Usual interpretations of the quantum theory, beginning with Bohr's interpretation, consider that randomness in quanlum mechanics arises from (objeclive) restrictions to our capacity of making precise measurements of the corresponding state variables. I show that this assumption is problematic and leaves open important questions concerning the role and nature of quantum randomness. On the basis of a concept of state introduced elsewhere and on the basis of a distinction between the principles of separability and locality in quantum mechanics, I suggest in this paper a different sense in which quantum randomness is objective. In order to carry out the proposed task a distinction is made between two different types of objective randomness. Objective epistemic randomness arises from the limitations that the physical structure of the world imposes upon our possibilities of coming to know (measure) this structure. Objective non-epistemic randomness or systemic randomness is to be expressed in terms of a state description in a fundamental theory of physics. It is shown that the non-Boolean structure of properties of quantum theory, as this structure has been constructed and interpreted in Martínez 1991a, can be inlerpreled as an expression of the non-separability of the theory, Thus, the irreducibility of the transition probabilities that generate the non-Boolean structure of properties can be interpreted in this way as systemic randomness. In the case of quantum mechanics systemic randomness and non-separability are two sides of the same coin.
Usual interpretations of the quantum theory, beginning with Bohr's interpretation, consider that randomness in quanlum mechanics arises from (objeclive) restrictions to our capacity of making precise measurements of the corresponding state variables. I show that this assumption is problematic and leaves open important questions concerning the role and nature of quantum randomness. On the basis of a concept of state introduced elsewhere and on the basis of a distinction between the principles of separability and locality in quantum mechanics, I suggest in this paper a different sense in which quantum randomness is objective. In order to carry out the proposed task a distinction is made between two different types of objective randomness. Objective epistemic randomness arises from the limitations that the physical structure of the world imposes upon our possibilities of coming to know (measure) this structure. Objective non-epistemic randomness or systemic randomness is to be expressed in terms of a state description in a fundamental theory of physics. It is shown that the non-Boolean structure of properties of quantum theory, as this structure has been constructed and interpreted in Martínez 1991a, can be inlerpreled as an expression of the non-separability of the theory, Thus, the irreducibility of the transition probabilities that generate the non-Boolean structure of properties can be interpreted in this way as systemic randomness. In the case of quantum mechanics systemic randomness and non-separability are two sides of the same coin.
This paper deals with the notion of objective randomness in classical deterministic theories. After the introduction, section 2 establishes an important distinction between a strictly metaphysical thesis of determinism (as characterized in the Montague-Earman definition, for example), and the doctrine of determinism, which can be roughly characterized as a methodological set of principles. The doctrine of determinism is associated with the idea that probability assignments can only reflect our ignorance of facts, and it also grounds the (ontological) thesis of separability: A system or process can be characterized completely in terms of the properties that a system has when in a given state, independently of the properties of other systems, The key notions of "completeness" and "independence" are only briefly discussed, as they are examined more in depth elsewhere. Section three examines attempts to characterize a notion of objective randomness in ergodic theory. The characterization can be seen to be equivalent to the formulation of a notion of a "physically impossible process". One way of expressing this idea is grounded on the thesis of the "coarse graining" of our measuring instruments. This leads to the problem of distinguishing "objective" from "apparent" randomness. The problem seems to be intrinsic to any attempt of characterizing the required notion of physical impossibility (and thus of objective randomness) in terms of an ideal observer. The alternative of trying to characterize physical impossibility in terms of a theory of algorithms suffers from the difficulty that it is not clear what would be the required notion of (non-epistemic) computability. The "coarse graining" approach, as well as the alternative in terms of a theory of algorithms seem to share the usual confusion between a strictly metaphysical thesis of determinism and the (methodological) doctrine of determinism. In section four an alternative approach is suggested. It is noticed that a denial of the thesis of separability is compatible with a strict deterministic theory, and thus that at least some classical systems (the "statistical" ones) can be described in terms of non-separable states. We do not have to think that the impossibility of preparing a classical state is too only possible explanation for physical (objective) randomness in deterministic theories. This proposal is an elaboration of an idea of Blatt (1959), although Blatt was still trying to understand objective randomness within an ideal-observer framework.[S.M.]
