In this paper we attempt to analyze the concept of quantum probability within quantum computation and quantum computational logic. While the subjectivist interpretation of quantum probability explains it as a reliable predictive tool for an agent in order to compute measurement outcomes, the objectivist interpretation understands quantum probability as providing reliable information of a real state of affairs. After discussing these different viewpoints we propose a particular objectivist interpretation grounded on the idea that the Born rule provides information about an (...) intensive realm of reality. We then turn our attention to the way in which the subjectivist interpretation of probability is presently applied within both quantum computation and quantum computational logic. Taking as a standpoint our proposed intensive account of quantum probability we discuss the possibilities and advantages it might open for the modeling and development of both quantum computation and quantum computational logic. (shrink)

Experimental evidence of the last decades has made the status of ``collapses of the wave function'' even more shaky than it already was on conceptual grounds: interference effects turn out to be detectable even when collapses are typically expected to occur. Non-collapse interpretations should consequently be taken seriously. In this paper we argue that such interpretations suggest a perspectivalism according to which quantum objects are not characterized by monadic properties, but by relations to other systems. Accordingly, physical systems may possess (...) different properties with respect to different ``reference systems''. We discuss some of the relevant arguments, and argue that perspectivalism both evades recent arguments that single-world interpretations are inconsistent and eliminates the need for a privileged rest frame in the relativistic case. (shrink)

Three recent arguments seek to show that the universal applicability of unitary quantum theory is inconsistent with the assumption that a well-conducted measurement always has a definite physical outcome. In this paper I restate and analyze these arguments. The import of the first two is diminished by their dependence on assumptions about the outcomes of counterfactual measurements. But the third argument establishes its intended conclusion. Even if every well-conducted quantum measurement we ever make will have a definite physical outcome, this (...) argument should make us reconsider the objectivity of that outcome. (shrink)

In classical physics, probabilistic or statistical knowledge has been always related to ignorance or inaccurate subjective knowledge about an actual state of affairs. This idea has been extended to quantum mechanics through a completely incoherent interpretation of the Fermi-Dirac and Bose-Einstein statistics in terms of "strange" quantum particles. This interpretation, naturalized through a widespread "way of speaking" in the physics community, contradicts Born's physical account of Ψ as a "probability wave" which provides statistical information about outcomes that, in fact, cannot (...) be interpreted in terms of 'ignorance about an actual state of affairs'. In the present paper we discuss how the metaphysics of actuality has played an essential role in limiting the possibilities of understating things differently. We propose instead a metaphysical scheme in terms of powers with definite potentia which allows us to consider quantum probability in a new light, namely, as providing objective knowledge about a potential state of affairs. (shrink)

A bold and all-embracing exploration of the nature and progress of knowledge from one of today's great thinkers. Throughout history, mankind has struggled to understand life's mysteries, from the mundane to the seemingly miraculous. In this important new book, David Deutsch, an award-winning pioneer in the field of quantum computation, argues that explanations have a fundamental place in the universe. They have unlimited scope and power to cause change, and the quest to improve them is the basic regulating principle not (...) only of science but of all successful human endeavor. This stream of ever improving explanations has infinite reach, according to Deutsch: we are subject only to the laws of physics, and they impose no upper boundary to what we can eventually understand, control, and achieve. In his previous book, The Fabric of Reality, Deutsch describe the four deepest strands of existing knowledge-the theories of evolution, quantum physics, knowledge, and computation-arguing jointly they reveal a unified fabric of reality. In this new book, he applies that worldview to a wide range of issues and unsolved problems, from creativity and free will to the origin and future of the human species. Filled with startling new conclusions about human choice, optimism, scientific explanation, and the evolution of culture, The Beginning of Infinity is a groundbreaking book that will become a classic of its kind. (shrink)

In this paper we attempt to analyze the physical and philosophical meaning of quantum contextuality. We will argue that there exists a general confusion within the foundational literature arising from the improper “scrambling” of two different meanings of quantum contextuality. While the first one, introduced by Bohr, is related to an epistemic interpretation of contextuality which stresses the incompatibility of measurement situations described in classical terms; the second meaning of contextuality is related to a purely formal understanding of contextuality as (...) exposed by the Kochen–Specker theorem which focuses instead on the constraints of the orthodox quantum formalism in order to interpret projection operators as preexistent or actual properties. We will show how these two notions have been scrambled together creating an “omelette of contextuality” which has been fully widespread through a popularized “epistemic explanation” of the KS theorem according to which: The measurement outcome of the observableAwhen measured together withBor together withCwill necessarily differ in case\, and\. We will show why this statement is not only improperly scrambling epistemic and formal perspectives, but is also physically and philosophically meaningless. Finally, we analyze the consequences of such widespread epistemic reading of KS theorem as related to statistical statements of measurement outcomes. (shrink)

