Quantum Physics is usually defined as a theory that affirms a primary role of randomness and probability. Eleven well-known quantum experiments are examined and the result is the coexistence of both random and causal type behaviour. We need both to describe experiments. Quantum Mechanics states the general overcoming of causality and this statement constitutes an unlimited generalization, not supported by experience. Determinism and indeterminism are philosophical systems, that universalize causality or chance. The crucial point is the difference between epistemic and intrinsic randomness. In the first aspect, randomness does not have a fundamental meaning, in the second, randomness of the individual event is explained, but the detection of high stable regularities remains to be explained. The article addresses the question of entanglement and various aspects of probability theory, including the law of large numbers, arriving at the thesis that many relevant questions are unresolved. A causal description is in quantum mechanics impossible in principle, given its assumptions. In order not to contradict experience, both points of view are necessary, causal and random. This is the state of the research, to return to and start again from.
Quantum Physics is usually defined as a theory that affirms a primary role of randomness and probability. Eleven well-known quantum experiments are examined and the result is the coexistence of both random and causal type behaviour. We need both to describe experiments. Quantum Mechanics states the general overcoming of causality and this statement constitutes an unlimited generalization, not supported by experience. Determinism and indeterminism are philosophical systems, that universalize causality or chance. The crucial point is the difference between epistemic and intrinsic randomness. In the first aspect, randomness does not have a fundamental meaning, in the second, randomness of the individual event is explained, but the detection of high stable regularities remains to be explained. The article addresses the question of entanglement and various aspects of probability theory, including the law of large numbers, arriving at the thesis that many relevant questions are unresolved. A causal description is in quantum mechanics impossible in principle, given its assumptions. In order not to contradict experience, both points of view are necessary, causal and random. This is the state of the research, to return to and start again from.
There is still no scientific consensus on the existence of ontic randomness. Understanding it is especially important for physics, as the probabilistic nature of quantum mechanics is believed to be irreducible. This theory aims to explain how the existence of true randomness is possible for the referential of a non-omniscient observer.The theory is built on a toy model in two thought experiments. We propose the concept of invisible and inaccessible laws as explanation for the occurrence of unpredictability and states that it represents the physical reification of Gödel's incompleteness theorem.The article proposes that the geometry of spacetime is able to explain several physical phenomena in the set of dimensional random events. Among these are the event horizon in black holes, the hypersensitivity to initial conditions, and the Heisenberg's uncertainty principle. We develope the theorem of dimensional randomness for proving that a non-causal theory in a dimensionally incomplete space have correspondence with a causal theory in a dimensionally complete space. The theorem is used to question the fundamentally probabilistic nature of quantum mechanics through an implicit assumption that is made about the number of dimensions in spacetime for the development of Bell's theorem.
Quantum mechanics has achieved unparalleled success as an operational theory, describing a wide range of experiments to remarkable accuracy. However, the physical foundations on which it rests remain as puzzling as they were a century ago, and a concise statement of the physical principles that underlie quantum mechanics is still outstanding. One promising approach holds that these principles should be formulated in terms of information, since many of the counter-intuitive effects in quantum theory concern questions such as what one can know about a quantum system and how the information encoded therein can be processed and distributed between parties. Another challenging feature of quantum theory is its incompatibility with the other cornerstone of modern physics, general relativity. In order to reconcile the two, one must identify and retain only the essential concepts and principles of each theory, and in the case of general relativity, causality has been identified as such a concept. This raises the question of how our classical understanding of causality must change when quantum theory is taken into account. In order to address these questions about information, knowledge and causality, I turn to the framework of causal models. In classical statistics, causal models explain the relations among a set of variables in terms of causal influences, which makes them a powerful tool for structuring our knowledge about complex systems and developing strategies for interacting with them. More importantly, the framework provides the conceptual underpinnings and mathematical methods for addressing questions about causation, information and knowledge in a rigorous manner. In this thesis, I develop a version of the classical causal models framework that is compatible with quantum theory and explore its physical implications. \n \n \nA first step is to define quantum versions of fundamental elements such as variables, conditionals and belief propagation rules. This allows one to consider the question of what one can come to know about a quantum variable from the point of view of causal modelling. The conditionals relating quantum variables are found to have a richer structure than their classical counterparts, which can be exploited for the task of discerning causal relations given limited data -- a central problem in classical causal modelling. The mathematical properties of quantum conditionals also establish a correspondence between various classes of two-party correlations, such as bound and distillable entanglement, and the types of causal structures that can give rise to them, which may become a useful tool for entanglement theory and quantum information processing. In the context of open quantum systems dynamics, quantum causal models provide a clear physical explanation of not completely positive maps and, more broadly, of non-Markovian quantum dynamics. Finally, I consider the possibility of non-classical effects in the way that different causal mechanisms are combined -- that is, non-classical causal structures. For the simple case of two causally ordered variables, I propose indicators that witness different classes of combinations of causal mechanisms, including a non-classical mixture, and describe an experiment realizing examples of the different classes. \n \n \nAs these results illustrate, the framework of quantum causal models provides both greater conceptual clarity and a comprehensive mathematical formalism for studying a diverse set of problems, ranging from foundational questions to applications in open systems dynamics and the exploration of non-classical causal structures, which are likely to feature in a future theory of quantum gravity. The material presented in this thesis is intended as a foundation and inspiration for further applications of quantum causal models.
