This paper introduces an overview of a new perspective to understanding the notion of scientific theory\n"interpretation". The main thesis proposes that interpretation should consist of a certain kind of articulation between the theory to be interpreted and those theories providing a mathematical and conceptual framework as well as empirical meaning to their\nterms. In the conclusion, and in relation to the historical example of Maxwell's electrodynamics\nre-interpretation, the authors point at some of the conditions and interpretation should fulfill to be "adequate". Lastly, the authors provide a perspective on\nhow these ideas could be applied to analyze Quantum Mechanics interpretation problems.
This paper introduces an overview of a new perspective to understanding the notion of scientific theory\n"interpretation". The main thesis proposes that interpretation should consist of a certain kind of articulation between the theory to be interpreted and those theories providing a mathematical and conceptual framework as well as empirical meaning to their\nterms. In the conclusion, and in relation to the historical example of Maxwell's electrodynamics\nre-interpretation, the authors point at some of the conditions and interpretation should fulfill to be "adequate". Lastly, the authors provide a perspective on\nhow these ideas could be applied to analyze Quantum Mechanics interpretation problems.
The philosophy of quantum theory Resumen: La teoria quàntica representa una de les fites més importants de la història de la ciència del segle XX, tant pel que fa a les seues implicacions teòriques i tecnològiques com pel que fa als problemes conceptuals que planteja la seua interpretació. Aquest article constitueix una revisió de les propostes interpretatives del formalisme quàntic d’ençà que la teoria es va axiomatitzar a les acaballes de la dècada dels anys 20 del segle passat. Aquestes propostes incideixen en problemes filosòfics com la no-localitat, l’indeterminisme, la probabilitat o el realisme científic, per a cadascun dels quals s’ofereix una resposta temptativa a partir de la interpretació del formalisme corresponent. Abstract: Quantum theory represents one of the most important milestones in the history of science in the 20th century, both in terms of its theoretical and technological implications and in terms of the conceptual problems posed by its interpretation. This article constitutes a review of the interpretive proposals of the quantum formalism since the theory was axiomatized at the end of the decade of the 20s of the last century. These proposals rise philosophical problems such as non-locality, indeterminism, probability or scientific realism, for each of which a tentative answer is offered based on the interpretation of the corresponding formalism. Palabras clave: Teoria quàntica, problema de la mesura, variables ocultes, molts mons, col.lapse objectiu. Keywords: Quantum theory, measurement problem, hidden variables, many worlds, objective collapse.
This paper presents a bundle definition for 'scientific understanding' through which the empirically equivalent interpretations of quantum mechanics can be evaluated with respect to the understanding they generate. This definition of understanding is based on a sufficient and necessary criterion, as well as a bundle of conditions ― where a theory can be called better understandable than others, whenever it fulfills a higher number of bundle criteria. Thereby the definition of understanding is based on the one hand on the objective number of criteria a theory fulfills, as well as, on the other hand, on the individual's preference of bundle criteria. Applying the definition onto three interpretations of quantum mechanics, the interpretation of David Bohm appears as most understandable, followed by the interpretation of Tim Maudlin and the Kopenhagen interpretation.
Quantum mechanics is basically a mathematical recipe on how to construct physical models. Historically its origin and main domain of application has been in the microscopic regime, although it strictly seen constitutes a general mathematical framework not limited to this regime. Since it is a statistical theory, the meaning and role of probabilities in it need to be defined and understood in order to gain an understanding of the predictions and validity of quantum mechanics. The interpretational problems of quantum mechanics are also connected with the interpretation of the concept of probability. In this thesis the use of probability theory as extended logic, in particular in the way it was presented by E. T. Jaynes, will be central. With this interpretation of probabilities they become a subjective notion, always dependent on one's state of knowledge or the context in which they are assigned, which has consequences on how things are to be viewed, understood and tackled in quantum mechanics. For instance, the statistical operator or density operator, is usually defined in terms of probabilities and therefore also needs to be updated when the probabilities are updated by acquisition of additional data. Furthermore, it is a context dependent notion, meaning, e.g., that two observers will in general assign different statistical operators to the same phenomenon, which is demonstrated in the papers of the thesis. It is also presented an alternative and conceptually clear approach to the problematic notion of "probabilities of probabilities", which is related to such things as probability distributions on statistical operators. In connection to this, we consider concrete numerical applications of Bayesian quantum state assignment methods to a three-level quantum system, where prior knowledge and various kinds of measurement data are encoded into a statistical operator, which can then be used for deriving probabilities of other measurements. The thesis also offers examples of an alternative quantum state assignment technique, using maximum entropy methods, which in some cases are compared with the Bayesian quantum state assignment methods. Finally, the interesting and important problem whether the statistical operator, or more generally quantum mechanics, gives a complete description of "objective physical reality" is considered. A related concern is here the possibility of finding a "local hidden-variable theory" underlying the quantum mechanical description. There have been attempts to prove that such a theory cannot be constructed, where the most well-known impossibility proof claiming to show this was given by J. S. Bell. In connection to this, the thesis presents an idea for an interpretation or alternative approach to quantum mechanics based on the concept of space-time.
Abstract The purpose of this book is to present an interpretation of quantum mechanics. But what are we talking about when we speak of “quantum mechanics?” Are we talking about a single theory or about many related theories? And what do we mean by “interpretation” here? In this chapter, I will address these questions in an introductory way. Of course, I do not intend to take part in the extensive discussions about what a scientific theory is, what is meant by interpreting a theory, in what situation we encounter equivalent theories, and many other questions related to or derived from these. My aim here is to present some preliminary ideas in a way that I hope will be sufficient to avoid misunderstandings in the following chapters. But, above all, I will state my position as to why, after so many years and so much literature on the subject, the interpretation of quantum mechanics deserves further discussion.
Quantum Mechanics, almost 80 years after its arrival, is a well established and experimentally not falsified theory. It has predicted and explained a whole series of natural phenomena of a very delicate nature. But its interpretation has not gained universal acceptance. Many scientists have considered the conceptual framework of quantum theory to be unsatisfactory. The very foundations of Quantum Mechanics is a matter that needs to be resolved in order to achieve and gain a deep physical understanding of the underlying physical procedures that constitute our world.
The de Broglie–Bohm interpretation (Bohmian mechanics, hidden-variables theory, causal interpretation
or pilot-wave theory) is one of the interpretations of quantum mechanics which opposes
to the claim of standard interpretation on the completeness of description of the state of quantummechanical
system, that description in Bohmian mechanics is completed by defining positions of
the particles of the system i.e. hidden variables and their dynamics. These facts are the basis of motivation
for the introduction of a new theory that can describe dubious axiomatic requirements of
standard interpretation. The presented theory is deterministic and explicitly nonlocal. Originators
of Bohmian mechanics were L. de Broglie (1927.) and D. Bohm (1952.) who presented mathematically
more general and conceptual elaborate formulation. Along with the historical overview,
a note is given about the main properties of the theory, such as the issue of nonlocality and hidden
variables. The aim of this paper is to present and explain the main ideas and properties of the
theory as well as to give a systematic overview of present and historical mathematical construction
of the theory and most of all to discuss implications of de Broglie–Bohm theory on the ontology of
quantum-mechanical picture, showcasing examples of the equivalency of the description of a free
particle as a propagation of the plane wave in space or as the ensemble of the trajectories and of
the spreading of the Gaussian wave packet. The main example of the obvious conceptual clashing
of the interpretations is presented: the double-slit experiment, with a detailed examination of the
Bohmian mechanics’ predictions using presented formalism on the two double-slit experiment.
The graphs of trajectories for given examples are obtained.