Orthodox quantum mechanics includes the principle that an observable of a system possesses a well-defined value if and only if the presence of that value in the system is certain to be confirmed on measurement. Modal interpretations reject the controversial ‘only if’ half of this principle to secure definite outcomes for quantum measurements that leave the apparatus entangled with the object it has measured. However, using a result that turns on the construction of a Kochen–Specker contradiction, I argue that modal (...) interpretations cannot deliver a metaphysically tenable conception of properties in quantum mechanics unless they also abandon the less controversial ‘if’ half of the orthodox principle. (shrink)

We clarify Bohr’s interpretation of quantum mechanics by demonstrating the central role played by his thesis that quantum theory is a rational generalization of classical mechanics. This thesis is essential for an adequate understanding of his insistence on the indispensability of classical concepts, his account of how the quantum formalism gets its meaning, and his belief that hidden variable interpretations are impossible.

In this paper we present a new categorical approach which attempts to provide an original understanding of QM. Our logos categorical approach attempts to consider the main features of the quantum formalism as the standpoint to develop a conceptual representation that explains what the theory is really talking about —rather than as problems that need to be bypassed in order to allow a restoration of a classical “common sense” understanding of what there is. In particular, we discuss a solution to (...) Kochen-Specker contextuality through the generalization of the meaning of global valuation. This idea has been already addressed by the so called topos approach to QM —originally proposed by Isham, Butterfiled and D ̈oring— in terms of sieve-valued valuations. The logos approach to QM presents a different solution in terms of the notion of intensive valuation. This new solution stresses an ontological reading of the quantum formalism and the need to restore an objective conceptual representation and understanding of quantum physical reality. (shrink)

The Austrian physicist Wolfgang Pauli (1900-1958) was often called the conscience of physics. He was famous for his sharp and critical mind which made him a central figure among the founders of quantum physics. He also was an outstanding philosopher, especially interested in finding a new conception of reality and of causality. A careful study of the original sources of the past culminated in his study of Kepler and of medieval symbolism, a concept that played a central role in his (...) discussion with Carl Jung on what they called the psycho-physical problem. Pauli considered the sharp distinctions between knowledge and faith and between spirit and matter as dangerous. He thought they should complement each other in our comprehension of reality. Professor Laurikainen here for the first time describes Pauli's ideas in detail. His book is based on the large and as yet unpublished correspondence between Pauli and M. Fierz. Its careful analysis adds depth and clarity to the few publications by Pauli on philosophical problems and explains why Pauli grasped the meaning of atomic theory more deeply than even Niels Bohr himself. The book should interest both philosophers and physicists and should encourage further studies on Pauli the humanist and his contribution to our understanding of reality. (shrink)

In this paper we intend to discuss the importance of providing a physical representation of quantum superpositions which goes beyond the mere reference to mathematical structures and measurement outcomes. This proposal goes in the opposite direction to the project present in orthodox contemporary philosophy of physics which attempts to “bridge the gap” between the quantum formalism and common sense “classical reality”—precluding, right from the start, the possibility of interpreting quantum superpositions through non-classical notions. We will argue that in order to (...) restate the problem of interpretation of quantum mechanics in truly ontological terms we require a radical revision of the problems and definitions addressed within the orthodox literature. On the one hand, we will discuss the need of providing a formal redefinition of superpositions which captures explicitly their contextual character. On the other hand, we will attempt to replace the focus on the measurement problem, which concentrates on the justification of measurement outcomes from “weird” superposed states, and introduce the superposition problem which focuses instead on the conceptual representation of superpositions themselves. In this respect, after presenting three necessary conditions for objective physical representation, we will provide arguments which show why the classical representation of physics faces severe difficulties to solve the superposition problem. Finally, we will also argue that, if we are willing to abandon the presupposition according to which ‘Actuality = Reality’, then there is plenty of room to construct a conceptual representation for quantum superpositions. (shrink)

In this paper we address a deeply interesting debate that took place at the end of the last millennia between David Mermin, Adan Cabello and Michiel Seevinck, regarding the meaning of relationalism within quantum theory. In a series of papers, Mermin proposed an interpretation in which quantum correlations were considered as elements of physical reality. Unfortunately, the very young relational proposal by Mermin was too soon tackled by specially suited no-go theorems designed by Cabello and Seevinck. In this work we (...) attempt to reconsider Mermin's program from the viewpoint of the Logos Categorical Approach to QM. Following Mermin's original proposal, we will provide a redefinition of quantum relation which not only can be understood as a preexistent element of physical reality but is also capable to escape Cabello’s and Seevinck's no-go-theorems. In order to show explicitly that our notion of ontological quantum relation is safe from no-go theorems we will derive a non-contextuality theorem. We end the paper with a discussion regarding the physical meaning of quantum relationalism. (shrink)

