Related papers: Incompleteness theorem for physics
The proofs of Kleene, Chaitin and Boolos for G\"odel's First Incompleteness Theorem are studied from the perspectives of constructivity and the Rosser property. A proof of the incompleteness theorem has the Rosser property when the…
To operate reliably under changing conditions, complex systems require feedback on how effectively they use resources, not just whether objectives are met. Current AI systems process vast information to produce sophisticated predictions,…
This book represents a continuation, an elaboration, and possibly a clear explanation of the ideas which were expounded in the previous book Time and Methods in Environmental Interfaces Modeling (henceforth abbreviated as TM, Mihailovic et…
Demonstrations of quantum entanglement which confirm the violation of Bell's inequality indicate that under certain conditions action at a distance is possible. This consequence seems to contradict the relativistic principle of causality,…
A possible solution for the problem of non-existence of universal time is given by utilizing Goedel's incompleteness theorem.
Recently, a delicately designed Gedankenexperiment was proposed to check the self-consistence of quantum theory in the description of the agents who are using this theory. It was demonstrated that the quantum theory is inconsistent. Here a…
We present an equivalence theorem to unify the two classes of uncertainty relations, i.e., the variance-based ones and the entropic forms, which shows that the entropy of an operator in a quantum system can be built from the variances of a…
The long lasting discussion on the completeness of quantum theory (QT) has not yet come to an end. The discussion is impeded by the lack of a clear understanding of what makes up the contents of a theory of physics in general and of QT…
There is an increasing interest in applying recent advances in AI to automated reasoning, as it may provide useful heuristics in reasoning over formalisms in first-order, second-order, or even meta-logics. To facilitate this research, we…
This paper revisits the foundations of mathematical proof through the lens of Aristotle's threefold conception of truth: sensory evidence, axiomatic definition, and syllogistic deduction. I argue that modern mathematics has too often…
The Frauchiger-Renner argument aims to show that `quantum theory cannot consistently describe the use of itself': in many-party settings where agents are themselves subject to quantum experiments, agents may make predictions that contradict…
Amplitudes are the major logical object in Quantum Theory. Despite this fact they presents no physical reality and in consequence only observables can be experimetally checked. We discuss the possibility of a theory of Quantum Probabilities…
The new axiom in set theory, axiom of the empty sets, allows another way to formulate Bell inequality in quantum mechanics. The new axiom emerges from the historical and philosophical analysis of set theory.
The de Finetti representation theorem for continuous variable quantum system is first developed to approximate an N-partite continuous variable quantum state with a convex combination of independent and identical subsystems, which requires…
We give a mathematical definition for the notion of inconclusive quantum measurements. In physics, such measurements occur at intermediate stages of a complex measurement procedure, with the final measurement result being operationally…
We apply the algebraic theory of infinite classical lattices from Part I to write an axiomatic theory of measurements, based on Mackey's axioms for quantum mechanics. The axioms give a complete theory of measurements in the sense of Haag…
The famous G\"odel incompleteness theorem states that for every consistent sufficiently rich formal theory T there exist true statements that are unprovable in T. Such statements would be natural candidates for being added as axioms, but…
We start with a discussion of the use of mathematics to model the real world then justify the role of Hilbert space formalism for such modelling in the general context of quantum logic. Following this, the incompleteness of the…
In his famous thought experiment, Wigner assigns an entangled state to the composite quantum system made up of Wigner's friend and her observed system. While the two of them have different accounts of the process, each Wigner and his friend…
The stipulation that no measurable quantity could have an infinite value is indispensable in physics. At the same time, in mathematics, the possibility of considering an infinite procedure as a whole is usually taken for granted. However,…