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Izumi Ojima

Publications and source records attributed to Izumi Ojima.

At least 19 recordsLinked to original sources
arXiv2024

Reexamination of the hierarchy problem from a novel geometric perspective

A lucid interpretation of the longstanding hierarchy problem is proposed based on the unconventional model of the universe recently proposed by the authors. Our heuristic cosmological model is developed by considering Penrose and Petit's original ideas as the Weyl curvature hypothesis, conformal cyclic cosmology, and the twin universe model. The uniqueness of our model lies in its incorporation of dark energy and matter, and its single key parameter, adjusted by observational data, is the radius ($R_{dS}$) of a four-dimensional ($4D$) hypersphere called de Sitter space. We presuppose that our $4D$ universe originated from the spontaneous conformal symmetry (SCS) breaking of a light field with a null distance. We show that in this SCS breaking state, the energy--momentum tensor of the space-like electromagnetic field, whose existence is inevitable for quantum electromagnetic field interactions (Greenberg--Robinson theorem), becomes isomorphic to the divergence-free Einstein tensor in the general theory of relativity. Furthermore, we reveal the $R_{dS}$ dependency of the $4D$ gravitational field. Based on these findings, we show an intriguing relation between the magnitude of the gravitational coupling constant and $R_{dS}$. A solution to the hierarchy problem is derived by assuming that $R_{dS}$ depends on the "newly defined cosmological time".

physics.gen-ph↗
arXiv2022

Conserved relativistic Ertel's current generating the vortical and thermodynamic aspects of spacetime

Motivated by Aoki et al.'s recent research on conserved charges and entropy current, we investigated the conservation of relativistic Ertel's current, which has received little attention outside the field of geophysical fluid dynamics. Ertel's charge is an important indicator of the correlation between vortex vectors and entropy gradient fields in Earth's meridional heat transport. We first show that in the generalized Hamiltonian structure of baroclinic fluids, the duality between the total energy and the Casimir as a function of Ertel's charge plays an important role in the nonrelativistic case. Then, by extending the result to relativistic cases, we show that this finding has far-reaching implications not only for spacetime issues in cosmology but also for the foundation of quantum field theory. An especially important finding is that, as an unreported dual form of the Einstein field equation, we identify a special equation satisfied not only by the vortex tensor field generated by the conserved charge but also by the Weyl tensor in interpreting the physical nature of the metric tensor $g^{μν}$, which appears in the cosmological term $Λg^{μν}$.

gr-qc↗
arXiv2018

Category theory as a foundation for soft robotics

Soft robotics is an emerging field of research where the robot body is composed of compliant and soft materials. It allows the body to bend, twist, and deform to move or to adapt its shape to the environment for grasping, all of which are difficult for traditional hard robots with rigid bodies. However, the theoretical basis and design principles for soft robotics are not well-founded despite their recognized importance. For example, the control of soft robots is outsourced to morphological attributes and natural processes; thus, the coupled relations between a robot and its environment are particularly crucial. In this paper, we propose a mathematical foundation for soft robotics based on category theory, which is a branch of abstract math where any notions can be described by objects and arrows. It allows for a rigorous description of the inherent characteristics of soft robots and their relation to the environment as well as the differences compared to conventional hard robots. We present a notion called the category of mobility that well describes the subject matter. The theory was applied to a model system and analysis to highlight the adaptation behavior observed in universal grippers, which are a typical example of soft robotics. This paper paves the way to developing a theoretical background and design principles for soft robotics.

cs.RO↗
arXiv2018

Local reservoir model for choice-based learning

Decision making based on behavioral and neural observations of living systems has been extensively studied in brain science, psychology, and other disciplines. Decision-making mechanisms have also been experimentally implemented in physical processes, such as single photons and chaotic lasers. The findings of these experiments suggest that there is a certain common basis in describing decision making, regardless of its physical realizations. In this study, we propose a local reservoir model to account for choice-based learning (CBL). CBL describes decision consistency as a phenomenon where making a certain decision increases the possibility of making that same decision again later, which has been intensively investigated in neuroscience, psychology, etc. Our proposed model is inspired by the viewpoint that a decision is affected by its local environment, which is referred to as a local reservoir. If the size of the local reservoir is large enough, consecutive decision making will not be affected by previous decisions, thus showing lower degrees of decision consistency in CBL. In contrast, if the size of the local reservoir decreases, a biased distribution occurs within it, which leads to higher degrees of decision consistency in CBL. In this study, an analytical approach on local reservoirs is presented, as well as several numerical demonstrations. Furthermore, a physical architecture for CBL based on single photons is discussed, and the effects of local reservoirs is numerically demonstrated. Decision consistency in human decision-making tasks and in recruiting empirical data are evaluated based on local reservoir. In summary, the proposed local reservoir model paves a path toward establishing a foundation for computational mechanisms and the systematic analysis of decision making on different levels.

stat.ML↗
arXiv2016

Local state and sector theory in local quantum physics

We define a new concept of local states in the framework of algebraic quantum field theory (AQFT). Local states are a natural generalization of states and give a clear vision of localization in the context of QFT. In terms of them, we can find a condition from which follows automatically the famous DHR selection criterion in DHR-DR theory. As a result, we can understand the condition as consequences of physically natural state preparations in vacuum backgrounds. Furthermore, a theory of orthogonal decomposition of completely positive (CP) maps is developed. It unifies a theory of orthogonal decomposition of states and order structure theory of CP maps. By using it, localized version of sectors is formulated, which gives sector theory for local states with respect to general reference representations.

