Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

World Futures

Degeneracy of the local structure renormalizing infinite time and space

Yukio‐Pegio Gunji

Published Sep 1, 1997• 0 citations
Publisher

Abstract

A model for a system consisting of elements which detect the measurement apparatus of other elements is proposed. By any apparatus one can observe locally, however it can refer to non‐local property because apparatus itself is indefinite. In taking this aspect into consideration, I formulate expressions for a local interaction referring to non‐local property. This formalization can satisfy the aspect of what is called, internal measurement. This system shows teleological global motion toward criticality which is relevant to the degeneracy of a specific element featuring D ? Hom(Z), E) by which infinite time and space are renormalized.

DOI
10.1080/02604027.1997.9972651

Related papers

The Infinite Apparatus in the Quantum Theory of Measurement

Don Robinson

It has been suggested that the measuring apparatus used to measure quantum systems ought to be idealized as consisting of an infinite number of quantum systems. Let us call this the infinity assumption. The suggestion that we ought to make the infinity assumption has been made in connection with two closely related but distinct problems. One is the problem of determining the importance of the limitations on measurement incorporated into the Wigner-Araki-Yanase quantum theory of measurement. The other is the measurement problem. These problems are not internal to the quantum mechanical formalism. They arise when we obtain particular formal results in applying the quantum mechanical formalism to measurement interactions. The formal results are problematic because they resist explanation. Various authors have claimed that by making the infinity assumption we can neglect the limitations on measurement. Bub (1988) and (1989) claims it allows us to solve the measurement problem. I will argue that both claims are unjustified.

PSA Proceedings of the Biennial Meeting of the Philosophy of Science Association•Jan 1, 1990•2 citations

A mathematical model for measurements

Akitaka Kishimoto

We will give a new model for measurements of a quantum system, expressed as the compact operators on a Hilbert space, such that the measuring apparatuses are described by a unital separable non-type I nuclear simple C$^*$-algebra equipped with certain unital endomorphisms and pure states. An interaction between the quantum system and the apparatus is specified by a unitary associated with the combined system as before. Magnifying to the classical level some aspects of the quantum system so captured in the apparatus is explicitly done by applying the endomorphism; then the resulting state is the superposition of {\em phases} with weights. Nature will then choose each phase according to the probability prescribed by the weights just as does one when multiple phases appear as in phase transition. Thus in our model state-reduction (or collapse of the wave function) is a primary event; whether this corresponds to the measurement of an observable or which one if it does is another matter.

•Mar 31, 2013•0 citations

Measurement As Spontaneous Symmetry Breaking, Non-locality and Non-Boolean Holism

Partha Ghose

It is shown that having degenerate ground states over the domain of the wavefunction of a system is a sufficient condition for a quantum system to act as a measuring apparatus for the system. Measurements are then instances of spontaneous symmetry breaking to one of these ground states, induced by environmental perturbations. Together with non-Boolean holism this constitutes an optimal formulation of quantum mechanics that does not imply non-locality.

arXiv:1008.2510•Aug 15, 2010•3 citations

Formalism locality in quantum theory and quantum gravity

Lucién Hardy

Introduction Indefinite causal structure poses particular problems for theory formulation since many of the core ideas used in the usual approaches to theory construction depend on having definite causal structure. For example, the notion of a state across space evolving in time requires that we have some definite causal structure so we can define a state on a space-like hypersurface. We will see that many of these problems are mitigated if we are able to formulate the theory in a formalism-local (or F-local) fashion. A formulation of a physical theory is said to be F-local if, in making predictions for any given arbitrary space-time region, we need only refer to mathematical objects pertaining to that region. This is a desirable property both on the grounds of efficiency and since, if we have indefinite causal structure, it is not clear how to select some other space-time region on which our calculations may depend. The usual ways of formulating physical theories (the time-evolving state picture, the histories approach, and the local-equations approach) are not F-local. We set up a framework for probabilistic theories with indefinite causal structure. This, the causaloid framework, is F-local. We describe how quantum theory can be formulated in the causaloid framework (in an F-local fashion). This provides yet another formulation of quantum theory. This formulation, however, may be particularly relevant to the problem of finding a theory of quantum gravity. The problem of quantum gravity is to find a theory that reduces in appropriate limits to general relativity and quantum theory (including, at least, those situations in which those two theories have been experimentally confirmed).

arXiv:0804.0054•Cambridge University Press eBooks•Jun 10, 2010•15 citations

Local Observables

Huzihiro Araki

Abstract In this chapter we consider for each space-time domain the set of all those observables which can be measured there and we discuss its basic properties, especially in connection with the vacuum state.

•Oct 21, 1999•0 citations

Self-Consistent Global Modes: An Informational Framework for the Convergence of Quantum Mechanics and Emergent Phenomenology.

