Fast moving classical variables can generate quantum mechanical behavior. We demonstrate how this can happen in a model. The key point is that in classically evolving systems one can still define a conserved quantum energy. For the fast variables, the energy levels are far separated, such that one may assume these variables to stay in their ground state. This forces them to be entangled, so that, consequently, the slow variables are entangled as well. The fast variables could be the vacuum (...) fluctuations caused by unknown super heavy particles. The emerging quantum effects in the light particles are expressed by a Hamiltonian that can have almost any form. The entire system is ontological, and yet allows one to generate interference effects in computer models. This seemed to lead to an inexplicable paradox, which is now resolved: exactly what happens in our models if we run a quantum interference experiment in a classical computer is explained. The restriction that very fast variables stay predominantly in their ground state appears to be due to smearing of the physical states in the time direction, preventing their direct detection. Discussions are added of the emergence of quantum mechanics, and the ontology of an EPR/Bell Gedanken experiment. (shrink)

The violation of Bell inequalities seems to establish an important fact about the world: that it is non-local. However, this result relies on the assumption of the statistical independence of the measurement settings with respect to potential past events that might have determined them. Superdeterminism refers to the view that a local, and determinist, account of Bell inequalities violations is possible, by rejecting this assumption of statistical independence. We examine and clarify various problems with superdeterminism, looking in particular at its (...) consequences on the nature of scientific laws and scientific reasoning. We argue that the view requires a neo-Humean account of at least some laws, and creates a significant problem for the use of statistical independence in other parts of physics and science more generally. (shrink)

The dynamics-from-permutations of classical Ising spins is generalized here for an arbitrarily long chain. This serves as an ontological model with discrete dynamics generated by pairwise exchange interactions defining the unitary update operator. The model incorporates a finite signal velocity and resembles in many aspects a discrete free field theory. We deduce the corresponding Hamiltonian operator and show that it generates an exact terminating Baker–Campbell–Hausdorff formula. Motivation for this study is provided by the Cellular Automaton Interpretation of Quantum Mechanics. We (...) find that our ontological model, which is classical and deterministic, appears as if of quantum mechanical kind in an appropriate formal description. However, it is striking that small deformations of the model turn it into a genuine quantum theory. This supports the view that quantum mechanics stems from an epistemic approach handling physical phenomena. (shrink)

Bell’s theorem cannot be proved if complementary measurements have to be represented by random variables which cannot be added or multiplied. One such case occurs if their domains are not identical. The case more directly related to the Einstein–Rosen–Podolsky argument occurs if there exists an ‘element of reality’ but nevertheless addition of complementary results is impossible because they are represented by elements from different arithmetics. A naive mixing of arithmetics leads to contradictions at a much more elementary level than the (...) Clauser–Horne–Shimony–Holt inequality. (shrink)

We consider processes of emergence within the conceptual framework of the Information Loss principle and the concepts of systems conserving information; systems compressing information; and systems amplifying information. We deal with the supposed incompatibility between emergence and computability tout-court. We distinguish between computational emergence, when computation acquires properties, and emergent computation, when computation emerges as a property. The focus is on emergence processes occurring within computational processes. Violations of Turing-computability such as non-explicitness and incompleteness are intended to represent partially the (...) properties of phenomenological emergence, such as logical openness, given by the observer’s cognitive role; structural dynamics where change regards rules rather than only values; and multi-modelling where multiple non-equivalent models are required to model such structural dynamics. In this way, we validate, from an epistemological viewpoint, models and simulations of phenomenological emergence where the sequence of events constitutes the natural, analogical non-Turing computation which a cognitive complex system can reproduce through learning. Reproducibility through learning is different from Turing-like computational iteration. This paper aims to open a new, non-reductionist understanding of the conceptual relationship between emergence and computability. (shrink)

This is a textbook on quantum mechanics. It is addressed to graduates and advanced undergraduates. The book presents quantum theory as a logically coherent system, placing stronger emphasis on the theory' s probabilistic structure and on the role of symmetries. It makes students aware of foundational problems from the very beginning, but at the same time, it urges them to adopt a pragmatic attitude towards the quantum formalism. The book consists of five parts. Part I is a review of classical (...) physics, including probability theory, and a historical introduction to quantum theory. Part II presents quantum theory in terms of six fundamental principles. The principles are presented together with the necessary mathematical background and with applications to simple systems. Part III analyses the properties of quantum particles. It starts with the description of symmetries, continues to non-relativistic particles, the introduction of spin, and particle statistics. It concludes with a symmetries-based introduction to relativistic quantum systems and with the first steps towards relativistic quantum field theory. Part IV presents techniques adapted to specific problems: the structure and spectra of composite systems, decays and transitions, particle scattering, and open quantum systems. Finally, Part V revisits quantum foundations: quantum measurement theory, the major interpretations of quantum theory, and the frontiers of quantum theory in contemporary research. (shrink)

Philosophers, theologians, physicists, and psychologists join their efforts to reflect on the crucial issues of limit and infinity, time and eternity, empty space and material space. The volume offers an invaluable contribution to some of the most important issues of our times: questions on God and consciousness are discussed in parallel with quantum theory, black holes, the inflationary universe, the Big Bang, and string theory, from different perspectives and angles, ranging from neuroscience to AI.

An intricate quantum statistical effect guides us to a deterministic, non-causal quantum universe with a given fixed initial and final state density matrix. A concept is developed on how and where something like macroscopic physics can emerge. However, the concept does not allow philosophically crucial free will decisions. The quantum world and its conjugate evolve independently, and one can replace fixed final states on each side just with a common matching one. This change allows for external manipulations done in the (...) quantum world and its conjugate, which do not otherwise alter the basic quantum dynamics. In a big bang/big crunch universe, the expanding part can be attributed to the quantum world and the contracting one to the conjugate one. The obtained bi-linear picture has several noteworthy consequences. (shrink)

The contrast between the past-future symmetry of mechanical theories and the time-arrow observed in the behaviour of real complex systems doesn’t have nowadays a fully satisfactory explanation. If one confides in the Laplace-dream that everything be exactly and completely describable by the known mechanical differential equations, the whole experimental evidence of the irreversibility of real complex processes can only be interpreted as an illusion due to the limits of human brain and shortness of human history. In this work it is (...) surmised that in the description of real events it would be more reasonable to renounce exactness and completeness of mechanical differential equations, assuming that also further effects exist in nature, governed by different kinds of rules, in spite of being so weak to be directly unobservable in single motions. This surmise can explain not only the time-arrow, but also why, in particular cases, it can happen that approximate and/or statistical models represent an improvement of mechanical theories instead of an approximation: this happened for Boltzmann gas-model and also for the famous work of Max Planck on blackbody-radiation. And it also appears as a more promising “working hypothesis”, stimulating and guiding us to learn more about limits and origin of the basic equations, and also about the nature of chance and the meaning of probability, which is nowadays not clear in spite of the fundamental role it plays in physics. Particularly that kind of probability which gives the connection between quantum–mechanical differential equations and observable events. (shrink)