Physics in a finite geometry

• URL: http://arxiv.org/abs/2212.02915v1
• Date: Tue, 6 Dec 2022 12:14:08 GMT
• Title: Physics in a finite geometry
• Authors: Arkady Bolotin
• Abstract summary: negating the axiom of infinity results in physics acting in a finite geometry where it is ensured that all classical field theories are quantizable. This paper shows that negating the axiom of infinity results in physics acting in a finite geometry where it is ensured that all classical field theories are quantizable.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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, not only does such possibility run counter to computational feasibleness, but it also leads to the most serious problem in modern physics, to wit, the emergence of infinities in calculated physical quantities. Particularly, having agreed on the axiom of infinity for set theory -- the backbone of the theoretical foundations of calculus integrated in every branch of physics -- one could no longer rule out the existence of a classical field theory which is not quantizable, let alone renormalizable. By contrast, the present paper shows that negating the axiom of infinity results in physics acting in a finite geometry where it is ensured that all classical field theories are quantizable.

Related papers

• Minimal operational theories: classical theories with quantum features [41.94295877935867]
  We show that almost all minimal theories with conditioning satisfy two quantum no-go theorems. As a relevant example, we construct a minimal toy-theory with conditioning where all systems are classical.
  arXiv  Detail & Related papers  (2024-08-02T16:24:09Z)
• Completeness of qufinite ZXW calculus, a graphical language for finite-dimensional quantum theory [0.11049608786515838]
  We introduce the qufinite ZXW calculus - a graphical language for reasoning about finite-dimensional quantum theory. We prove the completeness of this calculus by demonstrating that any qufinite ZXW diagram can be rewritten into its normal form. Our work paves the way for a comprehensive diagrammatic description of quantum physics, opening the doors of this area to the wider public.
  arXiv  Detail & Related papers  (2023-09-22T17:23:58Z)
• Connecting classical finite exchangeability to quantum theory [69.62715388742298]
  Exchangeability is a fundamental concept in probability theory and statistics. We show how a de Finetti-like representation theorem for finitely exchangeable sequences requires a mathematical representation which is formally equivalent to quantum theory.
  arXiv  Detail & Related papers  (2023-06-06T17:15:19Z)
• Contextual unification of classical and quantum physics [0.0]
  We develop the idea that the usual formalism of quantum mechanics stops working when countable infinities of particles are encountered. This is because the dimension of the corresponding Hilbert space becomes uncountably infinite, leading to the loss of unitary equivalence. We show that it provides a natural way to describe the "Heisenberg cut", as well as a unified mathematical model including both quantum and classical physics.
  arXiv  Detail & Related papers  (2022-09-03T16:51:19Z)
• Correspondence Between the Energy Equipartition Theorem in Classical Mechanics and its Phase-Space Formulation in Quantum Mechanics [62.997667081978825]
  In quantum mechanics, the energy per degree of freedom is not equally distributed. We show that in the high-temperature regime, the classical result is recovered.
  arXiv  Detail & Related papers  (2022-05-24T20:51:03Z)
• Let the Mathematics of Quantum Speak: Allowed and Unallowed Logic [0.0]
  The mathematics/formalism of quantum, compared with classical, physics, may be fairly basically characterized by non-commutative algebras replacing commutative. One may have the latter only in a haven' of approximately commutative algebras of quasi-classical macroscopic observables', and moreover that yes-no actual world' would plainly be an extra ingredient' to the base quantum theory itself.
  arXiv  Detail & Related papers  (2021-12-30T22:03:33Z)
• Quantum realism: axiomatization and quantification [77.34726150561087]
  We build an axiomatization for quantum realism -- a notion of realism compatible with quantum theory. We explicitly construct some classes of entropic quantifiers that are shown to satisfy almost all of the proposed axioms.
  arXiv  Detail & Related papers  (2021-10-10T18:08:42Z)
• Quantum Measurement Theory for Systems with Finite Dimensional State Spaces [0.0]
  We develop the theory in a deductive manner from the basic postulates for quantum mechanics. We derive an axiomatic characterization of all the physically realizable finite quantum measurements.
  arXiv  Detail & Related papers  (2021-10-07T07:09:38Z)
• Gentle Measurement as a Principle of Quantum Theory [9.137554315375919]
  We propose the gentle measurement principle (GMP) as one of the principles at the foundation of quantum mechanics. We show, within the framework of general probabilistic theories, that GMP imposes strong restrictions on the law of physics.
  arXiv  Detail & Related papers  (2021-03-28T11:59:49Z)
• Symmetries in Foundation of Quantum Theory and Mathematics [0.0]
  We consider finite quantum theory (FQT) where states are elements of a space over a finite ring or field with characteristic $p$ and operators of physical quantities act in this space. We prove that, with the same approach to symmetry, FQT and finite mathematics are more general than standard quantum theory and classical mathematics.
  arXiv  Detail & Related papers  (2020-03-05T04:46:04Z)
• Bell's theorem for trajectories [62.997667081978825]
  A trajectory is not an outcome of a quantum measurement, in the sense that there is no observable associated with it. We show how to overcome this problem by considering a special case of our generic inequality that can be experimentally tested point-by-point in time.
  arXiv  Detail & Related papers  (2020-01-03T01:40:44Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.