A number of issues related to measurement show that self-consistency is lacking in quantum mechanics as this theory has been generally understood. Each issue is presented as a point in this paper. Each point can be resolved by incorporating a cognitive component in quantum mechanics. Measurement in quantum mechanics involves the meaning of the physical circumstances of the experiment. This meaning is in part independent of what traditionally are considered purely physical considerations.
A number of issues related to measurement show that self-consistency is lacking in quantum mechanics as this theory has been generally understood. Each issue is presented as a point in this paper. Each point can be resolved by incorporating a cognitive component in quantum mechanics. Measurement in quantum mechanics involves the meaning of the physical circumstances of the experiment. This meaning is in part independent of what traditionally are considered purely physical considerations.
In most textbooks, measurement does not receive the full attention it deserves and sometimes is even not treated at all, apart a brief and cryptic mention of the “reduction of the wave packet.” However, in the last decades, the situation has profoundly changed and it is time to consider measurement a fundamental part of quantum mechanics, even, to a certain extent, an important generalization of the traditional theory (see also Chs. 14–15). This chapter consists of three major parts. In the first block (Secs. 9.1–9.4) we develop the main physical features of the measurement process: the heart of the argument is here represented by the aspects related to the interpretation. In the second part (Secs. 9.5–9.8) we discuss several special (and partly interdependent) topics of measurement: the heart here is represented by experimental aspects. In the third part (Secs. 9.9–9.12) we deal with the measurement process on a more formal plane, making use, in particular, of the generalization represented by the concepts of effect and positive operator valued measure (POVM). As we have said, the measurement problem is one of the most fundamental issues in the conceptual structure of quantum mechanics (as described in Sec. 9.1) and has a long history that will be examined in Sec. 9.2. In this context, the existence of apparently paradoxical quantum states comes about: the so-called Schrödinger cat states (see Sec. 9.3).
THE PROBLEM Within classical physics the relation between physical theory and ordinary experience was conceived in the following way: ordinary experience is something that can be described and understood in terms of physics. Such a description involves, apart from physical theory, certain approximations. But the conditons under which those approximations apply (they correspond to the initial conditions of, say, celestial mechanics), taken together with the theory, are supposed to be sufficient for giving a full account of ordinary experience. Consequently, classical theory of measurement (which, like any other theory of measurement, links together terms of ordinary experience and theoretical terms), is a piece of applied physics and all processes which happen during measurement can be analysed on the basis of the equations of motion only. When we enter quantum mechanics (QM), we are apparently presented with a completely different picture. For according to the current interpretation of elementary quantum mechanics, ordinary experience – and this now means classical physics – and physical theory (and this now means QM), belong to two completely different levels and it is impossible to give an account of the first in terms of the second. Any transition from the quantum level to the level of classical physics must be taken, not as a transition within QM from the general to the particular, but as an essentially new element which is incapable of further analysis.
We introduce a model which allows to represent the probabilities associated with an arbitrary measurement situation as it appears in different domains of science–from cognitive science to physics–and use it to explain the emergence of quantum probabilities (the Born rule) as uniform fluctuations on this measurement situation. The model exploits the geometry of simplexes to represent the states both of the system and the measuring apparatus, in a way that the measurement probabilities can be derived as the Lebesgue measure of suitably defined convex subregions of the simplex under consideration. Although the model we propose, which we call the uniform tension-reduction (UTR) model, is an abstract construct, it admits physical realizations. In this article we consider a very simple and evocative one, using a material point particle which is acted upon by special elastic membranes, which by breaking and collapsing are able to "release the tension" and produce the different possible outcomes. This easy to visualize mechanical realization allows one to gain considerable insight into the possible hidden structure of a measurement process, be it from a measurement associated with a situation in cognitive science or in physics, or in any other domain. We also show that the UTR-model can be further generalized into a model describing conditions of lack of knowledge generated by non-uniform fluctuations, which we call the general tension-reduction (GTR) model. In this more general framework, which is more suitable to describe typical experiments in cognitive science, we define and motivate a notion of universal measurement, describing the most general possible condition of lack of knowledge in a measurement, emphasizing that the uniform fluctuations characterizing quantum measurements can also be understood as an average over all possible forms of non-uniform fluctuations which can be actualized in a measurement context. This means that the Born rule of quantum mechanics can be understood as a first order approximation of a more general non-uniform theory, thus explaining part of the great success of quantum probability in the description of different domains of reality. And more specifically, also providing a possible explanation for the success of quantum cognition, a research field in cognitive science employing the quantum formalism as a modeling tool. This is the first part of a two-part article. In the second part (Aerts and Sassoli de Bianchi, 2014a), the proof of the equivalence between universal measurements and uniform measurements, and its significance for quantum theory as a first order approximation, is given and further analyzed.