The twentieth century was marked by two scientific revolutions. On the one hand, quantum mechanics questioned our understanding of nature and physics. On the other hand, came the realisation that information could be treated as a mathematical quantity. They together brought forward the age of information. A conceptual leap took place in the 1980's, that consisted in treating information in a quantum way as well. The idea that the intuitive notion of information could be governed by the counter-intuitive laws of quantum mechanics proved extremely fruitful, both from fundamental and applied points of view. The notion of randomness plays a central role in that respect. Indeed, the laws of quantum physics are probabilistic: that contrasts with thousands of years of physical theories that aimed to derive deterministic laws of nature. This, in turn, provides us with sources of random numbers, a crucial resource for information protocols. The fact that quantum theory only describes probabilistic behaviours was for some time regarded as a form of incompleteness. But nonlocality, in the sense of Bell, showed that this was not the case: the laws of quantum physics are inherently random, i.e., the randomness they imply cannot be traced back to a lack of knowledge. This observation has practical consequences: the outputs of a nonlocal physical process are necessarily unpredictable. Moreover, the random character of these outputs does not depend on the physical system, but only of its nonlocal character. For that reason, nonlocality-based randomness is certified in a device-independent manner. In this thesis, we quantify nonlocality-based randomness in various frameworks. In the first scenario, we quantify randomness without relying on the quantum formalism. We consider a nonlocal process and assume that it has a specific causal structure that is only due to how it evolves with time. We provide trade-offs between nonlocality and randomness for the various causal structures that we consider. Nonlocality-based randomness is usually defined in a theoretical framework. In the second scenario, we take a practical approach and ask how much randomness can be certified in a practical situation, where only partial information can be gained from an experiment. We describe a method to optimise how much randomness can be certified in such a situation. Trade-offs between nonlocality and randomness are usually studied in the bipartite case, as two agents is the minimal requirement to define nonlocality. In the third scenario, we quantify how much randomness can be certified for a tripartite process. Though nonlocality-based randomness is device-independent, the process from which randomness is certified is actually realised with a physical state. In the fourth scenario, we ask what physical requirements should be imposed on the physical state for maximal randomness to be certified, and more specifically, how entangled the underlying state should be. We show that maximal randomness can be certified from any level of entanglement. El siglo XX estuvo marcado por dos revoluciones científicas. Por un lado, la mecánica cuántica cuestionó nuestro entendimiento de la naturaleza y de la física. Por otro lado, quedó claro que la información podía ser tratada como un objeto matemático. Juntos, ambas revoluciones dieron inicio a la era de la información. Un salto conceptual ocurrió en los años 80: se descubrió que la información podía ser tratada de manera cuántica. La idea de que la noción intuitiva de información podía ser gobernada por las leyes contra intuitivas de la mecánica cuántica resultó extremadamente fructífera tanto desde un punto de vista teórico como práctico. El concepto de aleatoriedad desempeña un papel central en este respecto. En efecto, las leyes de la física cuántica son probabilistas, lo que contrasta con siglos de teorías físicas cuyo objetivo era elaborar leyes deterministas de la naturaleza. Además, esto constituye una fuente de números aleatorios, un recurso crucial para criptografía. El hecho de que la física cuántica solo describe comportamientos aleatorios fue a veces considerado como una forma de incompletitud en la teoría. Pero la no-localidad, en el sentido de Bell, probó que no era el caso: las leyes cuánticas son intrínsecamente probabilistas, es decir, el azar que contienen no puede ser atribuido a una falta de conocimiento. Esta observación tiene consecuencias prácticas: los datos procedentes de un proceso físico no-local son necesariamente impredecibles. Además, el carácter aleatorio de estos datos no depende del sistema físico, sino solo de su carácter no-local. Por esta razón, el azar basado en la no-localidad está certificado independientemente del dispositivo físico. En esta tesis, cuantificamos el azar basado en la no-localidad en varios escenarios. En el primero, no utilizamos el formalismo cuántico. Estudiamos un proceso no-local dotado de varias estructuras causales en relación con su evolución temporal, y calculamos las relaciones entre aleatoriedad y no-localidad para estas diferentes estructuras causales. El azar basado en la no-localidad suele ser definido en un marco teórico. En el segundo escenario, adoptamos un enfoque práctico, y examinamos la relación entre aleatoriedad y no-localidad en una situación real, donde solo tenemos una información parcial, procedente de un experimento, sobre el proceso. Proponemos un método para optimizar la aleatoriedad en este caso. Hasta ahora, las relaciones entre aleatoriedad y no-localidad han sido estudiadas en el caso bipartito, dado que dos agentes forman el requisito mínimo para definir el concepto de no-localidad. En el tercer escenario, estudiamos esta relación en el caso tripartito. Aunque el azar basado en la no-localidad no depende del dispositivo físico, el proceso que sirve para generar azar debe sin embargo ser implementado con un estado cuántico. En el cuarto escenario, preguntamos si hay que imponer requisitos sobre el estado para poder certificar una máxima aleatoriedad de los resultados. Mostramos que se puede obtener la cantidad máxima de aleatoriedad indiferentemente del nivel de entrelazamiento del estado cuántico.
