If we take the state function of quantum mechanics to describe belief states, arguments by Stairs and Friedman-Putnam show that the projection postulate may be justified as a kind of minimal change. But if the state function takes on a physical interpretation, it provides no more than what I call a fortuitous approximation of physical measurement processes, that is, an unsystematic form of approximation which should not be taken to correspond to some one univocal "measurement process" in nature. This fact (...) suggests that the projection postulate does not provide a proper locus for interpretive investigation. Readers will also find section 3's analysis of fortuitous approximations of independent interest and presented without the perils of quantum mechanics. (shrink)

Theological engagement with quantum physics has, to this day, been dominated by the Copenhagen interpretation. However, philosophers and physicists working in the “quantum foundations” field have largely abandoned the Copenhagen view on account of what is widely seen as its troublesome antirealism. Other metaphysical approaches have come to the fore instead, which often take a strongly realist flavor, such as de Broglie-Bohm, or Everett's “Many-Worlds” interpretation. In the spirit of recent quantum foundations work, this article introduces a collection of studies (...) aimed at taking quantum theology “beyond Copenhagen.” The present article advocates a commitment to “quantum fundamentalism,” which could resolve some of the enduring ontological problems faced by existing theological work with quantum mechanics, especially in discussions of quantum special divine action. Taking quantum fundamentalism literally would mean a departure from the Copenhagen interpretation, and the article suggests the need for a new research program to lay the groundwork in the natural theology of quantum foundations. (shrink)

Scientific realism is typically associated with metaphysics. One current incarnation of such an association concerns the requirement of a metaphysical characterization of the entities one is being a realist about. This is sometimes called “Chakravartty’s Challenge”, and codifies the claim that without a metaphysical characterization, one does not have a clear picture of the realistic commitments one is engaged with. The required connection between metaphysics and science naturally raises the question of whether such a demand is appropriately fulfilled, and how (...) metaphysics engages with science in order to produce what is called “scientific metaphysics”. Here, we map some of the options available in the literature, generating a conceptual spectrum according to how each view approximates science and metaphysics. This is done with the purpose of enlightening the current debate on the possibility of epistemic warrant that science could grant to such a metaphysics, and how different positions differently address the thorny issue concerning such a warrant. (shrink)

A scientific theory offers models for the phenomena in its domain; these models involve theoretical quantities, and a model's structure is the set of relations it imposes on these quantities. A fundamental demand in scientific practice is for those quantities to be clearly and feasibly related to measurement. This demand for empirical grounding can be articulated by displaying the theory-dependent criteria for a procedure to count as a measurement and for identifying the quantity it measures.

Previous work has shown that the problem of measurement in quantum mechanics is not correctly seen as one of understanding some allegedly univocal process of measurement in nature which corresponds to the projection postulate. The present paper introduces a new perspective by showing that how we are to understand the nature of the change of quantum mechanical state on measurement depends very sensitively on the interpretation of the state function, and by showing how attention to this dependence can greatly sharpen (...) the problems and relations between them. In particular, the problems take a form resembling their traditional formulation only on an inexact value interpretation, according to which the state function attributes inexact values of quantities to systems. On other interpretations we can apply (with various drawbacks) the subensemble idea, according to which a discontinuous change of quantum mechanical description results on measurement simply because we need a new state function to describe a new object. (shrink)

The standard axiomatization of quantum mechanics (QM) is not fully explicit about the role of the time-parameter. Especially, the time reference within the probability algorithm (the Born Rule, BR) is unclear. From a probability principle P1 and a second principle P2 affording a most natural way to make BR precise, a logical conflict with the standard expression for the completeness of QM can be derived. Rejecting P1 is implausible. Rejecting P2 leads to unphysical results and to a conflict with a (...) generalization of P2, a principle P3. All three principles are shown to be without alternative. It is thus shown that the standard expression of QM completeness must be revised. An absolutely explicit form of the axioms is provided, including a precise form of the projection postulate. An appropriate expression for QM completeness, reflecting the restrictions of the Gleason and Kochen-Specker theorems is proposed. (shrink)