Quantum mechanics was developed as a response to the inadequacy of classical physics in explaining certain physical phenomena. While it has proved immensely successful, it also presents several features that severely challenge our classicality based intuition. Randomness in quantum theory is one such and is the central theme of this dissertation. Randomness is a notion we have an intuitive grasp on since it appears to abound in nature. It a icts weather systems and nancial markets and is explicitly used in sport and gambling. It is used in a wide range of scienti c applications such as the simulation of genetic drift, population dynamics and molecular motion in fluids. Randomness (or the lack of it) is also central to philosophical concerns such as the existence of free will and anthropocentric notions of ethics and morality. The conception of randomness has evolved dramatically along with physical theory. While all randomness in classical theory can be fully attributed to a lack of knowledge of the observer, quantum theory qualitatively departs by allowing the existence of objective or intrinsic randomness. It is now known that intrinsic randomness is a generic feature of hypothetical theories larger than quantum theory called the non-signalling theories. They are usually studied with regards to a potential future completion of quantum mechanics or from the perspective of recognizing new physical principles describing nature. While several aspects have been studied to date, there has been little work in globally characterizing and quantifying randomness in quantum and non-signalling theories and the relationship between them. This dissertation is an attempt to ll this gap. Beginning with the unavoidable assumption of a weak source of randomness in the universe, we characterize upper bounds on quantum and non-signalling randomness. We develop a simple symmetry argument that helps identify maximal randomness in quantum theory and demonstrate its use in several explicit examples. Furthermore, we show that maximal randomness is forbidden within general non-signalling theories and constitutes a quantitative departure from quantum theory. We next address (what was) an open question about randomness ampli cation. It is known that a single source of randomness cannot be ampli ed using classical resources alone. We show that using quantum resources on the other hand allows a full ampli cation of the weakest sources of randomness to maximal randomness even in the presence of supra-quantum adversaries. The signi cance of this result spans practical cryptographic scenarios as well as foundational concerns. It demonstrates that conditional on the smallest set of assumptions, the existence of the weakest randomness in the universe guarantees the existence of maximal randomness. The next question we address is the quanti cation of intrinsic randomness in non-signalling correlations. While this is intractable in general, we identify cases where this can be quanti ed. We nd that in these cases all observed randomness is intrinsic even relaxing the measurement independence assumption. We nally turn to the study of the only known resource that allows generating certi able intrinsic randomness in the laboratory i.e. entanglement. We address noisy quantum systems and calculate their entanglement dynamics under decoherence. We identify exact results for several realistic noise models and provide tight bounds in some other cases. We conclude by putting our results into perspective, pointing out some drawbacks and future avenues of work in addressing these concerns.
The principle of cause and effect is deeply rooted in human experience, so much so that it is routinely and tacitly assumed throughout science, even by scientists working in areas where time symmetry is theoretically ingrained, as it is in both classical and quantum physics. Experiments are said to cause their results, not the other way around. In this informal paper, we argue that this assumption should be replaced with a more general notion of mutual influence — bi‐directional relations or constraints on joint values of two or more variables. From an analysis based on quantum entropy, it is proposed that quantum measurement is a unitary three‐interaction, with no collapse, no fundamental randomness, and no barrier to backward influence.Experimental results suggesting retrocausality are seen frequently in well‐controlled laboratory experiments in parapsychology and elsewhere, especially where a random element is included. Certain common characteristics of these experiments give the appearance of contradicting well‐established physical laws, thus providing an opportunity for deeper understanding and important clues that must be addressed by any explanatory theory. We discuss how retrocausal effects and other anomalous phenomena can be explained without major injury to existing physical theory. A modified quantum formalism can give new insights into the nature of quantum measurement, randomness, entanglement, causality, and time.
[I] think I can safely say that nobody understands quantum mechanics. Richard Feynman, The Character of Physical Law Quantum mechanics [is] that mysterious, confusing discipline, which none of us really understands but which we know how to use. It works perfectly, as far as we can tell, in describing physical reality, but it is a ‘counter-intuitive discipline’… Murray Gell-Mann, Questions for the Future [The quantum] postulate implies a renunciation as regards the causal space-time co-ordination of atomic processes. Niels Bohr, Atomic Theory and the Description of Nature It should be emphasized, however, that the probability function does not in itself represent a course of events in the course of time. It represents a tendency for events and our knowledge of events. The probability function can be connected with reality only if one essential condition is fulfilled: if a new measurement is made to determine a certain property of the system. [T]he idea of an objective real world whose smallest parts exist objectively in the same sense as stones or trees exist, independently of whether or not we observe them…is impossible … Werner Heisenberg, Physics and Philosophy [In] quantum theory it is the principle of causality , or more accurately that of determinism , which must be dropped and replaced by something else.… We now have a new form of the law of causality.… It is as follows: if in a certain process the initial conditions are determined as accurately as the uncertainty relations permit, then the probabilities of all possible subsequent states are governed by exact laws. Max Born, The Restless Universe
Recent tremendous development of quantum information theory has led to a number of quantum technological projects, e.g. quantum random generators. This development had stimulated a new wave of interest in quantum foundations. One of the most intriguing problems of quantum foundations is the elaboration of a consistent and commonly accepted interpretation of a quantum state. Closely related problem is the clarification of the notion of quantum randomness and its interrelation with classical randomness. In this short review, we shall discuss basics of classical theory of randomness (which by itself is very complex and characterized by diversity of approaches) and compare it with irreducible quantum randomness. We also discuss briefly “digital philosophy”, its role in physics (classical and quantum) and its coupling to the information interpretation of quantum mechanics (QM).