Abstract In their paper Unsharp Quantum Reality, Paul Busch and Gregg Jaeger explain the conception of unsharp reality in terms of Positive Operator Valued (POV) measures, potentiality, and single-case probabilities. The present paper discusses their conception from a philosophical point of view, focusing on the ontological interpretation of POV measures employed in it and on its relation to Peter Mittelstaedt’s work on the semantics and ontology of quantum mechanics. Busch and Jaeger extend Mittelstaedt’s approach by adding a realistic interpretation of unsharp quantum properties to it. Their account of unsharp quantum reality generalizes Heisenberg’s potentiality interpretation of quantum states. In order to explain the transition from potential to actual quantum properties, they suggest a Ghirardi-Rimini-Weber (GRW) collapse theory. Their approach comes close to recent work on quantum propensities. However, the question remains what unsharp quantum reality means when no measurement takes place, as for example claimed in the quark model of the subatomic constitution of matter.
Abstract In their paper Unsharp Quantum Reality, Paul Busch and Gregg Jaeger explain the conception of unsharp reality in terms of Positive Operator Valued (POV) measures, potentiality, and single-case probabilities. The present paper discusses their conception from a philosophical point of view, focusing on the ontological interpretation of POV measures employed in it and on its relation to Peter Mittelstaedt’s work on the semantics and ontology of quantum mechanics. Busch and Jaeger extend Mittelstaedt’s approach by adding a realistic interpretation of unsharp quantum properties to it. Their account of unsharp quantum reality generalizes Heisenberg’s potentiality interpretation of quantum states. In order to explain the transition from potential to actual quantum properties, they suggest a Ghirardi-Rimini-Weber (GRW) collapse theory. Their approach comes close to recent work on quantum propensities. However, the question remains what unsharp quantum reality means when no measurement takes place, as for example claimed in the quark model of the subatomic constitution of matter.
Paul Busch has emphasized on various occasions the importance for physics of going beyond a merely instrumentalist view of quantum mechanics. Even if we cannot be sure that any particular realist interpretation describes the world as it actually is, the investigation of possible realist interpretations helps us to develop new physical ideas and better intuitions about the nature of physical objects at the micro level. In this spirit, Paul Busch himself pioneered the concept of “unsharp quantum reality”, according to which there is an objective non-classical indeterminacy—a lack of sharpness—in the properties of individual quantum systems. We concur with Busch’s motivation for investigating realist interpretations of quantum mechanics and with his willingness to move away from classical intuitions. In this article we try to take some further steps on this road. In particular, we pay attention to a number of prima facie implausible and counter-intuitive aspects of realist interpretations of unitary quantum mechanics. We shall argue that from a realist viewpoint, quantum contextuality naturally leads to “perspectivalism” with respect to properties of spatially extended quantum systems, and that this perspectivalism is important for making relativistic covariance possible.
The Einstein-Podolsky-Rosen (EPR) reality criterion is generalized to fit with the notion of positive-operator-valued observables occurring in quantum optics, stochastic quantum mechanics, and other fields of quantum physics. The resulting concept of unsharp reality for quantum systems is illustrated within stochastic spin space where it leads to a notion of unsharp spin property. Finally we investigate the possibility of joint spin measurements and give a brief discussion of the EPR-Bell argument for unsharp spin properties.
We elaborate on a new interpretation of quantum mechanics which we introduced recently.The main hypothesis of this new interpretation is that quantum particles are entities interacting with matter conceptually, which means that pieces of matter function as interfaces for the conceptual content carried by the quantum particles.We explain how our interpretation was inspired by our earlier analysis of non-locality as non-spatiality and a specific interpretation of quantum potentiality, which we illustrate by means of the example of two interconnected vessels of water.We show by means of this example that philosophical realism is not in contradiction with the recent findings with respect to Leggett's inequalities and their violations.We explain our recent work on using the quantum formalism to model human concepts and their combinations and how this has given rise to the foundational ideas of our new quantum interpretation.We analyze the equivalence of meaning in the realm of human concepts and coherence in the realm of quantum particles, and how the duality of abstract and concrete leads naturally to a Heisenberg uncertainty relation.We illustrate the role played by interference and entanglement and show how the new interpretation explains the problems related to identity and individuality in quantum mechanics.We put forward a possible scenario for the emergence of the reality of macroscopic objects.
