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Istituto Lombardo - Accademia di Scienze e Lettere - Rendiconti di Scienze

INTERPRETAZIONE DELLA TEORIA QUANTISTICA, COSMOLOGIA E GRAVITAZIONE

Giovanni Maria Prosperi

Published Feb 12, 2025• 0 citations
Publisher

Abstract

On the line of a recent paper, the problem of interpretation of Quantum Theory (QT) is reconsidered in a cosmological perspective and of Bohr’s idea that the classical language is the language of our experience and QT acquires a meaning only with a reference to it. A classical or macroscopic level is distinguished and a quantum or microscopic one that is perceived only through the modifications that it induces in the first. The macroscopic state is specified by a classical energy-momentum tensor and conserved currents, which are supposed to have always well-defined values. The microscopic dynamics are expressed by the usual QT formalism. Fundamental idea: the usual probability rule of QT, based on an observables self-ajoint operators correspondence, is replaced with a distribution of probability directly for the macroscopic variables, defined in terms of the corresponding quantum operators and a quantum density operator. For the universe, a variance of the standard model with Ω=1 is assumed, one inflaton, a Goldstone type potential, initial time at t =−∞, expectation values of all fundamental fields vanishing for t → −∞. The scalar fluctuations in the cosmic microwave background can be correctly explained giving appropriate values to the potential parameters, but the absence of the tensor fluctuations remains not understood. This seems to suggest that gravity is a pure classical phenomenon, what could be consistently accommodated in our framework but it is inconsistent with the usual formalism.

