Abstract. Processes undergoing quantum mechanics exhibit quantum interference effects. In this case, quantum probabilities result to be different from classical ones because they contain an additional so called quantum interference term. We use ambiguous figures to analyse if during perception-cognition by human subjects we can observe violation of the classical probability field and the presence of quantum interference. The experiments, conducted on a group of 256 subjects, evidence that we indeed have such a quantum effect. Therefore, mental states, during perception and cognition of ambiguous figures, appear to follow quantum mechanics.

We have executed for the first time an experiment on mental obesrvables concluding that there exists equivalence (that is to say, quantum like behavior) between quantum and cognitive entities.Such result has enabled us to formulate an abstract quantum mechanical formalism that is able to describe cognitive entities and their time dynamics.

For the first time we perform an experiment to test the possibility of Bell's inequality violation in mental states, during perception-cognition in humans. We study under a theoretical and experimental framework, a Bell-type test for human perception-cognition of ambiguous figures. It is performed a detailed analysis which demonstrates that, although we have not yet been able to violate Bell's inequality in the present performed experiment, there are strong theoretical arguments supporting our expectation to violate it by a simple articulation of the same experiment. In this framework we introduce for the first time what we retain to represent quantum cognitive observables. We consider that our analysis provides a solid ground for further investigations on quantum behaviour of cognitive systems. Therefore we reaffirm that quantum mechanics is a Giano Bifronte theory (two-faced Giano, a mythological God of the past), looking from one hand to physical reality and from the other hand to the sphere of mental reality and cognitive dynamics.

According to a procedure previously introduced from Y. Ilamed and N. Salingaros, we start giving proof of two existing Clifford algebras, the Si that has isomorphism with that one of Pauli matrices and the N i,±1 where N i stands for the dihedral Clifford algebra. The salient feature is that we show that the N i,±1 may be obtained from the Si algebra when we attribute a numerical value (+1 or −1) to one of the basic elements (e 1 , e 2 , e 3 ) of the Si. We utilize such result to advance a criterium under which the Si algebra has as counterpart the description of quantum systems that in standard quantum mechanics are considered in absence of observation and quantum measurement while the N i,±1 attend when a quantum measurement is performed on such system with advent of wave function collapse. The physical content of the criterium is that the quantum measurement with wave function collapse induces the passage in the considered quantum system from the Si to N i,+1 or to the N i,−1 algebras, where each algebra has of course its proper rules of commutation. After a proper discussion on the difference between decoherence and wave function collapse, we re-examine the von Neumann postulate on quantum measurement, and we give a proper justification of such postulate by using the Si algebra. Soon after we study some applications of the above mentioned criterium to some cases of interest in standard quantum mechanics, analyzing in particular a two state quantum system, the case of time dependent interaction of such system with a measuring apparatus and finally the case of a quantum system plus measuring apparatus developed at the order n = 4 of the considered Clifford algebras and of the corresponding density matrix in standard quantum mechanics. In each of such cases examined, we find that the passage from the algebra Si to N i,±1 , considered during the quantum measurement of the system, actually describes the collapse of the wave function. Therefore we conclude that the actual quantum measurement has as counterpart in the Clifford algebraic description, the passage from the Si to the N i,±1 Clifford algebras, reaching in this E. Conte ( ) 588 Int J Theor Phys (2010) 49: 587-614 manner the objective to reformulate von Neumann postulate on quantum measurement and proposing a self-consistent formulation of quantum theory.

My discussion is articulated under the neurological as well as the psychological profile. I insist in particular on the view that mental events arise in analogy with quantum probability fields. I review some results obtained on quantum cognition discussing in detail those that we obtained on quantum interference in mental states during perception-cognition in ambiguous figures. Frequently, I use the approach to quantum mechanics by Clifford algebra. I insist in particular on two recent results. The first is the justification that I obtain of the von Neumann postulate on quantum measurement and the second relates my Clifford demonstration on the logical origins of quantum mechanics and thus on the arising feature that quantum mechanics relates conceptual entities. The whole discussion aims me to support the conclusion that we think in a quantum probabilistic manner.Key Words: quantum cognition, Clifford algebra, quantum probability fields, logical origins of quantum mechanics NeuroQuantology 2010; 4: S3-47 Introductory Remarks 1With the advent of functional brain imaging technologies, neuroscience and neuropsychology have reached satisfactory levels of understanding and knowledge. It is of great relevance that has been identified brain areas that are involved in a wide variety of brain functions including learning and memory. On the other hand, the genetic and biochemical approaches offer a constant contribution in this direction producing step by step new important advances under the profile of the investigation, research, and clinic application. NeuroQuantology | December 2010 | Vol 8 | Issue 4 | Supplement Issue 1| Page S3-47 Conte E., On the possibility that we think in a quantum probabilistic manner ISSN 1303 5150 www.neuroquantology.com S4 NeuroQuantology | December 2010 | Vol 8 | Issue 4 | Supplement Issue 1| Page S3-47 Conte E., On the possibility that we think in a quantum probabilistic manner ISSN 1303 5150 www.neuroquantology.com S5 NeuroQuantology | December 2010 | Vol 8 | Issue 4 | Supplement Issue 1| Page S3-47 Conte E., On the possibility that we think in a quantum probabilistic manner NeuroQuantology | December 2010 | Vol 8 | Issue 4 | Supplement Issue 1| Page S3-47 Conte E., On the possibility that we think in a quantum probabilistic manner ISSN 1303 5150 www.neuroquantology.com S7 NeuroQuantology | December 2010 | Vol 8 | Issue 4 | Supplement Issue 1| Page S3-47 Conte E., On the possibility that we think in a quantum probabilistic manner ISSN 1303 5150 www.neuroquantology.com S8 NeuroQuantology | December 2010 | Vol 8 | Issue 4 | Supplement Issue 1| Page S3-47 Conte E., On the possibility that we think in a quantum probabilistic manner ISSN 1303 5150 www.neuroquantology.com S9 NeuroQuantology | December 2010 | Vol 8 | Issue 4 | Supplement Issue 1| Page S3-47 Conte E., On the possibility that we think in a quantum probabilistic manner ISSN 1303 5150 www.neuroquantology.com S11