I describe the main ideas of constructive physics and its role for the probability interpretation of quantum theory. It is shown how the explicit probability space for quantum systems gives the formal representation of entanglement and decoherence.
In this course, I talk about the source of mathematical constructivism and its role in the future development of theoretical physics. I describe what physical constructivism is and why it is necessary for the penetration of exact methods of theoretical physics to the area of complex systems, which formally belong to the others natural disciplines. I describe the concrete heuristic for the creating of models of constructive quantum theory the method of collective behavior. I represent the constructive viewpoint on the quantum computer, which treats it as the model object of many particle quantum physics, and the practical recommendation concerning its building. Due to the known inertia of the educational system constructive methods in mathematics remains mostly unknown to the wide physical community, and I hope that this course will stimulate the interest to the new possibilities, which these methods open. These possibilities represent interest to natural scientists and for programmers as well.
The quantum theory of decoherence plays an important role in a pragmatist interpretation of quantum theory. It governs the descriptive content of claims about values of physical magnitudes and offers advice on when to use quantum probabilities as a guide to their truth. The content of a claim is to be understood in terms of its role in inferences. This promises a better treatment of meaning than that of Bohr. Quantum theory models physical systems with no mention of measurement: it is decoherence, not measurement, that licenses application of Born's probability rule. So quantum theory also offers advice on its own application. I show how this works in a simple model of decoherence, and then in applications to both laboratory experiments and natural systems. Applications to quantum field theory and the measurement problem will be discussed elsewhere.
Abstract The reconstruction of quantum physics has been connected with the interpretation of the quantum formalism, and has continued to be so with the recent deeper consideration of the relation of information to quantum states and processes. This recent form of reconstruction has mainly involved conceiving quantum theory on the basis of informational principles, providing new perspectives on physical correlations and entanglement that can be used to encode information. By contrast to the traditional, interpretational approach to the foundations of quantum mechanics, which attempts directly to establish the meaning of the elements of the theory and often touches on metaphysical issues, the newer, more purely reconstructive approach sometimes defers this task, focusing instead on the mathematical derivation of the theoretical apparatus from simple principles or axioms. In its most pure form, this sort of theory reconstruction is fundamentally the mathematical derivation of the elements of theory from explicitly presented, often operational principles involving a minimum of extra‐mathematical content. Here, a representative series of specifically information‐based treatments—from partial reconstructions that make connections with information to rigorous axiomatizations, including those involving the theories of generalized probability and abstract systems—is reviewed.
There exist dozens of interpretations of quantum theory, but they do not seem to contribute much to understanding the theory.This paper attempts to clarify some issues that are discussed in those interpretations.The main keywords are: "Classical ontology", Indeterminism, Probability, Predictions, The necessity of classical concepts, Minimal interpretation, Lattice, Physical objects, Alternatives to quantum theory?, Measurement, Realism.One of the main points of this paper is the role of predictions in understanding any theory of physics.
There exist dozens of interpretations of quantum theory, but they do not seem to contribute much to understanding the theory. This paper attempts to clarify some issues that are discussed in those interpretations. The main keywords are: "Classical ontology", Indeterminism, Probability, Predictions, The necessity of classical concepts, Minimal interpretation, Lattice, Physical objects, Alternatives to quantum theory?, Measurement, Realism. One of the main points of this paper is the role of predictions in understanding any theory of physics.
How should we model an observer within quantum mechanics or quantum field theory? How can classical physics emerge from a quantum model, and why should classical probability be useful? How can we model a selective measurement entirely within a closed quantum system? This paper sketches a new physical theory of probability based on an attempt to model classical information within a purely quantum system. We model classical information using a version of Zurek's theory of Quantum Darwinism, with emphasis on quantum information encoded using projection operators localised in spacetime. This version of Quantum Darwinism is compatible with quantum field theory, and does not require any artificial division of a quantum system into subsystems. The main innovation is our attempt to provide a physical explanation of probability. Decoherence is the physical mechanism behind Quantum Darwinism or the `branching of quantum worlds'. Assuming a type of perfect decoherence we construct a conventional probabilistic model for classical information. This, however, is not our theory of natural probability, and does not quite demonstrate the validity of Bayesian reasoning. Instead, our theory of natural probability arises from careful consideration of errors in decoherence: roughly speaking, we don't observe low probability events because they are swamped by quantum noise.