An Investigation on the Basic Conceptual Foundations of Quantum Mechanics by Using the Clifford Algebra

We review our approach to quantum mechanics adding also some new interesting results. We start by giving proof of two important theorems on the existence of the and Clifford algebras. This last algebra gives proof of the von Neumann basic postulates on the quantum measurement explaining thus in an algebraic manner the wave function collapse postulated in standard quantum theory. In this manner we reach the objective to expose a self-consistent version of quantum mechanics. We give proof of the quantum like Heisenberg uncertainty relations, the phenomenon of quantum Mach Zender interference as well as quantum collapse in some cases of physical interest We also discuss the problem of time evolution of quantum systems as well as the changes in space location. We also give demonstration of the Kocken-Specher theorem, and also we give an algebraic formulation and explanation of the EPR . By using the same approach we also derive Bell inequalities. Our formulation is strongly based on the use of idempotents that are contained in Clifford algebra. Their counterpart in quantum mechanics is represented by the projection operators that are interpreted as logical statements, following the basic von Neumann results. Using the Clifford algebra we are able to invert such result. According to the results previously obtained by Orlov in 1994, we are able to give proof that quantum mechanics derives from logic. We show that indeterminism and quantum interference have their origin in the logic.Comment: forthcoming papers; http://www.m-hikari.com/astp/forth/index.htm

Addendum to Quantum Wave Function Collapse of a System Having Three anti Commuting Elements.

We indicate a new way in the solution of the problem of the quantum measurement . In past papers we used the well-known formalism of the density matrix using an algebraic approach in a two states quantum spin system S, considering the particular case of three anticommuting elements. We demonstrated that, during the wave collapse, we have a transition from the standard Clifford algebra, structured in its space and metrics, to the new spatial structure of the Clifford dihedral algebra. This structured geometric transition, which occurs during the interaction of the S system with the macroscopic measurement system M, causes the destruction of the interferential factors. In the present paper we construct a detailed model of the (S+M) interaction evidencing the particular role of the Time Ordering in the (S+M) coupling since we have a time asymmetric interaction . We demonstrate that , during the measurement , the physical circumstance that the fermion creation and annihilation operators of the S system must be destroyed during such interaction has a fundamental role

Quantum Cognition : A comment to the paper entitled : A More Realistic Quantum Mechanical Model of Conscious Perception During Binocularly rivalry by Mohammad Reza Paraan,Fatemeh Bakouie and Shahriar Gharibzadeh.: Quantum Cognition Analysis in Binocularly rivarly

I discuss briefly the foundations of quantum cognition taking as reference an article that appeared on Frontiers in Computational Neuroscience Keywords: consciousness, quantum state, mixed state, probability distribution, dominance duration, quantum superposition principle, quantum collapse, quantum cognition , cognitive science In Frontiers in Computational Neuroscience , general commentary , the authors M. Reza Paraan, F. Bakouie and S. Gharibzadeh ,in date 20 February , 2014(doi:10.3389/fncom.2014.00015) (Paraan M.R. et al, 2014) published a paper entitled A More Realistic Quantum Mechanical Model of Conscious Perception During Binocularly rivalry , discussing and criticizing the basic experimental and theoretical results that I and Khrennikov obtained (Conte E. et al.,2009) examining the possible role of quantum mechanics during the perception and the cognition of ambiguous figures. First of all we retain that , in order to criticize the results of authors , it is appropriate that scholars are aware about all the articulated research that the criticized authors have explained about the matter so to be sure to have fully explored all the obtained results. This is the reason to report in references a long list of publications that such authors have realized (). Unfortunately it may happen that scholars sometimes have not the opportunity to look at all the scientific production of another author and in some cases instead it may contribute to a better definition of his/her production. The feature that such authors seem to outline , is contained in the following their sentence : " Technically, a wave-function is a superposition of all the real possible states of a quantum system. We believe that this is an inappropriate take on the problem which leads to inconsistencies within the model. The developers of these two quantum mechanical models believe that the actualization of each quantum state is equal to the activation of neural correlates of consciousness (NCC) of the corresponding perception; a state is actualized when a quantum system is measured (observed) and subsequently its wave-function " collapses " to that constituent state. Therefore, we believe that wave-function is not a legitimate representation, because it does not describe a real state of a system and is doomed to collapse, and on the other hand, specific NCC of MS (Mixed States duration) or that of indeterminate perception demand a distinct associated quantum state. Their model takes into account the periods when their subjects report indeterminate perception. Indeterminate perception resembles MS in that they are both mental states and are mediated by specific neural correlates. But Conte et al. represent indeterminacy state by the wave-function of the two-state system rather than an additional third quantum state. Technically, a wave-function is a superposition of all the real possible states of a quantum system. We believe that this is an inappropriate take on the problem which leads to inconsistencies within the model " (Paraan M.R. et al, 2014)

On the logical origins of quantum mechanics demonstrated by using Clifford algebra

We review a rough scheme of quantum mechanics using the Clifford algebra. Following the steps previously published in a paper by another author [31], we demonstrate that quantum interference arises in a Clifford algebraic formulation of quantum mechanics. In 1932 J. von Neumann showed that projection operators and, in particular, quantum density matrices can be interpreted as logical statements. In accord with a previously obtained result by V. F Orlov , in this paper we invert von Neumann’s result. Instead of constructing logic from quantum mechanics , we construct quantum mechanics from an extended classical logic. It follows that the origins of the two most fundamental quantum phenomena , the indeterminism and the interference of probabilities, lie not in the traditional physics by itself but in the logical structure as realized here by the Clifford algebra

A New Method for Analysis of Heart Rate Variability, Asymmetry and BRS. Part I .

: In the present paper we give a new method for estimation and quantification of Heart Rate Variability (HRV) in the VLF,LF,HF bands using the basic concept of variability previously introduced. The method enables to quantify ANS modulation of R-R intervals. In the subsequent paper we will give detailed exposition of the performed and confirming experiments