The aim of this paper is to give a systematic account of the so-called “measurement problem” in the frame of the standard interpretation of quantum mechanics. It is argued that there is not one but five distinct formulations of this problem. Each of them depends on what is assumed to be a “satisfactory” description of the measurement process in the frame of the standard interpretation. Moreover, the paper points out that each of these formulations refers not to a unique problem, (...) but to a set of sub-problems. (shrink)

Customary discussions of quantum measurements are unrealistic, in the sense that they do not reflect what happens in most actual measurements even under ideal circumstances. Even theories of measurement which discard the projection postulate tend to retain two unrealistic assumptions of the von Neumann theory: that a measurement consists of a single physical interaction, and that the topic of every measurement is information wholly contained in the quantum state of the object of measurement. I suggest that these unrealistic assumptions originate (...) from an overly literal interpretation of the operator formalism of quantum mechanics. I also suggest, following Park, that some issues can be clarified by distinguishing the sense of the term ''''measurement'''' occurring in the quantum-mechanical operator formalism, and the sense of ''''measurement'''' that refers to actual processes of gaining information about the physical world. (shrink)

I defend the projection postulate against two of Margenau's criticisms. One involves two types of nonideal measurements, measurements that disturb and measurements that annihilate. Such measurements cannot be characterized using the original version of the projection postulate. This is one of the most interesting and powerful objections to the projection postulate since most realistic measurements are nonideal, in Margenau's sense. I show that a straightforward generalization of the projection postulate is capable of handling the more realistic kinds of measurements considered (...) by Margenau. His other objection involves the EPR (Einstein-Podolsky-Rosen) situation. He suggests that there is a significant potential for violations of the no-superluminalsignals requirement of the special theory of relativity, if projections occur in this situation and others like it. He also suggests that what is paradoxical about this situation disappears if the projection postulate is rejected. I show that it is not possible to use measurements on pairs of spatially-separated systems whose states are entangled to transmit information superluminally, and generalize this result to include nonideal measurements. I also show that EPR's dilemma does not really depend on the projection postulate. (shrink)

Although there is a complete consensus among working physicists with respect to the practical and operational meanings of quantum states, and also a rather loosely formulated general philosophic view called the Copenhagen interpretation, a great deal of confusion and divergence of opinions exist as to the details of the measurement process and its effects upon quantum states. This paper reviews the current expositions of the measurement problem, limiting itself for lack of space primarily to the writings of physicists; it calls (...) attention to inconsistencies and proposes resolutions. Except for a summary of the properties of statistical matrices which are needed in Part II, the first part is non-mathematical and deals largely with two kinds of probability, reducible and irreducible probabilities, which need to be distinguished for a proper understanding of the measurement act. (shrink)

This is the second, mathematically more detailed part of a paper consisting of two articles, the first having appeared in the immediately preceding issue of this Journal. It shows that a measurement converts a pure case into a mixture with reducible probabilities. The measurement as such permits no inference whatever as to the state of the physical system subjected to measurement after the measurement has been performed. But because the probabilities after the act are classical and therefore reducible, it is (...) often possible to adjust them so that Von Neumann's projection postulate is true. Among the more specific features dealt with in Part II is the occurrence of negative joint probabilities for the measurement of non-commuting operators in certain (not all!) quantum states. The general conclusions reached are stated at the end of the article. (shrink)

This paper is concerned with the description of the process of measurement within the context of a quantum theory of the physical world. It is noted that quantum mechanics permits a quasi-classical description of those macroscopic phenomena in terms of which the observer forms his perceptions. Thus, the process of measurement in quantum mechanics can be understood on the quasi-classical level by transcribing from the strictly classical observables of Newtonian physics to their quasi-classical counterparts the known rules for the measurement (...) of the former. The remaining physical problem is the delineation of the circumstances in which the correlation of a peculiarly quantum mechanical observable A with a classically measurable observable B can result in a significant measurement of A. This is undertaken within the context of quantum theory. The resulting clarification of the process of measurement has important implications relative to the philosophic interpretation of quantum mechanics. (shrink)

