A Theory of Quantum Preparation and the Corresponding Advantage of the Relative-Collapse Interpretation of Quantum Mechanics as Compared to the Conventional One
Analyzing two standard preparators, the Stern-Gerlach and the hole-in-the-screen ones, it is demonstrated that four entities are the basic ingredients of the theory: the composite-system preparator-plus-object state (coming about as a result of a suitable interaction between the subsystems), a suitable preparator observable, one of its characteristic projectors called the triggering event, and, finally, the conditional object state corresponding to the occurrence of the triggering event. The concepts of a conditional state and of retrospective apparent ideal occurrence are discussed in the conventional interpretation of quantum mechanics. In the general theory of a preparator in this interpretation first-kind and second-kind preparators are distinguished. They are described by the same entities in the same way, but in terms of different physical mechanisms. In this article the relative-collapse interpretation is extended to encompass also preparators (besides measuring apparatuses). In this interpretation also the mechanisms become the same and one has only one kind of preparators.
Analyzing two standard preparators, the Stern-Gerlach and the hole-in-the-screen ones, it is demonstrated that four entities are the basic ingredients of the theory: the composite-system preparator-plus-object state (coming about as a result of a suitable interaction between the subsystems), a suitable preparator observable, one of its characteristic projectors called the triggering event, and, finally, the conditional object state corresponding to the occurrence of the triggering event. The concepts of a conditional state and of retrospective apparent ideal occurrence are discussed in the conventional interpretation of quantum mechanics. In the general theory of a preparator in this interpretation first-kind and second-kind preparators are distinguished. They are described by the same entities in the same way, but in terms of different physical mechanisms. In this article the relative-collapse interpretation is extended to encompass also preparators (besides measuring apparatuses). In this interpretation also the mechanisms become the same and one has only one kind of preparators.
Based on an analysis of two conventional preparators, the Stern-Gerlach and the hole-in-the-screen ones, it is argued that four entities can be taken as the basic ingredients of a rather general theory of a quantum preparator. These are the composite-system (object plus preparator) state coming about as a result of a suitable interaction between the subsystems, a suitable preparator projector called the triggering event, the conditional quantum state (density operator) of the quantum object coming about as a consequence of the occurrence of the triggering event on the preparator, and, finally, a unitary evolution operator of the object subsystem acting after preparation. The concepts of a general conditional state and of retrospective apparent ideal occurrence (which appears in the theory) are discussed in considerable detail. Ideal occurrence and the selective Lüders formula, which are made use of, are reviewed. Dynamical and geometrical preparators are distinguished in the general theory. They are described by the same entities in the same way, but in terms of different physical mechanisms from the point of view of standard interpretation with collapse.
The preparation procedure, an undefined notion in quantum theory, has not had the relevance that it deserves in the interpretation of quantum mechanical formalism.Here we utilize the concepts of identical and similar preparation procedures to show the conceptual differences between the statistical and the conventional interpretation of quantum formalism.Although the statistical understanding, and its final logical consequence, hidden variables theories (this connexion being explained in the text), have a great intuitive appeal due to its fewer ontological difficulties, both recent experimental results and theoretical developments seem to support an epistemic alternative closer to the conventional one.Nevertheless, we must not rule out the possibility that new theorems or new explanatory principles may modify the reigning supremacy of this interpretation. 1.-Introduction.Although the conventional interpretation of the quantum mechanical formalism (CIQM), very close to the Copenhagen interpretation, is still dominant (is used in almost all textbooks), there are physical situations that ask for an interpretation of the quantum mechanical formalism (QMF) in terms of the Statistical Interpretation of Quantum Mechanics (SIQM) or even for hidden variables theories (HVT).The SIQM and HVT are different research programs, but they are closely related, as we will see further below.To introduce properly the distinctions between the three previous acronyms we will ask an old and apparently simple question.Is the wave function associated to an individual system or to a statistical ensemble?A first tentative answer could be formulated as follows.QMF introduces probabilities, and probabilities are related to statistical ensembles.Otherwise, the same concept of probability would lose its meaning.In QM, if it is said that you would get some concrete result with 0,63 probability it means that if the experiment is carried out 100 times, that concrete result would appear approximately 63 times.Hence, the obvious answer will be that the