In order to claim that one has experimentally tested whether a noncontextual ontological model could underlie certain measurement statistics in quantum theory, it is necessary to have a notion of noncontextuality that applies to unsharp measurements, i.e., those that can only be represented by positive operator-valued measures rather than projection-valued measures. This is because any realistic measurement necessarily has some nonvanishing amount of noise and therefore never achieves the ideal of sharpness. Assuming a generalized notion of noncontextuality that applies to arbitrary experimental procedures, it is shown that the outcome of a measurement depends deterministically on the ontic state of the system being measured if and only if it is associated with a projector. Hence for every unsharp measurement, its outcome necessarily has an indeterministic dependence on the ontic state. We defend this proposal against alternatives. In particular, we demonstrate why considerations parallel to Fine's theorem do not challenge this conclusion.
One of the most puzzling facts about quantum mechanics is that although quantum theory offers a very accurate framework encompassing phenomena going from chemistry to high energy physics, it does not provide us with clear indications favoring some world view in the relativistic domain. Consequently, many physicists have held an instrumentalist point of view. Even though in non-relativistic physics already exists a realistic interpretation of quantum mechanics due to Heisenberg, who considers quantum states as states of disposition (the real tendency interpretation), the efforts for extending this interpretation to the relativistic domain were found wanting. The basic problem is the dependence of the states on the frame within which collapse takes place. We show here that a suitable use of the causal structure of the devices involved in the measurement process allows us to introduce a covariant notion for the collapse of quantum states and to preserve the tendency interpretation in relativistic quantum mechanics. However, we shall see that this extended interpretation requires the introduction of a relational concept of reality.
This tome is a formal presentation of the unsharp observable approach to quantum mechanics using the positive operator valued (POV) concept of an observable. It is intended for philosophers and mathematicians as well as physicists. This is a very formalistic book. There are, however, portions that should be read by all experimentalists performing quantum mechanical studies as well as graduate students completing their first graduate year quantum mechanics course. If we interpret quantum mechanics as making statistical predictions on the results of states prepared in identical fashions, we will often find that the observed probabilities are nearly, but not exactly, the expected 1 or 0 for measurements that are expected to always give the same result. Hence, rather than demanding sharp measures with probabilities of exactly 1 or 0, quantum mechanics allows a reasonable interpretation of unsharp results of nearly 1 or nearly 0. As the authors point out in chapter II, POV measures and the associated unsharp measures are not essential for an interpretation of quantum mechanical results. However, more sharp variables, and hence a larger Hilbert space, will be needed than are required by the unsharp approach. Also, the theoretical interpretation will often not be as straightforward with only sharp observables. As I have previously stated, all graduate students, both those of a theoretical and those of an experimental bent, should read parts of this book (after they have completed a normal introduction using sharp variables). They should at least read the first chapter which explains the unsharp variable measure concept as well as giving some examples, one of which is the Stern - Gerlach experiment. In chapter VII, the last chapter, the Stern - Gerlach experiment photon polarization and other quantum optical experiments and wave-particle duality experiments for photons are examined in detail using the POV formalism. This would also be an excellent chapter for all graduate students to read. Some sections may send them back to some of the intermediate chapters, hopefully to peruse in greater detail. The intermediate chapters contain the formal development of the POV formalism and compare it to the normal method. There is also a brief introduction to measurement theory using unsharp observables. As the authors state, this is not intended to be a complete solution to the problem of measurement theory. The next two chapters deal with uncertainty and phase space formalism as considered by the unsharp observables. Philosophers of physics and mathematicians will find this an excellent introduction to the POV formalism and the distinction between sharp and unsharp measurements. Many texts will gloss over both the philosophical and mathematical consequences inherent in the full statistical formalism of quantum mechanics. This monograph is not, by the authors' admission, a full treatment of quantum measurement theory. Also, although in the introduction the authors discuss the importance of applying quantum mechanics to individual objects, this book mainly considers the interpretations as statistical measures. There is little attempt to deal with the quantum mechanical interpretations of the behaviour of a single particle. That is, questions about measurements on a single particle or the interpretation of the wavefunction for a single particle are not fully covered. The authors claim that the POV approach is also the best for individual systems, but do little in applications. The major example given is in the last chapter where they consider interference measurements for single photons. They might have referenced more of the current alternative approaches to measurement theory of single particle wavefunctions. The readers of this journal will be disappointed, but not surprised, that the covariant nature of observables is restricted almost entirely to the Galilei group. The only Poincare group material is the example of photon localization in the last chapter. This is a reflection of the great difficulty of applying the special or the general theories of relativity to the Hilbert space formalism.