of quantum consciousnessQuantum entanglement and its reduction in "cognitive" quantum measurement could provide a direct test of quantum consciousness. Andrei Khrennikov [1] has proposed a mathematical formulation of "quantum like" behavior based on his proposal that so called context dependent probabilities could provide alternative description for quantum mechanical interference phenomenon. In quantum theory context would correspond to the choice of quantization axis. Khrennikov has also proposed a modification of Bell inequalities so that they apply on conditional probabilities: this would make it possible to avoid the task of preparing entangled state of brains. The hope is that one could forget completely the microscopic structure of quantum brain and test quantum like behavior by making simple experiments involving just questions to the subject persons and finding whether or not classical rules for conditional probabilities hold true or not. 1. First experiment Bistable percepts induced by ambiguous figures are especially attractive from the point of view of experimentation. The question would be "Which of the two possible percepts?" and the outcome would be answer to this question. The first experiment reported in [2] was following.
2. Second experiment Second experimental test is more complex and involves generalization of Bell's inequality so that it involves conditional probabilities [1] Let A,B,C=+/ be arbitrary dichotomous random variables satisfying Kolmogorov axioms characterizing classical probability. Then the following analog of Bell inequality can be shown to hold true: P(A=+,B=+) + P(C=+,B=)≥ P(A=+,C=+). In terms of conditional probabilities one has P(A=+/B=+)/P(B=+) + P(C=+/B=)/P(C=+) ≥ P(A=+/C=+)/P(C=+). If the random variables are symmetrically distributed so that one has P(X=+/)=1/2, for X=A,B,C one obtains P(A=+/B=+)+P(C=+/B=)≥ P(A=+/C=+) . Note that this form of equality is by no means necessary. The symmetric distributions for the random variables would however correspond to maximal entanglement in spin system given best hopes for the violation of the Bell inequality.
3. Criticism and possible improvement of the experiment In the case of spin pairs the tests of quantum behavior are carried out for the members of spin pair by putting them to magnetic fields having different directions. Now the pair of experiments is made for a single subject person. Hence there is no need to prepare quantum entangled pair of conscious entities. The use of ensemble is the problematic aspect of experiments. Human beings are extremely complex systems and one can argue that it is impossible to prepare an ensemble of identical systems in cognitive sense. A possible manner to avoid the problem would be the replacement of ensembles with a time series of experiments performed for a single subject person. In both experiments one could perform the two kinds of experiments many times to single subject person and deduce various probabilities and cos(θ) from the outcome of the experiments. 4. Interpretation in terms of zero energy ontology and DNA as tqc The discussions with Elio Conte led to the realization that in zero energy ontology the experiments differ from the corresponding experiments for twospin system only in that spacelike entanglement is replaced with time like entanglement. The experiment would be essentially a measurement of probabilities defined by the matrix elements of Mmatrix defining the generalization of Smatrix. Hence Bell's inequalities and their generalizations should apply in genuine quantum sense. By performing the experiments for a single subject person as time series one might be therefore able study whether quantum consciousness in the sense of TGD makes sense. Quantum consciousness approach however requires that bistable percepts have genuine microscopic quantum states as their physical correlates. This is not assumed in the approach of Khrennikov.
References [1] A. Khrennikov (2004), Bell's inequality for conditional probabilities as a test for quantum like behaviour of mind, arXiv:quantph/0402169. [2] E. Conte, O. Todarello, A. Federici, J. P. Zbilut (2008), Minds States Follow Quantum Mechanics During Perception and Cognition of Ambigious Figures: A Final Experimental Confirmation, arXiv:0802.1835v1 [physics.genph]. [3] B. Shipman (1998), The geometry of momentum mappings on generalized flag manifolds, connections with a dynamical system, quantum mechanics and the dance of honeybee. B. Shipman (1998), On the geometry of certain isospectral sets in the full KostantToda lattice. B. Shipman (1998), A symmetry of order two in the full KostantToda lattice.