wave function should be related with statistical ensembles.However, despite its intuitiveness this idea does not capture completely what we want to express.The real problem to analyze could be best introduced with the following example.Imagine that we prepare identically two radioactive atoms with half-life of 30 minutes.By preparation we understand all those theoretical methods and physical procedures necessary to fully characterize the state of the system.It is, thus, a macroscopic reproducible act that lefts the system, without destroying it, in a concrete state after the procedure.In quantum theory, this preparation is represented by a vector state (or a density matrix).Identically in this context will mean identity of procedures, that is that the experimenter has repeated all previous operations, so that there is no difference whatsoever between them.Note, however, that identical preparations are not necessarily followed by identical results, so there is
A detailed theory of quantum premeasurement dynamics is presented in which a unitary composite-system operator that contains the relevant object-measuring-instrument interaction brings about the final premeasurement state. It does not include collapse, and it does not consider the environment. It is assumed that a discrete degenerate or non-degenerate observable is measured. Premeasurement is defined by the calibration condition, which requires that every initially statistically sharp value of the measured observable has to be detected with statistical certainty by the measuring instrument. The entire theory is derived as a logical consequence of this definition using the standard quantum formalism. The study has a comprehensive coverage, hence the article is actually a topical review. Connection is made with results of other authors, particularly with basic works on premeasurement. The article is a conceptual review, not a historical one. General exact premeasurement is defined in 7 equivalent ways. Nondemolition premeasurement, defined by requiring preservation of any sharp value of the measured observable, is characterized in 10 equivalent ways. Overmeasurement, i. e., a process in which the observable is measured on account of being a function of a finer observable that is actually measured, is discussed. Disentangled premeasurement, in which, by definition, to each result corresponds only one pointer-observable state in the final composite-system state, is investigated. Ideal premeasurement, a special case of both nondemolition premeasurement and disentangled premeasurement, is defined, and its most important properties are discussed. Finally, disentangled and entangled premeasurements, in conjunction with nondemolition or demolition premeasurements, are used for classification of all premeasurements.
This paper continues the discussion of the thermal interpretation of quantum physics. While Part II and Part III of this series of papers explained and justified the reasons for the departure from tradition, the present Part IV summarizes the main features and adds intuitive explanations and new technical developments. It is shown how the spectral features of quantum systems and an approximate classical dynamics arise under appropriate conditions. Evidence is given for how, in the thermal interpretation, the measurement of a qubit by a pointer q-expectation may result in a binary detection event with probabilities given by the diagonal entries of the reduced density matrix of the prepared qubit. Differences in the conventions about measurement errors in the thermal interpretation and in traditional interpretations are discussed in detail. Several standard experiments, the double slit, Stern--Gerlach, and particle decay are described from the perspective of the thermal interpretation.
The conventional postulate for the probabilistic interpretation of quantum mechanics is asymmetric in preparation and measurement, making retrodiction reliant on inference by use of Bayes' theorem. Here, a more fundamental symmetric postulate is presented, from which both predictive and retrodictive probabilities emerge immediately, even where measurement devices more general than those usually considered are involved. It is shown that the new postulate is perfectly consistent with the conventional postulate.
In this article we discuss the problem of finding an interpretation of quantum mechanics which provides an objective account of physical reality. In the first place we discuss the problem of interpretation and analyze the importance of such an objective account in physics. In this context we present the problems which arise when interpreting the quantum wave function within the orthodox formulation of quantum mechanics. In connection to this critic, we expose the concept of 'entity' as an epistemological obstruction. In the second part of this paper we discuss the relation between actuality and potentiality in classical and quantum physics, and continue to present the concept of 'ontological potentiality' which is distinguished from the generic Aristotelian notion of potentiality in terms of 'becoming actual'. In this paper our main aim is to provide an objective interpretation of quantum mechanics which allows us to discuss the meaning of physical reality according to the theory. For this specific propose we present the concept of 'faculty' in place of the concept of 'entity'. Within our theory of faculties, we continue to discuss and interpret two paradigmatic experiments of quantum mechanics such as the double-slit and Schrodinger's cat.