The Hidden Measurement Formalism: What Can Be Explained and Where Quantum Paradoxes Remain

In the hidden measurement formalism that we havedeveloped in Brussels we explain quantum structure asdue to the presence of two effects; (a) a real change ofstate of the system under influence of the measurement and (b) a lack of knowledge abouta deeper deterministic reality of the measurementprocess. We show that the presence of these two effectsleads to the major part of the quantum mechanical structure of a theory describing a physicalsystem, where the measurements to test the properties ofthis physical system contain the two mentioned effects.We present a quantum machine, with which we can illustrate in a simple way how the quantumstructure arises as a consequence of the two effects. Weintroduce a parameter that measures the amount of lackof knowledge on the measurement process, and by varying this parameter, we describe acontinuous evolution from a quantum structure (maximallack of knowledge) to a classical structure (zero lackof knowledge). We show that for intermediate values of∈ we find a new type of structure that isneither quantum nor classical. We analyze the quantumparadoxes in the light of these findings and show thatthey can be divided into two groups: (1) The group(measurement problem and Schrodinger cat paradox) where theparadoxical aspects arise mainly from the application ofstandard quantum theory as a general theory (e.g., alsodescribing the measurement apparatus). This type of paradox disappears in the hiddenmeasurement formalism. (2) A second group collecting theparadoxes connected to the effect of nonlocality (theEinstein-Podolsky-Rosen paradox and the violation of Bell's inequalities). We show that theseparadoxes are internally resolved because the effect ofnonlocality turns out to be a fundamental property ofthe hidden-measurement formalism itself.

[1]  J. Neumann,et al.  The Logic of Quantum Mechanics , 1936 .

[2]  I. Segal.  Postulates for General Quantum Mechanics , 1947 .

[3]  B. Coecke.  Hidden measurement model for pure and mixed states of quantum physics in Euclidean space , 1995 .

[4]  Diederik Aerts,et al.  The Origin of the Non-Classical Character of the Quantum Probability Model , 1987 .

[5]  Diederik Aerts,et al.  Example of a macroscopical classical situation that violates Bell inequalities , 1982 .

[6]  Diederik Aerts,et al.  Quantum, classical and intermediate I: a model on the Poincaré sphere , 1997 .

[7]  B. Coecke,et al.  Classical Physical Entities with a Quantum Description , 1997 .

[8]  B. Coecke.  Generalization of the proof on the existence of hidden measurements to experiments with an infinite set of outcomes , 1995 .

[9]  Diederik Aerts,et al.  Quantum structures, separated physical entities and probability , 1994 .

[10]  Diederik Aerts,et al.  Quantum, classical and intermediate: An illustrative example , 1994 .

[11]  Diederik Aerts,et al.  A physical example of quantum fuzzy sets, and the classical limit. , 1993 .

[12]  How do we have to Change Quantum Mechanics in Order to Describe Separated Systems , 1984 .

[13]  S. Aerts,et al.  Conditional probabilities with a quantal and a kolmogorovian limit , 1996 .

[14]  Tobias J. Hagge,et al.  Physics , 1929, Nature.

[15]  David B. Malament.  Quantum Probability--Quantum Logic. Itamar Pitowsky , 1992 .

[16]  Diederik Aerts,et al.  A mechanistic classical laboratory situation violating the Bell inequalities with 2-2 , 1991 .

[17]  Diederik Aerts.  The description of separated systems and quantum mechanics and a possible explanation for the probab , 1988 .

[18]  Diederik Aerts,et al.  Quantum, classical and intermediate II: the vanishing vector space structure , 1997 .

[19]  Franco Selleri,et al.  Quantum Paradoxes and Physical Reality , 1989 .

[20]  J. Neumann.  Mathematical Foundations of Quantum Mechanics , 1955 .

[21]  B. Coecke.  A hidden measurement representation for quantum entities described by finite-dimensional complex Hilbert spaces , 1995 .

[22]  B. Coecke.  Superposition states through correlations of the second kind , 1996 .

[23]  Albert Einstein,et al.  Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? , 1935 .

[24]  Gérard G. Emch,et al.  Mathematical and conceptual foundations of 20th-century physics , 1984 .

[25]  A Representation for Compound Quantum Systems as Individual Entities: Hard Acts of Creation and Hidden Correlations , 1998, quant-ph/0105093.

[26]  Diederik Aerts,et al.  Quantum, classical and intermediate: a measurement model , 1994 .

[27]  Dirk Aerts,et al.  A possible explanation for the probabilities of quantum mechanics , 1986 .

[28]  P. Dirac.  Principles of Quantum Mechanics , 1982 .

[29]  Luigi Accardi,et al.  The Probabilistic Roots of the Quantum Mechanical Paradoxes , 1984 .

[30]  Diederik Aerts.  Quantum structures: An attempt to explain the origin of their appearance in nature , 1995 .