Friday, February 22, 2008

On direct testing of quantum consciousness

Quantum 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.

  1. Consider a group S of subject persons. Divide it into two groups U and V containing equally many subject persons. Represent for members of U the question A (bistable percept A). From this one can deduce the probalities p(A=+) and p(A=-). Represent for members of V the question B and and immediately after than the question A (bistable percept A) for those who answered B=-. This experiment gives the conditional probabilities p(A=x/B=y).

  2. The quantity

    cos(θx) = [p(A=x)- p(B=+)p(A=x/B=+) -p(B=-)p(A=x/B=-)]/[2(p(B=+)p(B=-)p(A=x/B=+)p(A=x/B=-)1/2], x=+/-.

    measures the failure of the basic rule

    p(A=x)=p(B=+)p(A=x/B=+) +p(B=-)p(A=x/B=-)

    for classical conditional probability. Note that in quantum theory similar rules applies to transition amplitudes (conditional probability amplitudes) corresponding to the addition of a complete set of states in the inner product between two states (for instance, repeated application of this gives rise to path integral formulation).

  3. One can describe the situation in terms of "quantum like state"

    Ψ(A=x)= [p(B=+)p(A=x/B=+)]1/2 +e+/- [p(B=-)p(A=x/B=-)]1/2

    satisfying p(A=+x) =|Ψ(A=x)|2. If cos(θx) is non-vanishing one can say that that the situation is quantum like. Conte and collaborators conclude that this is indeed the case [2].

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.

  1. The test is following. Consider a group S of subject persons divided into subgroups U and V as above. Pose to the members of U question B and immediately after that question A for those who answered B=+ and question C for those who answered B=-1. For group V represent first the question C and for those who answer C=+ represent the question A. The failure of inequality could regarded as a direct proof for quantum like behavior. That failure does not occur does not of course mean that system is classical but only that the quantal effects are not large enough.

  2. The analogy with Bell's inequality suggest that the questions are analogous to posing the spins of spin pair in spin singlet state to an external magnetic fields determining the quantization axis. The inequality tend to fail when the directions of the magnetic fields for the two spins differ enough. Thus the failure is expected if the questions, in other words ambiguous figures producing bistable percepts differ enough.

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 two-spin system only in that space-like entanglement is replaced with time like entanglement. The experiment would be essentially a measurement of probabilities defined by the matrix elements of M-matrix defining the generalization of S-matrix. 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.

  1. If the vision about DNA as topological quantum computer makes sense, the question to the answer "Which of the two possible percepts?" can be regarded as a qubit which is some function of a large number of qubits and same function irrespective of the ambiguous figure used. This could hold quite generally, at least for a given sensory modality. The qubits appearing as arguments of this function are determined by the sensory input defined by the ambiguous figure. The ambiguous figure would take the role of magnetic field determining the directions of quantization axes for a large collection of qubits appearing as arguments of the Boolean function (one cannot exclude the possibility that neuronal synchrony forces all these axes to have same direction). Qubit could correspond to spin or some spin like variable. The quantization axes could correspond in this case to the direction of external magnetic field acting on 1-gate of tqc.

  2. Qubit could be replaced with an n-state system: this would require a generalization of the Bell inequalities. The model of DNA as tqc suggests that qubit might be replaced with qutrit defined by a quark triplet (third quark with vanishing color isospin would correspond to ill-defined truth value. The inability of subject persons to identify the percept always indeed encourages to consider this option. Color group SU(3) (SO(3) subset SU(3)) defines the set of possible quantization axes as points of the flag manifold F= SU(3)/U(1)× U(1) (SO(3)/SO(2)= S2). Quantization axes would be determined by the direction of color magnetic field in color Lie algebra and sensory input would define a sequence of 1-gates at the lipids ends of the braid strands, and realized as color rotations of the flux tube defining braid strand. This hypothesis would conform with the proposal of Barbara Shipman that honeybee dance that quarks are in some mysterious manner involved with cognition [3].

For background see that chapter DNA as Topological Quantum Computer of "Genes and Memes".

References

[1] A. Khrennikov (2004), Bell's inequality for conditional probabilities as a test for quantum like behaviour of mind, arXiv:quant-ph/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.gen-ph].

[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 Kostant-Toda lattice.

B. Shipman (1998), A symmetry of order two in the full Kostant-Toda lattice.

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