Moises Enrique Benitez Alonso

This paper proposes an integrative ontological framework—termed the Self-Consistent Global Mode (SCGM) model—that addresses the conceptual gap between fundamental physics, quantum non-locality, and high-level emergent phenomenology. Drawing from relational quantum mechanics, integrated information theory, and the non-local real properties of the universe, we posit that the observable universe represents a single, self-consistent mathematical solution within a broader Hilbert space topology. Rather than treating fundamental physical laws as isolated mechanical constraints, the SCGM model formulates them as structural expressions of a fundamental, information-based "source code." Under this framework, dark matter, dark energy, and non-local quantum correlations are reinterpreted not as missing physical entities, but as boundary conditions, geometric tensions, or marginal projections between adjacent global modes of higher structural coherence. Furthermore, the paper explores how conscious observation and intentional systems might interact with these fundamental informational conduits. By framing physical reality as a hierarchical network of self-consistent modes, this model provides a non-dogmatic, logically structured foundation aimed at fostering future mathematical formalization and empirical testing regarding the nature of physical law and observer-system interactions.

•Oct 30, 2026•0 citations
A model for a system consisting of elements which detect the measurement apparatus of other elements is proposed. By any apparatus one can observe locally, however it can refer to non‐local property because apparatus itself is indefinite. In taking this aspect into consideration, I formulate expressions for a local interaction referring to non‐local property. This formalization can satisfy the aspect of what is called, internal measurement. This system shows teleological global motion toward criticality which is relevant to the degeneracy of a specific element featuring D ? Hom(Z), E) by which infinite time and space are renormalized.
It has been suggested that the measuring apparatus used to measure quantum systems ought to be idealized as consisting of an infinite number of quantum systems. Let us call this the infinity assumption. The suggestion that we ought to make the infinity assumption has been made in connection with two closely related but distinct problems. One is the problem of determining the importance of the limitations on measurement incorporated into the Wigner-Araki-Yanase quantum theory of measurement. The other is the measurement problem. These problems are not internal to the quantum mechanical formalism. They arise when we obtain particular formal results in applying the quantum mechanical formalism to measurement interactions. The formal results are problematic because they resist explanation. Various authors have claimed that by making the infinity assumption we can neglect the limitations on measurement. Bub (1988) and (1989) claims it allows us to solve the measurement problem. I will argue that both claims are unjustified.
We will give a new model for measurements of a quantum system, expressed as the compact operators on a Hilbert space, such that the measuring apparatuses are described by a unital separable non-type I nuclear simple C∗^*∗-algebra equipped with certain unital endomorphisms and pure states. An interaction between the quantum system and the apparatus is specified by a unitary associated with the combined system as before. Magnifying to the classical level some aspects of the quantum system so captured in the apparatus is explicitly done by applying the endomorphism; then the resulting state is the superposition of {\em phases} with weights. Nature will then choose each phase according to the probability prescribed by the weights just as does one when multiple phases appear as in phase transition. Thus in our model state-reduction (or collapse of the wave function) is a primary event; whether this corresponds to the measurement of an observable or which one if it does is another matter.
Introduction Indefinite causal structure poses particular problems for theory formulation since many of the core ideas used in the usual approaches to theory construction depend on having definite causal structure. For example, the notion of a state across space evolving in time requires that we have some definite causal structure so we can define a state on a space-like hypersurface. We will see that many of these problems are mitigated if we are able to formulate the theory in a formalism-local (or F-local) fashion. A formulation of a physical theory is said to be F-local if, in making predictions for any given arbitrary space-time region, we need only refer to mathematical objects pertaining to that region. This is a desirable property both on the grounds of efficiency and since, if we have indefinite causal structure, it is not clear how to select some other space-time region on which our calculations may depend. The usual ways of formulating physical theories (the time-evolving state picture, the histories approach, and the local-equations approach) are not F-local. We set up a framework for probabilistic theories with indefinite causal structure. This, the causaloid framework, is F-local. We describe how quantum theory can be formulated in the causaloid framework (in an F-local fashion). This provides yet another formulation of quantum theory. This formulation, however, may be particularly relevant to the problem of finding a theory of quantum gravity. The problem of quantum gravity is to find a theory that reduces in appropriate limits to general relativity and quantum theory (including, at least, those situations in which those two theories have been experimentally confirmed).
This paper proposes an integrative ontological framework—termed the Self-Consistent Global Mode (SCGM) model—that addresses the conceptual gap between fundamental physics, quantum non-locality, and high-level emergent phenomenology. Drawing from relational quantum mechanics, integrated information theory, and the non-local real properties of the universe, we posit that the observable universe represents a single, self-consistent mathematical solution within a broader Hilbert space topology. Rather than treating fundamental physical laws as isolated mechanical constraints, the SCGM model formulates them as structural expressions of a fundamental, information-based "source code." Under this framework, dark matter, dark energy, and non-local quantum correlations are reinterpreted not as missing physical entities, but as boundary conditions, geometric tensions, or marginal projections between adjacent global modes of higher structural coherence. Furthermore, the paper explores how conscious observation and intentional systems might interact with these fundamental informational conduits. By framing physical reality as a hierarchical network of self-consistent modes, this model provides a non-dogmatic, logically structured foundation aimed at fostering future mathematical formalization and empirical testing regarding the nature of physical law and observer-system interactions.