Much of the recent discussion of problematic aspects of quantum-mechanical measurement centers around that feature of quantum theory which is called "the projection postulate." This is roughly the claim that a change of a certain sort occurs in the state of a physical system when a measurement is made on the system. In this paper an argument for the projection postulate due to von Neumann is considered. Attention is focused on trying to provide an understanding of the notion of "the (...) state of a physical system" which is compatible with the argument von Neumann offers. An attempt is made to formulate the argument in terms of an objectivistic interpretation of probability concepts. It is seen that such an interpretation does not provide a suitable way of understanding the argument. An attempt is made to illustrate the source of this failure in terms of a non-quantum-mechanical example. (shrink)

The purpose of this paper is to solve a serious problem for the projection postulate involving the time-energy uncertainty relation. The problem was recently raised by Teller, who believes that the problem is insoluble and, consequently, that the projection postulate should no longer be regarded as a serious focus for interpretive investigation.

The only observational quantity which quantum mechanics needs to address islocation. The typical primitive observation on a microsystem (e.g., photon) isdetection at alocation (e.g., by a photomultiplier “looking at” a grating). To analyze an experiment, (a) form a conceptual ensemble of replicas of it, (b) assign a wave function (in “position representation”) to its initial condition, (c) evolve the wave function by the Schrödinger equation (known, once and for all, as a function of the system's composition), (d) compute the probability (...) for particle detection at various times and places. The initial wave function is chosen on the basis of experience with such treatments. Key experiments are thus treated: (i) time-of-flight, (ii) Stern-Gerlach, (iii) Franck-Hertz, (iv) photon recoil, (v) photoionization. Quantum states, dynamical variables, and measurements, and the usual postulates about them, are superfluous. The explicit treatments are nonrelativistic; the existence of relativistic generalizations is left open. (shrink)

In a recent paper, Prugovečki offered a theory of simultaneous measurements based upon an axiomatic description of the measurement act which excludes certain illustrations of simultaneous measurement previously discussed by the present writers. In this article, the fundamental conceptions of state preparation, state determination, and measurement which underlie our research are compared to Prugovečki's interpretations of the analogous constructs in his theory of measurement.

Recent work by Wan and McLean has shown that all quantum measurements may be reduced to local position measurements. Using an array of particle detectors as the measuring apparatus we show how a model employing superselection rules and unitary evolution leads to a single detector triggering in each act of measurement. We also present an explicit model of particle detection as a unitary ionization process producing a single ion in the detector, subsequent amplification of which to the visible can be (...) described adequately in classical terms. (shrink)

A reproducibility principle is formulated and adopted as the guiding criterion for the acceptance of an experimental procedure as a simultaneous measurement of several observables. It is pointed out that this criterion can be applied to classical as well as quantum physics, and that it incorporates compatible as well as incompatible observables. The concept of fuzzy probability measure is presented as a possible mathematical tool for the description of statistical processes involving measurements of incompatible observables.

The central problem in the quantum theory of measurement, how to describe the process of state reduction in terms of the quantum mechanical formalism, is solved on the basis of the relativity of quantal states, which implies that once the apparatus is detected in a well-defined state, the object state must reduce to a corresponding one. This is a process termed by Schrödinger disentanglement. Here, it is essential to observe that Renninger's negative result does constitute an actual measurement process. From (...) this point of view, Heisenberg's interpretation of his microscope experiment and the Einstein-Podolsky-Rosen arguments are reinvestigated. Satisfactory discussions are given to various experimental situations, such as the Stern-Gerlach-type experiment, successive measurements, macroscopic measurements, and Schrödinger's cat. Finally it is proposed to regard a state vector in quantum mechanics as an irreducible physical construct, in Margenau's sense, that is not further analyzable both mathematically and conceptually. (shrink)