Interpretation of quantum theory in a cosmological perspective

Eur. Phys. J. Plus (2024) 139:628 https://doi.org/10.1140/epjp/s13360-024-05351-4 Regular Article Interpretation of quantum theory in a cosmological perspective G. M. Prosperi2,1,a , M. Baldicchi1,2 1 Dipartimento Di Fisica dell’Università Di Milano, Milan, Italy 2 I.N.F.N., Sezione Di Milano, Milan, Italy Received: 18 November 2023 / Accepted: 9 June 2024 © The Author(s) 2024 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 CDM model with   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 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. 1 Introduction In classical physics, the state and the evolution of a system is described in terms of a set of quantities having always well-defined values and changing continuously in time. On the contrary, in quantum physics it is not possible to ascribe to a quantity definite value independently of an actual observation. This last circumstance is an obvious consequence of the fact that the usual probability definition depends on the state vector in a quadratic way, while the evolution of it obeys a linear equation. However, in order we can talk of an observation, the result must be stated in any case in definite terms. For this reason, Bohr [1] maintained that ordinary intuitive models are not possible for the microscopic objects to which quantum theory (QT) applies. On the contrary, in an experiment on them, the setup and the results should be expressed in classical terms; classical language being the language of our experience. An obvious immediate objection that can be made to Bohr’s point of view is that at a fundamental level, even the experimental apparatuses should obey QT rules, and so no statement even about them could be made independently of a further observation. To overcome this difficulty, von Neumann proposed a theory of measurement, in which even the apparatus is actually treated according QT [2]. Let us denote a certain object by I and an apparatus to observe the quantity A I corresponding to a self-adjoint operator  I by II. To be such an apparatus, II must be a system that reacts in a different way according the eigenstate of ÂI in which I is, if this is supposed to be a defined eigenstate. Let be ψ1 , ψ2 , . . . ψr , . . . the eigenvectors of ÂI , α1 , α2 , . . . αr , . . . the corresponding eigenvalues, 0 , 1 , . . . r , . . . the eigenvectors the quantity MII , or the set of the compatible quantities (e.g. the charges of a system of counters), relative to II which is modified by the interaction with I and μ0, μ1 , . . . μr . . . the corresponding eigenvalues. Then, if we further assume II initially in the state 0 , as result of the interaction, we must have and, if we consider I in the more general state ψ   ψs 0 → ψs s s cs ψs , ψ0 →  cs ψs s . (1.1) (1.2) s Consequently, the probability to observe the value αs when QT is applied to the system I, is identical to the probability to observe μs for MII when QT is applied even to II. Naturally, however, if we apply QT even toII, we must refer it to a third system III acting a e-mail: (corresponding author) 0123456789().: V,-vol 123 628 Page 2 of 18 Eur. Phys. J. Plus (2024) 139:628 as apparatus for the observation of MII on II. In this way, a chain of apparatuses is created, every one observing the preceding one, which extends to the nervous system of the human or conscious observer. For von Neumann, the important thing is that to apply QT to I and describe classically II+III is equivalent to apply QT to I + II and describe classicallyIII. That is, in a sense, the world is split in two parts, one described according to QT, regarded as the object, and the other regarded as the observer. The latter must include all conscious beings and has to be described classically. The border between the two can be shifted arbitrarily, but in last analysis what decides what happened is the conscious act of an "abstract ego". Note that, due to the entanglement which is established between the states of the nervous systems of two conscious observers looking to the same apparatus, von Neumann’s interpretation is intersubjective and not simply subjective. However, it implies also that the conscious act of a single being has effect on what all other conscious beings perceive, whatever are their distance and time. Among other considerations and independently of any philosophical attitude on the mind-brain problem, that brings also to obvious paradoxes like the well-known one of the Schrodinger cat. There are also difficulties with the possibility itself to realize in any given specific case a relation like Eq. (1.1), the interaction between I and II being not at our choice. Obviously, contrary to the usual assumption, the class of the actual observables should be much smaller than that of the self-adjoint operators. Finally, contrary to a common implicit attitude in any application of QT, no specific attention is given by von Neumann to the fact that the apparatuses should be macroscopic bodies made by a large number of components. For all such reasons the von Neumann proposal is not usually considered satisfactory. Many other attempts have been made from various points of view to make the theory consistent and an enormous literature has been produced, but no satisfactory solution has been given in our opinion. For a sample of the debates still going on in 1971, one can see reference [3], for a rather complete reference of the attempts before 1983 and a reproduction of a large set of select papers see reference [4] and for contributions after 1983 and a comparison with critical experiments see reference [5]. Concerning the last observation on the von Neumann treatment, what prevents in the usual text book axiomatic to treat a large body classically even at a macroscopic level is the possibility of oc (...truncated)