Abstract Although much has been written about the measurement problem, there is still significant disagreement about what the problem really is and what a solution should look like. In this chapter I present a brief introduction to quantum mechanics and the measurement problem, and then I argue that the measurement problem should be understood in part a problem of epistemology: solving the problem requires telling a consistent story about how the reality underlying quantum mechanics could allow us to reliably come to know about that reality via the medium of our empirical evidence for quantum mechanics, and an interpretation of quantum mechanics which fails to achieve this is self-undermining.
In quantum mechanics, the measurement problem is commonly regarded as reason for deep concern. It seems that, either, the problem can be solved and there is hope for quantum mechanics, or the theory better be left behind in search of another one. We investigate the prospect of finding a solution to the measurement problem—within quantum mechanics, as well as in theoretical frameworks beyond it. As we do so, there emerges a perspective on doing physics drawing from considerations in the philosophy of language and in epistemology. Developing this perspective for further aspects in physics reveals: The notion of a system is similarly problematic. Eventually, the question arises whether these are problems of specific physical theories, or rather of specific stances towards physics. In this regard, we examine in particular the role and understanding of assumptions.
We introduce a model which allows to represent the probabilities associated with an arbitrary measurement situation as it appears in different domains of science–from cognitive science to physics–and use it to explain the emergence of quantum probabilities (the Born rule) as uniform fluctuations on this measurement situation. The model exploits the geometry of simplexes to represent the states both of the system and the measuring apparatus, in a way that the measurement probabilities can be derived as the Lebesgue measure of suitably defined convex subregions of the simplex under consideration. Although the model we propose, which we call the uniform tension-reduction (UTR) model, is an abstract construct, it admits physical realizations. In this article we consider a very simple and evocative one, using a material point particle which is acted upon by special elastic membranes, which by breaking and collapsing are able to “release the tension” and produce the different possible outcomes. This easy to visualize mechanical realization allows one to gain considerable insight into the possible hidden structure of a measurement process, be it from a measurement associated with a situation in cognitive science or in physics, or in any other domain. We also show that the UTR-model can be further generalized into a model describing conditions of lack of knowledge generated by non-uniform fluctuations, which we call the general tension-reduction (GTR) model. In this more general framework, which is more suitable to describe typical experiments in cognitive science, we define and motivate a notion of universal measurement, describing the most general possible condition of lack of knowledge in a measurement, emphasizing that the uniform fluctuations characterizing quantum measurements can also be understood as an average over all possible forms of non-uniform fluctuations which can be actualized in a measurement context. This means that the Born rule of quantum mechanics can be understood as a first order approximation of a more general non-uniform theory, thus explaining part of the great success of quantum probability in the description of different domains of reality. And more specifically, also providing a possible explanation for the success of quantum cognition, a research field in cognitive science employing the quantum formalism as a modeling tool. This is the first part of a two-part article. In the second part (Aerts and Sassoli de Bianchi, 2014a), the proof of the equivalence between universal measurements and uniform measurements, and its significance for quantum theory as a first order approximation, is given and further analyzed.