The interpretation of quantum mechanics has been discussed since this theme first was brought up by Einstein and Bohr. This article describes a proposal for a new foundation of quantum theory, partly drawing upon ideas from statistical inference theory. The approach can be said to have an intuitive basis: The quantum states of a physical system are under certain conditions in one-to-one correspondence with the following: 1. Focus on a concrete question to nature and then 2. Give a definite answer to this question. This foundation implies an epistemic interpretation, depending upon the observer, but the objective world is restored when all observers agree on their observations on some variables. The article contains a survey of parts of the authors books on epistemic processes, which give more details about the theory. At the same time, the article extends some of the discussion in the books, and at places makes it more precise.
This article examines some experimental conditions that invite and possibly require recourse to quantum-mechanical-like mathematical models (QMLMs), models based on the key mathematical features of quantum mechanics, in scientific fields outside physics, such as biology, cognitive psychology, or economics. In particular, I consider whether the following two correlative features of quantum phenomena that were decisive for establishing the mathematical formalism of quantum mechanics play similarly important roles in QMLMs elsewhere. The first is the individuality and discreteness of quantum phenomena, and the second is the irreducibly probabilistic nature of our predictions concerning them, coupled to the particular character of the probabilities involved, as different from the character of probabilities found in classical physics. I also argue that these features could be interpreted in terms of a particular form of epistemology that suspends and even precludes a causal and, in the first place, realist description of quantum objects and processes. This epistemology limits the descriptive capacity of quantum theory to the description, classical in nature, of the observed quantum phenomena manifested in measuring instruments. Quantum mechanics itself only provides descriptions, probabilistic in nature, concerning numerical data pertaining to such phenomena, without offering a physical description of quantum objects and processes. While QMLMs share their use of the quantum-mechanical or analogous mathematical formalism, they may differ by the roles, if any, the two features in question play in them and by different ways of interpreting the phenomena they considered and this formalism itself. This article will address those differences as well.
Our main claim is that Bohr adopted a principle-theoretic approach to quantum mechanics in order to reconcile two principles: the distinction principle, which asserts the necessity of a clear epistemic distinction between a classical apparatus and a quantum system, and the non-separability principle, which asserts that the two systems are ontologically non-separable in any measurement process. The latter principle is a consequence of Bohr's argument that, during a measurement interaction, the quantum system and the measurement apparatus form a 'new kind of individuality'. To support our argument, we first demonstrate the overlooked fact that, according to Bohr, the measurement interaction is a physical, irreversible process and not merely an epistemic acquisition of new information. In this respect, quantum mechanics must be regarded not only as a universal theory, but also as revealing no non-arbitrary difference between a quantum realm and a classical realm; the distinction is purely pragmatic. The tension between the epistemic necessity to rely on a neatly distinguishable classical realm and the ontic non-separability of the quantum system and the classical apparatus inclined Bohr to refuse to provide a constructive account of the measurement process, such as that later proposed, for instance, by spontaneous dynamical reduction models.
The relational interpretation of quantum mechanics (RQM), introduced in its present form by Carlo Rovelli in 1996, involves a number of significant departures from other QM interpretations widely discussed in the literature. We begin here by summarizing these unique RQM features, with a focus on those that suggest altered insights into the nature of the randomness exhibited in QM phenomena. One of these RQM features is the assumption that all objects in the universe are quantum objects, regardless of their material complexity. And, the interaction of any two objects can result in new relational quantum states of each of the objects with the other as reference. But such new states do not replace relational states corresponding to previous interactions with other reference objects. In particular, such earlier relational states that include a variable considered to be random do not collapse to define a determined value of the variable, but instead simply take on that specific value in the state relative to the new reference. The concept of randomness associated with quantum state variables in RQM thus differs from that in other QM interpretations. Rather than take the usual pedantic approach of elaborate side-by-side comparisons between the RQM and other common QM interpretations, we illustrate these differences by describing in some detail the well-known "dual-slit" experiment in terms of RQM concepts, pointing out the important advantages over other interpretations along the way. Of course, we suggest no change in dual-slit experiment results, but believe that the interpretative modifications are helpful and profound.