Abstract: The standard formulation of Quantum Mechanics has raised from its beginning animated discussions about the interpretation of the counterintuitive properties of mental objects (wave functions or Schrödinger waves) introduced to represent the properties of the physical objects.Two questions have since then been formulated to which a universally accepted answer is still lacking. The first one (Bohr, von Neumann) concerns the ontological nature of physical reality (the existence of classical objects) and the role of the observer (wave packet collapse) in assessing it. The second one is the non local character of quantum physical quantities (Einstein Podolski Rosen [EPR] long distance correlation of particles). An alternative formulation of Quantum Mechanics, originally proposed in 1932 by Eugene Wigner, taken up by Richard Feynman in 1987, and reelaborated by myself in the years from 1998 to 2003, is possible. The mental objects of standard Quantum Mechanics (Schrödinger waves) no longer appear in this new formulation and are replaced by new ones (Wigner functions) which do not show any more the puzzling properties which worried Einstein. My conclusion from the preceding discussion is that different explanations of a given set of experimental data may be derived according to the different nature of the mental objects introduced to represent the properties of the physical objects involved. The confusion between these two kind of objects may be, however, very misleading. I will finally discuss two examples of this conclusion from Biology
Abstract: The standard formulation of Quantum Mechanics has raised from its beginning animated discussions about the interpretation of the counterintuitive properties of mental objects (wave functions or Schrödinger waves) introduced to represent the properties of the physical objects.Two questions have since then been formulated to which a universally accepted answer is still lacking. The first one (Bohr, von Neumann) concerns the ontological nature of physical reality (the existence of classical objects) and the role of the observer (wave packet collapse) in assessing it. The second one is the non local character of quantum physical quantities (Einstein Podolski Rosen [EPR] long distance correlation of particles). An alternative formulation of Quantum Mechanics, originally proposed in 1932 by Eugene Wigner, taken up by Richard Feynman in 1987, and reelaborated by myself in the years from 1998 to 2003, is possible. The mental objects of standard Quantum Mechanics (Schrödinger waves) no longer appear in this new formulation and are replaced by new ones (Wigner functions) which do not show any more the puzzling properties which worried Einstein. My conclusion from the preceding discussion is that different explanations of a given set of experimental data may be derived according to the different nature of the mental objects introduced to represent the properties of the physical objects involved. The confusion between these two kind of objects may be, however, very misleading. I will finally discuss two examples of this conclusion from Biology
[I] think I can safely say that nobody understands quantum mechanics. Richard Feynman, The Character of Physical Law Quantum mechanics [is] that mysterious, confusing discipline, which none of us really understands but which we know how to use. It works perfectly, as far as we can tell, in describing physical reality, but it is a ‘counter-intuitive discipline’… Murray Gell-Mann, Questions for the Future [The quantum] postulate implies a renunciation as regards the causal space-time co-ordination of atomic processes. Niels Bohr, Atomic Theory and the Description of Nature It should be emphasized, however, that the probability function does not in itself represent a course of events in the course of time. It represents a tendency for events and our knowledge of events. The probability function can be connected with reality only if one essential condition is fulfilled: if a new measurement is made to determine a certain property of the system. [T]he idea of an objective real world whose smallest parts exist objectively in the same sense as stones or trees exist, independently of whether or not we observe them…is impossible … Werner Heisenberg, Physics and Philosophy [In] quantum theory it is the principle of causality , or more accurately that of determinism , which must be dropped and replaced by something else.… We now have a new form of the law of causality.… It is as follows: if in a certain process the initial conditions are determined as accurately as the uncertainty relations permit, then the probabilities of all possible subsequent states are governed by exact laws. Max Born, The Restless Universe
In spite of the recent extraordinary progresses of experimental techniques it does not seem that, after more than seventy years from the birth of quantum mechanics, a unanimous consensus has been reached in the physicist's community on how to understand the "strange" properties of quantons, the wavelike/particlelike objects of the quantum world. In the first paragraph I will briefly recall some results on the problem of decoherence in large quantum systems, which at the same time may be viewed as an attempt of providing a "realistic" physical interpretation of the standard mathematical formulation of the theory. In the following ones I will present a derivation from first principles of the Wigner representation of quantum mechanics in phase space which eliminates altogether from the theory the Schrödinger waves and their questionable properties. This approach leads to the conclusion that the wave/particle duality has nothing to do with "probability waves", but is simply the manifestation of two complementary aspects (continuity vs. discontinuity) of an intrinsically nonlocal physical entity (the quantum field) which objectively exists in ordinary three dimensional space.
