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arXiv:0904.3677

Quantum theory can be collectively verified

Arindam Mitra

Published Apr 23, 2009• 0 citations
arXivHTMLPDF

Abstract

No theory of physics has been collectively scientifically verified in an experiment so far. It is pointed out that probabilistic structure of quantum theory can be collectively scientifically verified in an experiment. It is also argued that experimentalist point of view quantum theory is a complete theory.
DOI
10.48550/arxiv.0904.3677

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Quantum theory (QT) provides statistical predictions for various physical phenomena. To verify these predictions a considerable amount of data has been accumulated in the 'measurements' performed on the ensembles of identically prepared physical systems or in the repeated 'measurements' on some trapped 'individual physical systems'. The outcomes of these measurements are, in general, some numerical time series registered by some macroscopic instruments. The various empirical probability distributions extracted from these time series were shown to be consistent with the probabilistic predictions of QT. More than 70 years ago the claim was made that QT provided the most complete description of 'individual' physical systems and outcomes of the measurements performed on 'individual' physical systems were obtained in an intrinsically random way. Spin polarization correlation experiments (SPCEs), performed to test the validity of Bell inequalities, clearly demonstrated the existence of strong long-range correlations and confirmed that the beams hitting far away detectors somehow preserve the memory of their common source which would be destroyed if the individual counts of far away detectors were purely random. Since the probabilities describe the random experiments and are not the attributes of the 'individual' physical systems, the claim that QT provides a complete description of 'individual' physical systems seems not only unjustified but also misleading and counter productive. In this paper, we point out that we even do not know whether QT is predictably complete because it has not been tested carefully enough. Namely, it was not proven that the time series of existing experimental data did not contain some stochastic fine structures that could have been averaged out by describing them in terms of the empirical probability distributions. In this paper, we advocate various statistical tests that could be used to search for such fine structures in the data and to answer the title question of this paper. In our opinion a proper understanding of the statistical character of QT and of its limitations is crucial in the domains such as quantum optics and quantum information.
In this paper we discuss the principles of two fundamental theories of physics: mechanics and quantum mechanics. First, we consider two philosophical positions of the German physicist Heinrich Hertz. He established one of the both in the introduction of his well known Principles of Mechanics. This view - Hertz's "picture" concept - which has a long tradition in philosophy, particularly with regard to physics and later to other empirical sciences, serves as the starting point of an interpretation of the relationship between real systems and theoretical structures of modern science using the concept of fuzziness. This "fuzzy view" on philosophy of science gives particularly an interpretation of Hertz's earlier lecture on The Constitution of matter. Second we consider some principles of quantum mechanics, particularly Werner Heisenberg's uncertainty relation of subatomic object's position and momentum, and Max Born's probabilistic interpretation of the quantum mechanical wave function. These principles are parts of the so-called Copenhagen interpretation of quantum mechanics. Third, we argue that the "fuzzy approach" is fruitful for a "fuzzy" interpretation of quantum mechanics because fuzziness fills the gap between systems and phenomena in reality and the scientific theory of quantum mechanics - as every other scientific theory.
Quantum theory has been criticized for not being deterministic and therefore not universal: it cannot completely describe a measurement aimed at verifying its predictions (although any given apparatus can be considered as a quantum system). We investigate the possible alternatives. Theories where the observed world is deterministic but the observer is not (whatever the reason for that) lead to Bell’s nonseparability theorem. If, on the other hand, the observer too is deterministic, the theory is not verifiable. It follows that quantum theory must be the logically preferred option. Its inability to completely describe the measurement process appears to be not a flaw of the theory but a logical necessity which is analogous to Gödel’s undecidability theorem.
A fundamental problem in understanding the nature of time is to explain its 'directionality'. The commonplace view is that this directionality is provided by the 'flow of time'. Unfortunately this concept of 'time flow', which seems to make perfect sense to us in our everyday lives, has resisted philosophical and scientific analysis so well that today it is widely regarded as having no place in the scientific account of the world. Instead, various alternative physical concepts of the directionality of time have been developed, principally the notions of the time reversibility of physical laws or theories, and of the time asymmetry of physical processes. It is frequently argued by philosophers of physics that the scientific account of the directionality of time must be framed entirely in terms of these physical notions. The thesis of the present work is that this conclusion has been reached far too hastily. It is argued that the concept of time flow is a legitimate physical concept, and furthermore, that time flow plays a real part in quantum theory. A number of conceptual investigations are necessary to support this argument. Firstly, it is necessary to give an analysis of what a physical theory of time flow might be like, and how it might be empirically established. This is given in Chapter One, which at the same time is an overview of the results of later chapters. It is found in Chapter One that the concept of physical time flow has an important connection with the concept of time reversibility, which makes it necessary to give an analysis of this notion. A detailed discussion of reversibility and time symmetry is given in Chapters Two to Five. Here it is demonstrated that the orthodox analysis of the reversibility of probabilistic theories is flawed. This conclusion allows it to be shown, in Chapter Six, that, contrary to current scientific belief, quantum theory is profoundly irreversible. This result, together with the argument of Chapter One, allows a strong prima facie case for an interpretation of quantum probabilities as involving time flow to be given. However, because of the traditional problems with the notion of time flow, for this interpretation to become respectable it needs to be demonstrated that it is possible to construct a formal model of a physical ontology in which time flow can be represented. This is undertaken in Chapter Seven. In Chapter Eight, various points about the role of probabilities in quantum theory are discussed. Finally, in Chapter Nine, the implications of relativity theory for the proposed theory of time flow are considered. It is found that relativity theory poses a serious problem for a physical theory of time flow, but the implications of relativity theory for the proposed interpretation of quantum probabilities is not clear because of deeper foundational problems with quantum theory.