Related papers: Goedel and Physics
We discuss how developments in physics often imply in the need that spacetime acquires an increasingly richer and complex structure. General Relativity was the first theory to show us the way to connect space and time with the physical…
Our main purpose here is to study some qualitative aspects of space and time. These include the notion of space and time regarded as the containers of respectively bodies and events, the divisibility of space, and the unrepeatability of…
The observational evidence for the recent acceleration of the universe demonstrates that canonical theories of cosmology and particle physics are incomplete (or possibly incorrect) and that new physics is out there, waiting to be…
General relativity treats spacetime as dynamical and exhibits its breakdown at singularities. This failure is interpreted as evidence that quantum gravity is not a theory formulated within spacetime; instead, it must explain the very…
The 20th century has revealed two important limitations of scientific knowledge. On the one hand, the combination of Poincar\'e's nonlinear dynamics and Heisenberg's uncertainty principle leads to a world picture where physical reality is,…
I explore physics implications of the External Reality Hypothesis (ERH) that there exists an external physical reality completely independent of us humans. I argue that with a sufficiently broad definition of mathematics, it implies the…
In this first of two papers, strong limits on the accuracy of physical computation are established. First it is proven that there cannot be a physical computer C to which one can pose any and all computational tasks concerning the physical…
We provide a gauge-invariant theory of gravitation in the context of Weyl Integrable Space-Times. After making a brief review of the theory's postulates, we carefully define the observers' proper-time and point out its relation with…
Goedel's completeness theorem is concerned with provability, while Girard's theorem in ludics (as well as full completeness theorems in game semantics) are concerned with proofs. Our purpose is to look for a connection between these two…
The mathematical notion of incompleteness (eg of rational numbers, Turing-computable functions, and arithmetic proof) does not play a key role in conventional physics. Here, a reformulation of the kinematics of quantum theory is attempted,…
This article discusses what can be proved about the foundations of mathematics using the notions of algorithm and information. The first part is retrospective, and presents a beautiful antique, Godel's proof, the first modern incompleteness…
It has been commonly argued, on the basis of Goedel's theorem and related mathematical results, that true artificial intelligence cannot exist. Penrose has further deduced from the existence of human intelligence that fundamental changes in…
In light of G\"{o}del's undecidability results (incomplete theorems) for math, quantum indeterminism indicates that physics and the Universe may be indeterministic, incomplete, and open in nature, and therefore demand no single unification…
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic…
We consider the possibility of a past and future eternal universe, constructing geodesically complete inflating, loitering, and bouncing spacetimes. We identify the constraints energy conditions in General Relativity place on the building…
Goedel Incompleteness Theorem leaves open a way around it, vaguely perceived for a long time but not clearly identified. (Thus, Goedel believed informal arguments can answer any math question.) Closing this loophole does not seem obvious…
In this paper we apply the symmetry principle in order to search for an alternative unified explanation of several cosmological puzzles such as the present stage of accelerated expansion of the Universe and the Hubble tension issue, among…
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…
We give proofs of G\"odel's incompleteness theorems after A. Joyal. The proof uses internal category theory in an arithmetic universe, a predicative generalisation of topoi. Applications to L\"ob's Theorem are discussed.
Quantum mechanics, one of the most successful theories in the history of science, was created to account for physical systems not describable by classical physics. Though it is consistent with all experiments conducted thus far, many of its…