WJNS  Vol.3 No.3 , August 2013
A Clifford algebraic analysis gives mathematical explanation of quantization of quantum theory and delineates a model of quantum reality in which information, primitive cognition entities and a principle of existence are intrinsically represented ab initio
Author(s) Elio Conte*
ABSTRACT

The thesis of this paper is that Information, Cognition and a Principle of Existence are intrinsically structured in the quantum model of reality. We reach such evidence by using the Clifford algebra. We analyze quantization in some traditional cases of quantum mechanics and, in particular in quantum harmonic oscillator, orbital angular momentum and hydrogen atom. The results are confirmed analyzing human cognition behavior that evidences a very consistent agreement with the basic quantum mechanical foundations.


Cite this paper
Conte, E. (2013) A Clifford algebraic analysis gives mathematical explanation of quantization of quantum theory and delineates a model of quantum reality in which information, primitive cognition entities and a principle of existence are intrinsically represented ab initio. World Journal of Neuroscience, 3, 157-170. doi: 10.4236/wjns.2013.33021.
References
[1]   Bell, J.S. (1964) On the Einstein-Podolsky-Rosen paradox. Physics, 1, 195-200.

[2]   Von Neumann, J. (1932) Mathematische grundlagen der quantenmechanik. Springer-Verlag, Berlin.

[3]   Dirac, P.A.M. (1977) History of twentieth century of physics. Weiner Ac. Press, New York.

[4]   Dirac, P.A.M. (1971) The development of quantum mechanics. Gordon and Breach, New York.

[5]   Conte, E. (2010) A proof of Von Neumann’s postulate in quantum mechanics. In: Quantum Theory Reconsideration of Foundations 5, American Institute of Physics, New York, 201-205.

[6]   Conte, E. (2010) A reformulation of von Neumann’s postulates on quantum measurement by using two theorems in Clifford algebra. International Journal of Theoretical Physics, 49, 587-614. doi:10.1007/s10773-009-0239-z

[7]   Stapp, H.P. (2006) Quantum interactive dualism: An alternative to materialism. www-physics.lbl.gov/~stapp/QID.pdf

[8]   Conte, E. (2011) An investigation on the basic conceptual foundations of quantum mechanics by using the Clifford algebra. Advanced Studies in Theoretical Physics, 5, 485-544.

[9]   Conte, E. (2011) On the logical origins of quantum mechanics demonstrated by using Clifford Algebra: A proof that quantum interference arises in a Clifford algebraic formulation of quantum mechanics. Electronic Journal of Theoretical Physics, 8, 109-126.

[10]   Conte, E. (2011) On the logical origins of quantum mechanics demonstrated by using Clifford algebra. NeuroQuantology, 9, 231-242.

[11]   Conte, E. (2012) What is the reason to use Clifford algebra in quantum cognition? Part I: “It from qubit” on the possibility that the amino acids can discern between two quantum spin states. NeuroQuantology, 10, 561-565.

[12]   Conte, E., Todarello, O., Federici, A., Vitiello, F., Lopane, M. and Khrennikov, A.Y. (2004) A preliminary evidence of quantum like behaviour in measurements of mental states. In: Quantum Theory: Reconsideration of Foundations 2, Vaxjo University Press, Vaxjo, 679-702.

[13]   Orlov, Y.F. (1994) The logical origins of quantum mechanics. Annals of Physics, 234, 245-259. doi:10.1006/aphy.1994.1081

[14]   Eddington, A.S. (1946) Fundamental theory. Cambridge.

[15]   Bohm, D.J., Davies, P.G. and Hiley, B.J. (1982) Algebraic quantum mechanics and pregeometry. Unpublished, 1982.