1.1 Waves and particles in quantum mechanics In spite of the fact that the extraordinary progress of experimental techniques make us able to manipulate at will systems made of any small and well defined number of atoms, electrons and photons making therefore possible the actual performance of the gedankenexperimente that Einstein and Bohr had imagined to support their opposite views on the physical properties of the wavelike/particlelike objects (quantons) of the quantum world it does not seem that, after more than eighty years, a unanimous consensus has been reached in the physicist's community on how to understand their strange properties. Unfortunately, we cannot know whether Feynman would still insist in maintaining his famous sentence It is fair to say that nobody understands quantum mechanics. We can only discuss if, almost thirty years after his death, some progress towards this goal has been made. I believe that this is the case. I will show in fact that, by following the suggestions of Feynman himself, some clarification of the old puzzles can be achieved. This chapter therefore by no means is intended to provide an impartial review of the present status of the question but is focused on the exposure of the results of more than twenty years of research of my group in Rome, which in my opinion provide a possible way of connecting together at the same time the random nature of the events at the atomic level of reality and the completeness of their probabilistic representation by the principles of Quantum Mechanics.
The wave function gives probabilities, but is it a real physical quantity, as in the ontic interpretation of quantum mechanics, or just a measure of human belief about a physical system, as in an epistemic interpretation? These questions are introduced by treating Schrödinger’s cat and Wigner’s friend. An important question is whether quantum mechanics applies to macroscopic objects, for example, cats. SQUID experiments have been performed that see quantum interference in very large objects, whereas with most macroscopic objects quantum interference disappears because of decoherence. Various views of the meaning of quantum mechanics are discussed: the Copenhagen interpretation, continuous spontaneous localization, Everett’s many-worlds interpretation, Bohm’s hidden-variable model, and quantum Bayesianism. The latter holds that the wave function represents one’s best belief about the state of a quantum system, rather than an actual physical property. This leads to discussions of recent theories and experiments explicitly designed to test wave function reality.
Some aspects of the interpretation of microscopic physics in terms of quantum theory are discussed. It is first emphasized that quantum theory is formulated in a Cartesian coordinate system; in other coordinates the result obtained with the help of the Hamiltonian formalism and commutation relations between ''canonically conjugated'' coordinate and momentum operators leads to a wrong version of quantum mechanics. In this connection the Feynman integral formalism is also discussed. In this formalism the measure is not well defined, and there is no idea how to distinguish between the true version of quantum mechanics and an incorrect one. In this respect, the Feynman approach consists of a mnemonic rule to generate perturbation series from an undefined zero-order term. The origin of time in the quantum framework is then analyzed in detail and illustrated by the example of atomic collisions. It is shown that the time-dependent Schr ¨ odinger equation for the closed three-body (two nuclei + electron) system has no physical meaning because in the high-impact energy limit it transforms into an equation with two independent time-like variables; time naturally appears in the stationary Schr ¨ odinger equation as a result of extraction of a classical subsystem (two nuclei) from a closed three-body system. Finally, following the well-known Einstein-Rosen-Podolsky experiment and Bell's inequality, we reiterate that the wave function must be interpreted as an actual field of information, in a form as elementary as the usual material particles and electromagnetic fields. In fact, experimental measurements transfer this quantum information field into the classical world, which is directly discernable. In my conclusion, the relation between physical reality and its mathematical formulation is discussed. 2012 Physics Essays Publication. (DOI: 10.4006/0836-1398-25.1.27) R ´
The aim of such paper is to explain in detail the foundations of quantum cognition and to evidence the manner in which our pioneering experiments on quantum interference in humans should be correctly interpreted in the framework of a correct quantum mechanical elaboration. Often, studies on quantum cognition are elaborated from some authors evidencing that presently we have empirical evidence that the application of quantum rules gives better results respect to classical ones. Consequently, such studies are delineated as empirical tentative. It is not true. Quantum cognition is a scientific realization structured about robust quantum foundations and this is the reason because it gives such important results. Consequently, we discuss the evidence to correctly explain the foundations of this emerging discipline. In order to reach this objective we analyze the fundamental role of the abstract entity that is called quantum mechanical wave function. Soon after we describe the manner in which quantum operators must be entered in cognition studies by using the projectors that represent logic statements and thus relate directly our cognitive functions. We also discuss in detail the logical origins of quantum mechanics outlining that it does not represent a physical theory looking at the matter at microscopic level but a God Giano two faces looking simultaneously to material and to mental reality. We also discuss results establishing the nature of our consciousness and the unquestionable result that it obeys to the basic rules of quantum mechanics. We also give a further and pressing indication: in quantum cognition studies the quantum wave function must be intended as reconstructed experimentally a posteriori in our cognitive studies and cannot be confused with the standard examining elaboration that is used in usual textbooks of quantum mechanics. Also the question of the order effect is analyzed in detail using the important notion of reaction time of psychology. In substance, we give a total reformulation of the current quantum cognition studies evidencing that previous elaborations finalized to present the current status of this discipline as empirical tentative to characterize a quantum cognitive modelling result to be only approximate, incorrect and confusing prospects that damage the information about the robust structure of quantum cognition and therefore need to be rejected.