Quantum physics is non-causal, and randomness is so-called “intrinsic”. We propose no less than an 18th interpretation of it through non-Archimedean geometry to bring back causality, respect of the Kolmogorov axioms and the existence of hidden variables. For these latter ones, we show that they cannot be in any Hilbert space and hence could not be detected in any traditional experiment. We end through proposing two experiments which would prove the non-Archimedean nature of our universe. The first one consists in a new disruptive type of quantum radar. The second one explains how viscosity naturally occurs in fluid mechanics whereas Boltzmann’s approach only considers elastic shocks at the molecular scale.
Quantum physics is non-causal, and randomness is so-called “intrinsic”. We propose no less than an 18th interpretation of it through non-Archimedean geometry to bring back causality, respect of the Kolmogorov axioms and the existence of hidden variables. For these latter ones, we show that they cannot be in any Hilbert space and hence could not be detected in any traditional experiment. We end through proposing two experiments which would prove the non-Archimedean nature of our universe. The first one consists in a new disruptive type of quantum radar. The second one explains how viscosity naturally occurs in fluid mechanics whereas Boltzmann’s approach only considers elastic shocks at the molecular scale.
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 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.
A foundational tenet of standard quantum mechanics—a paradigm that has dominated theoretical physics since the early twentieth century—is the presumed existence of true, fundamental randomness at the smallest observable scales.1 Traditionally characterized by Heisenberg's Uncertainty Principle and conceptually modeled as a chaotic "quantum foam," the universe at the Planck length is theorized to dissolve into an unpredictable, boiling void.1 Under the orthodox Copenhagen interpretation, as well as many subsequent derivative models, the universe at its deepest ontological level is fundamentally non-deterministic.1 Events at this scale are said to occur strictly in accordance with statistical likelihoods rather than rigid causality; physical properties are considered undefined prior to the act of measurement, and the collapse of the wave function is treated as an irreducible, inherently stochastic process.
The quantum decomposition of a classical random variable is one of the deep results of quantum probability: it shows that any classical random variable or stochastic process has a built-in non-commutative structure which is intrinsic and canonical, and not artificially put by hands. Up to now the technique to deduce the quantum decomposition has been based on the theory of interacting Fock spaces and on Jacobi's tri-diagonal relation for orthogonal polynomials. Therefore it requires the existence of moments of any order and cannot be applied to random variables without this property. The problem to find an analogue of the quantum decomposition for random variables without finite moments of any order remained open for about fifteen years and nobody had any idea of how such a decomposition could look like. In the present paper we prove that any infinitely divisible random variable has a quantum decomposition canonically associated to its Lévy–Khintchin triple. The analytical formulation of this result is based on Kolmogorov representation of these triples in terms of 1–cocycles (helices) in Hilbert spaces and on the Araki–Woods–Parthasarathy–Schmidt characterization of these representation in terms of Fock spaces. It distinguishes three classes of random variables: (i) with finite second moment; (ii) with finite first moment only; (iii) without any moment. The third class involves a new type of renormalization based on the associated Lévy–Khinchin function.
Although classical probability theory, as it is encapsulated in the axioms of Kolmogorov and in his criterion for the independence of two events, can consistently be employed in quantum mechanics, this can only be accomplished at an exorbitant price. By considering first the classic two-slit experiment, and then the passage of one photon through three polarizers, the applicability of Kolmogorov's last axiom is called into question, but the standard rebuff of the Copenhagen interpretation is shown to be adequate to this challenge. In the EPR experiment of Aspect, and the violation of the Bell inequalities, the matter is more delicate: it is not directly Kolmogorov's last axiom, but rather his criterion of independence that is at issue. It is explained how two events with space-like separation cannot be independent in Kolmogorov's sense, even in the presence of hidden variables. The escape route of supposing the variables to be nonlocal, with a heavy metaphysical ballast of holism, which however is cosmically censored to prevent superluminal information transfer, has all the trappings of an ad hoc makeshift. The adoption of quantum mechanical probability, which does not obey the rules of Kolmogorov, but does survive empirical testing in terms of relative frequencies of events, is more economical. The solution is simple: correlations obey the rules of quantum mechanics and probability is a theory laden concept that is tested by, but not defined in terms of, the relative frequency of selected classes of events. Quantum mechanics appears to be nonlocal only if one tries to force it into a classical, realist straitjacket. However, this is a shortcoming of the straitjacket: it is not a property of quantum mechanics. That follows from the fact that a Bell telephone does not work!