In this paper we we will argue against the orthodox definition of quantum entanglement which has been implicitly grounded on several widespread presuppositions which have no relation whatsoever to the formalism of QM. We will show how these presuppositions have been introduced through a naive interpretation of the quantum mathematical structure which assumes dogmatically that the theory talks about "small particles" represented by pure states which suddenly "collapse" when a measurement takes place. In the second part of this paper we (...) will present a non-collapse approach to QM which makes no use whatsoever of particle metaphysics, escaping the need to make reference to space-time separability or the restriction to certain predictions of definite valued binary properties. Our paper ends up concluding the essential need to redefine the notion of quantum entanglement, at least in the cases of: i) non-collapse interpretations of QM; or, ii) any other interpretation which abandons the idea that QM makes reference to "small particles". (shrink)

In this paper we attempt to discuss what has Kochen-Specker theorem to say about physical invariance and quantum individuality. In particular, we will discuss the impossibility of making reference to objective physical properties within the orthodox formalism of quantum mechanics. Through an analysis of the meaning of physical invariance and quantum contextuality we will derive a Corollary to KS theorem that proves that a vector in Hilbert space cannot be interpreted coherently as an object possessing physical properties. As a consequence, (...) the notion of quantum object can be only defined in terms of nomological properties. We conclude the paper by analyzing the consequences of this Corollary to KS theorem for the ongoing debate about quantum individuality. (shrink)

In this paper we discuss the representational realist stance as a pluralist ontic approach to inter-theoretic relationships. Our stance stresses the fact that physical theories require the necessary consideration of a conceptual level of discourse which determines and configures the specific field of phenomena discussed by each particular theory. We will criticize the orthodox line of research which has grounded the analysis about QM in two metaphysical presuppositions —accepted in the present as dogmas that all interpretations must follow. We will (...) also examine how the orthodox project of "bridging the gap" between the quantum and the classical domains has constrained the possibilities of research, producing only a limited set of interpretational problems which only focus in the justification of "classical reality" and exclude the possibility of analyzing the possibilities of non-classical conceptual representations of QM. The representational realist stance introduces two new problems, namely, the superposition problem and the contextuality problem, which consider explicitly the conceptual representation of orthodox QM beyond the mere reference to mathematical structures and measurement outcomes. In the final part of the paper, we revisit, from a representational realist perspective, the quantum to classical limit and the orthodox claim that this inter-theoretic relation can be explained through the principle of decoherence. (shrink)

Pekka Lahti is a prominent exponent of the renaissance of foundational studies in quantum mechanics that has taken place during the last few decades. Among other things, he and coworkers have drawn renewed attention to, and have analyzed with fresh mathematical rigor, the threat of inconsistency at the basis of quantum theory: ordinary measurement interactions, described within the mathematical formalism by Schrödinger-type equations of motion, seem to be unable to lead to the occurrence of definite measurement outcomes, whereas the same (...) formalism is interpreted in terms of probabilities of precisely such definite outcomes. Of course, it is essential here to be explicit about how definite measurement results (or definite properties in general) should be represented in the formalism. To this end Lahti et al. have introduced their objectification requirement that says that a system can be taken to possess a definite property if it is certain (in the sense of probability 1) that this property will be found upon measurement. As they have gone on to demonstrate, this requirement entails that in general definite outcomes cannot arise in unitary measuring processes.In this paper we investigate whether it is possible to escape from this deadlock. As we shall argue, there is a way out in which the objectification requirement is fully maintained. The key idea is to adapt the notion of objectivity itself, by introducing relational or perspectival properties. It seems that such a “relational perspective” offers prospects of overcoming some of the long-standing problems in the interpretation of quantum mechanics. (shrink)

In this paper we provide a general account of the causal models which attempt to provide a solution to the famous measurement problem of Quantum Mechanics. We will argue that—leaving aside instrumentalism which restricts the physical meaning of QM to the algorithmic prediction of measurement outcomes—the many interpretations which can be found in the literature can be distinguished through the way they model the measurement process, either in terms of the efficient cause or in terms of the final cause. We (...) will discuss and analyze why both, ‘final cause’ and ‘efficient cause’ models, face severe difficulties to solve the measurement problem. In contradistinction to these schemes we will present a new model based on the immanent cause which, we will argue, provides an intuitive understanding of the measurement process in QM. (shrink)

This ground-breaking book brings together researchers from a wide range of disciplines to discuss the control and coordination of processes involved in perceptually guided actions. The research area of motor control has become an increasingly multidisciplinary undertaking. Understanding the acquisition and performance of voluntary movements in biological and artificial systems requires the integration of knowledge from a variety of disciplines from neurophysiology to biomechanics.