DOI
10.4081/scienze.2024.869

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On the line of a recent paper, the problem of interpretation of Quantum Theory (QT) is reconsidered in a cosmological perspective and of Bohr’s idea that the classical language is the language of our experience and QT acquires a meaning only with a reference to it. A classical or macroscopic level is distinguished and a quantum or microscopic one that is perceived only through the modifications that it induces in the first. The macroscopic state is specified by a classical energy-momentum tensor and conserved currents, which are supposed to have always well-defined values. The microscopic dynamics are expressed by the usual QT formalism. Fundamental idea: the usual probability rule of QT, based on an observables self-ajoint operators correspondence, is replaced with a distribution of probability directly for the macroscopic variables, defined in terms of the corresponding quantum operators and a quantum density operator. For the universe, a variance of the standard model with Ω=1 is assumed, one inflaton, a Goldstone type potential, initial time at t =−∞, expectation values of all fundamental fields vanishing for t → −∞. The scalar fluctuations in the cosmic microwave background can be correctly explained giving appropriate values to the potential parameters, but the absence of the tensor fluctuations remains not understood. This seems to suggest that gravity is a pure classical phenomenon, what could be consistently accommodated in our framework but it is inconsistent with the usual formalism.
We reconsider the problem of the interpretation of the Quantum Theory (QT) in the perspective of the entire universe and of Bphr idea that the classical language is the language of our experience and QT acquires a meaning only with a reference to it. We distinguish a classical or macroscopic level, and a quantum or microscopic one that is perceived only through the modifications that it induces in the first. The macroscopic state of the universe is assumed to be specified by a set of variables, a classical energy momentum tensor and some conserved currents, which are supposed to have a well defined value across the entire space-time. To the energy-momentum tensor a classical metric is related by the Einstein equation. The quantum state and dynamics are expressed by the usual QT formalism in terms of a density operator and the ordinary quantum operators in Heisenberg picture. For the macroscopic variables a basic distribution of probability is postulated in terms of a density and the corresponding quantum operators, so in some way their evolution is driven by the underlying QT. Such postulate essentially replaces the usual elfadjoint operators correspondence. For the Universe we adopt a variance of the ΛCDM model with Omega=1, one single inflaton with an Higgs type potential, the initial time at t=minus infinite. The expectation values of all fundamental fields are supposed to vanish for time going to minus infinite. In the framework the scalar fluctuation in the Cosmic Microwave Background are correctly explained giving appropriate calue to the parameters in the potential. As in more conventional models the absence of the tensor fluctuations remains not understood, if even a quantum metric is introduced. This seems to suggest that Gravity is a pure classical phenomenon, what could be consistently accommodated in our formalism by an appropriate even if somewhat ad hoc assumption
Abstract We reconsider the problem of the interpretation of the quantum theory (QT) in the perspective of the entire universe and of the Bohr's idea that the classical language is the language of our experience and QT acquires a meaning only with a reference to it. We distinguish a classical or macroscopic state, and a quantum or microscopic one that is perceived only through the modifications that it induces in the first. The macroscopic state is specified by a set of variables, a classical energy–momentum tensor and conserved currents, which are supposed to have always a well-defined value. The microscopic state and dynamics are expressed by the usual QT formalism. For the macroscopic variables, a basic distribution of probability is postulated in terms of quantum operators and a statistical operator, what replace the usual probability rule of QT. For the universe, a variance of the ΛCDM model with Ω=1\Omega = 1Ω=1 Ω = 1 is assumed, one inflaton, a Goldstone type potential, initial time at t=−∞t = - \inftyt=−∞ t = - ∞ , expectation values of all fundamental fields vanishing for t→−∞t \to - \inftyt→−∞ t → - ∞ . The scalar fluctuations in the cosmic microwave background is correctly explained, but the absence of the tensor fluctuations remains not understood. This seems to suggest that gravity is a pure classical phenomenon what perhaps could be accommodated in our framework.
Quantum cosmology is the quantum theory of the entire universe. Although strange at first sight, it is appropriate because (1) our world appears to be fundamentally quantum, (2) the classical description of gravity breaks down at singularities it would give at the beginning of the universe, and (3) our universe has many properties that cannot be explained by a classical description of them. A quantum state of the universe should obey certain constraints, such as the Wheeler-DeWitt equations. One approach to interpreting such a state is {\it Sensible Quantum Mechanics} (SQM), in which nothing is probabilistic, except, in a certain frequency sense, conscious perceptions. Sets of these perceptions can be deterministically realized with measures given by expectation values of positive-operator-valued {\it awareness operators}. These may be defined even when the quantum state itself is not normalizable, though there still seem to be problems of divergences when one has an infinite amount of inflation, producing infinitely large spatial volumes with presumably infinite measures of perceptions. Ratios of the measures for sets of perceptions (if finite) can be interpreted as frequency-type probabilities for many actually existing sets rather than as propensities for potentialities to be actualized, so there is nothing indeterministic in a specific SQM. One can do a Bayesian analysis to test between different specific SQMs. One can also make statistical predictions of what one might perceive within a specific SQM by invoking the {\it Conditional Aesthemic Principle}: among the set of all conscious perceptions, our perceptions are likely to be typical.
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 unsatisfactory status of the interpretation of the wave function of the Universe in canonical quantum gravity is reviewed. The ``naive interpretation'' obtained by straightforwardly applying the standard interpretive rules to the canonical quantization of general relativity is manifestly unacceptable; the ``WKB interpretation'' has only a limited domain of applicability; and the ``conditional probability interpretation'' requires one to pick out a ``preferred time variable'' (or preferred class of such variables) from among the dynamical variables. Evidence against the possibility of using a dynamical variable to play the role of ``time'' in the conditional probability interpretation is provided by the fact (proven here) that in ordinary Schr\"odinger quantum mechanics for a system with a Hamiltonian bounded from below, no dynamical variable can correlate monotonically with the Schr\"odinger time parameter t, and thus the role of t in the interpretation of Schr\"odinger quantum mechanics cannot be replaced by that of a dynamical variable. We also argue that the interpretive problems of quantum gravity are not alleviated by the incorporation of observers into the theory. Faced with these difficulties, we seek a formulation of canonical quantum gravity in which an appropriate nondynamical time parameter is present. By analogy with a parametrized form of ordinary Schr\"odinger quantum mechanics, we make a proposal for such a formulation. A specific proposal considered in detail yields a theory which corresponds at the classical level to general relativity with an arbitrary, unspecified cosmological constant. In minisuperspace models, this proposal yields a quantum theory with satisfactory interpretive properties, although it is unlikely that this theory will admit sufficiently many observables for general spacetimes. Nevertheless, we feel that the approach suggested here is worthy of further investigation.
Introduction Although the mathematical structure of quantum mechanics was understood within a few years after it was invented, numerous quantum paradoxes still disturb ‘simple-minded’ physicists. Most of them, as ‘naïve realists’, would probably never take Bohr's own over-philosophical and over-complicated treatment of these paradoxes seriously if they realized the philosophical consequences of the Copenhagen interpretation. To make my meaning clearer, let me quote Bohr's answer to Professor Hoffding's question regarding the double-slit experiment [1]. Bohr was asked: ‘What can the electron be said to be in its travel from the point of entry to the point of detection?’ And he replied: ‘ To be ? To be ? What does it mean to be ?’ However, if one questions the existence of microscopic constituents of macroscopic bodies, then the next logical step would be to question the existence of the macroscopic bodies and even ourselves. Needless to say, very few (if any) of us, when making experiments or analyzing their results, address the question of what it means ‘to be’ every time. Even in the context of elementary particles, probably nobody doubts that the particles exist and somehow travel from the point of entry to the point of detection. Moreover, within the accuracy allowed by the uncertainty relation, these particles can be localized and described just as well as macroscopic ‘classical’ objects.