[16]   Mehra, J. and Rechenberg, H. (1982) The historical development of quantum theory. Sprinegr-Verlag, New York. doi:10.1007/978-1-4612-5783-7

[17]   Pauli, W. (1926) über das wasserstoffspektrum vom standpunkt der neuen quantenmechanik. Zeitschrift für Physik, 36, 336-363. doi:10.1007/BF01450175

[18]   Laplace, P.S. (1799) Traité de mécanique celeste, tome I, premiere partie, livre II 165, GAUTFUER-VII.LAKS, Paris.

[19]   Lenz, W. (1924) über den bewegungsverlauf und quantenzustande der gestorten keplerbewegung. Zeitschrift für Physik, 24, 197-207. doi:10.1007/BF01327245

[20]   Bordley, R.F. (1983) Modeling quantum behavior with standard (nonquantum) probability theory. Journal of Mathematical Physics, 24, 2411-2421. doi:10.1063/1.525622

[21]   Bordley, R.F. (1997) Experiment-dependent probabilities in quantum-mechanics and psychology. Physics Essays, 10, 401-406. doi:10.4006/1.3036426

[22]   Kanheman, D., Slovic, P. and Tversky, A. (1982) Judgement under uncertainty: Heuristics and biases. Cambridge University Press, Cambridge. doi:10.1017/CBO9780511809477

[23]   Kanheman, D. and Tversky, A. (1979) Prospect theory: An analysis of decisions under risk. Econometrica, 47, 263-291. doi:10.2307/1914185

[24]   Hogarth, H. and Einborn, H. (1990) Venture theory: A model of decision weights. Management Science, 36, 780-803. doi:10.1287/mnsc.36.7.780

[25]   Chew, S. (1983) A generalisation of the quasilinear mean with applications to the ... and decision theory resolving the Allais paradox. Econometrica, 51, 1065-1092. doi:10.2307/1912052

[26]   Fishburn, P. (1988) Non linear preference and utility theory. John Hopkins University Press, Baltimore.

[27]   Segal, U. (1988) Does the preference reversal phenomenon necessarily contradict the independence axiom? American Economic Review, 78, 233-236.

[28]   Conte, E. (2011) On the logical origins of quantum mechanics demonstrated by using Clifford algebra: A proof that quantum interference arises in a Clifford algebraic formulation of quantum mechanics. Electronic Journal of Theoretical Physics, 8, 109-126.

[29]   Conte, E. (2011) On the logical origins of quantum mechanics demonstrated by using Clifford algebra. Neuroquantology, 9, 231-242.

[30]   Conte, E. (2012) What is the reason to use Clifford algebra in quantum cognition? Part I: “It from qubit” on the possibility that the amino acids can discern between two quantum spin states. Neuroquantology, 10, 561-565.

[31]   Conte, E., Todarello, O., Federici, A., Santacroce, N., Laterza, V. and Khrennikov, A.Y. (2012) May we verify non-existing dispersion free ensembles by application of quantum mechanics in experiments at perceptive and cognitive level? Neuroquantology, 10, 14-19.

[32]   Conte, E. (2012) Advances in application of quantum mechanics in neuroscience and psychology: A Clifford algebraic approach. Nova Science Publishers, New York.

[33]   Conte, E., Santacroce, N. and Federici, A. (2012) A possible quantum model of consciousness interfaced with a non-lipschitz chaotic dynamics of neural activity (Part I) and (Part II). Journal of Consciousness Exploration & Research, 3, 905-936.

[34]   Conte, E., Khrennikov, A.Y., Todarello, O., De Robertis, R., Federici, A. and Zbilut, J.P. (2012) On the possibility that we think in a quantum mechanical manner: An experimental verification of existing quantum interference effects in cognitive anomaly of conjunction fallacy. In: On the Borders of Complexity Cap, Nova Science Publishers, Inc., Hauppauge, 149-163.

[35]   Conte, E., Santacroce, N., Laterza, V., Conte, S., Federici, A. and Todarello, O. (2012) The brain knows more than it admits: A quantum model and its experimental confirmation. Electronic Journal of Theoretical Physics, 9, 72-110.

[36]   Conte, E., Khrennikov, A.Y., Todarello, O., De Robertis, R., Federici, A. and Zbilut, J.P. (2011) On the possibility that we think in a quantum mechanical manner: An experimental verification of existing quantum interference effects in cognitive anomaly of conjunction fallacy. Chaos and Complexity Letters, 4, 123-136.

[37]   Conte, E. (2010) The possibility that we think in a quantum probabilistic manner. Neuroquantology, 8, 3-47.

[38]   Conte, E., Todarello, O., Laterza, V., Khrennikov, A.Y., Mendolicchio, L. and Federici, A. (2010) A preliminary experimental verification of violation of bell inequality in a quantum model of Jung theory of personality formulated with Clifford algebra. Journal of Consciousness Exploration & Research, 1, 831-849.

[39]   Conte, E. (2009) A brief note on time evolution of quantum wave function and of quantum probabilities during perception and cognition of human subjects. Neuroquantology, 7, 435-448.

[40]   Conte, E., Khrennikov, A.Y., Todarello, O., Federici, A. and Zbilut, J.P. (2009) On the existence of quantum wave function and quantum interference effects in mental states: An experimental confirmation during perception and cognition in humans. Neuroquantology, 7, 204-212.

[41]   Conte, E., Khrennikov, A.Y., Todarello, O., Federici, A., Mendolicchio, L. and Zbilut, J.P. (2009) Mental states follow quantum mechanics during perception and cognition of ambiguous figures. Open Systems & Information Dynamics, 16, 1-17. doi:10.1142/S1230161209000074

[42]   Conte, E., Khrennikov, A.Y., Todarello, O., Federici, A. and Zbilut, J.P. (2008) A preliminary experimental verification on the possibility of bell inequality violation in mental states. Neuroquantology, 6, 214-221.

[43]   Conte, E. (2008) Testing quantum consciousness. Neuroquantology, 6, 126-139.

[44]   Conte, E., Todarello, O., Federici, A., Vitiello, F., Lopane, M., Khrennikov, A.Y. and Zbilut, J.P. (2007) Some remarks on an experiment suggesting quantum-like behavior of cognitive entities and formulation of an abstract quantum mechanical formalism to describe cognitive entity and its dynamics. Chaos, Solitons and Fractals, 31, 1076-1088. doi:10.1016/j.chaos.2005.09.061

[45]   Conte, E., Pierri, G.P., Federici, A., Mendolicchio, L. and Zbilut, J.P. (2006) A model of biological neuron with terminal chaos and quantum-like features. Chaos, Solitons and Fractals, 30, 774-780. doi:10.1016/j.chaos.2005.08.211

[46]   Conte, E., Pierri, G.P., Mendolicchio, L., Khrennikov, A.Y. and Zbilut, J.P. (2006) On some detailed examples of quantum like structures containing quantum potential states in the sphere of biological dynamics. Cornell University Library.

[47]   Conte, E., Khrennikov, A.Y. and Zbilut, J.P. (2006) The transition from ontic potentiality to actualization of states in quantum mechanical approach to reality: The proof of a mathematical theorem to support it. Cornell University Library.

[48]   Conte, E., Todarello, O., Federici, A., Vitiello, F., Lopane, M. and Khrennikov, A.Y. (2004) A preliminary evidence of quantum like behaviour in measurements of mental states. In: Quantum Theory: Reconsideration of Foundations 2, Vaxjo University Press, Vaxjo.

[49]   Conte, E. (2013) What is the reason to use Clifford algebra in quantum cognition? Part II: Information, cognition and the principle of existence are intrinsically structured in the quantum model of reality. NeuroQuantology, 11, 34-46.

[50]   Conte, E. (2013) Are information, cognition and the principle of existence intrinsically structured in the quantum model of reality? Advanced Studies in Theoretical Physics.

[51]   Khrennikov, A. (2010) Ubiquitous quantum structure. Springer, New York. doi:10.1007/978-3-642-05101-2

 
 
Top