math-ph↗
arXiv2015

Photon localization revisited

In the light of Newton-Wigner-Wightman theorem of localizability question, we have proposed before a typical generation mechanism of effective mass for photons to be localized in the form of polaritons owing to photon-media interactions. In this paper, the general essence of this example model is extracted in such a form as Quantum Field Ontology associated with Eventualization Principle, which enables us to explain the mutual relations back and forth, between quantum fields and various forms of particles in the localized form of the former.

quant-ph↗
arXiv2013

Notes on the Krupa-Zawisza Ultrapower of Self-Adjoint Operators

It is known that there is a difficulty in constructing the ultrapower of unbounded operators. Krupa and Zawisza gave a rigorous definition of the ultrapower A^{omega} of a selfadjoint operator A. In this note, we give alternative description of A^{omega} and the Hilbert space H(A) on which A^{omega} is densely defined, which provides a criterion to determine to which representing sequence (ξ_n)n of a given vector ξin dom(A^{omega}) has the property that A^{omega}ξ= (Aξ_n)_{omega} holds.

math.FA↗
arXiv2013

Derivation of Born Rule from Algebraic and Statistical Axioms

In the present paper we propose a new axiomatic system of algebraic and statistical axioms as working hypotheses, from which Born rule can be seen to emerge. In this process the concept of sectors defined as quasi-equivalence classes of factor states plays a crucial role.

quant-ph↗
arXiv2013

No Zero Divisor for Wick Product in $(S)^{\ast}$}

In White Noise Analysis (WNA), various random quantities are analyzed as elements of $(S)^{\ast}$, the space of Hida distributions ([1]). Hida distributions are generalized functions of white noise, which is to be naturally viewed as the derivative of the Brownian motion. On $(S)^{\ast}$, the Wick product is defined in terms of the $\mathcal{S}$-transform. We have found such a remarkable property that the Wick product has no zero devisors among Hida distributions. This result is a WNA version of Titchmarsh's theorem and is expected to play fundamental roles in developing the \textquotedblleft operational calculus\textquotedblright in WNA along the line of Mikusiński's version for solving differential equations.

math-ph↗
arXiv2011

New Interpretation of Equivalence Principle in General Relativity from the viewpoint of Micro-Macro duality

We propose a new interpretation of the equivalence principle underlying Einstein's general relativity: a free-falling frame with gravitational force eliminated locally in a small spacetime region shows the existence of a boundary level, below which gravity is absent and above which \textit{gravity emerges as condensation effect of microscopic motions} within each such frame and interrelates free-falling frames at different spacetime points. In this picture, gravitational field as a mediator of different free-falling frames shows a remarkable \textit{parallelism with an order parameter to specify "degenerate vacua"} in different thermodynamic pure phases due to the \textit{condensation effects} in phase transitions. As the physical basis of general relativity is found in the universality of mass point motions due to the constancy of [inertial $m$]/[gravitational $m$], the general relativistic notion of "spacetime" should be meaningful only in the validity regime of this constancy, which is \textit{of empirical nature}, contrary to the usual consensus. At the end, we comment on the impossibility to observe gravitational waves which would make gravitons and quantum gravity questionable.

physics.gen-ph↗
arXiv2011

Large Deviation Strategy for Inverse Problem

Taken traditionally as a no-go theorem against the theorization of inductive processes, Duhem-Quine thesis may interfere with the essence of statistical inference. This difficulty can be resolved by Micro-Macro duality \cite{Oj03, Oj05} which clarifies the importance of specifying the pertinent aspects and accuracy relevant to concrete contexts of scientific discussions and which ensures the matching between what to be described and what to describe in the form of the validity of duality relations. This consolidates the foundations of the inverse problem, induction method, and statistical inference crucial for the sound relations between theory and experiments. To achieve the purpose, we propose here Large Deviation Strategy (LDS for short) on the basis of Micro-Macro duality, quadrality scheme, and large deviation principle. According to the quadrality scheme emphasizing the basic roles played by the dynamics, algebra of observables together with its representations and universal notion of classifying space, LDS consists of four levels and we discuss its first and second levels in detail, aiming at establishing statistical inference concerning observables and states. By efficient use of the central measure, we will establish a quantum version of Sanov's theorem, the Bayesian escort predictive state and the widely applicable information criteria for quantum states in LDS second level. Finally, these results are reexamined in the context of quantum estimation theory, and organized as quantum model selection, i.e., a quantum version of model selection.

quant-ph↗
arXiv2011

Roles of Asymptotic Condition and S-Matrix as Micro-Macro Duality in QFT

Various versions of "independence" are actively inverstigated in quantum probability. In the context of relativistic QFT, we show here that the physical origin of "independence" can be sought in the asymptotic condition through which asymptotic fields and states exhibiting the independence emerge from the non-independent interacting Heisenberg fields in a kind of "central limit". From the algebraic viewpoint, this condition is equivalent to the on-shell condition to pick up free one-particle modes, which also reduces to Einstein's famous formula $E=mc^{2}$. A scenario to reconstruct interacting Heisenberg fields as Micro-objects from these "independent" =free Macro-objects intertwined by an S-matrix as a measurable quantity is formulated according to the Micro-Macro Duality associated with a new notion of a \textit{cocycle of K-T operators}.

physics.gen-ph↗
arXiv2011

Space(-Time) Emergence as Symmetry Breaking Effect

The microscopic origin of space(-time) geometry is explained on the basis of an emergence process associated with the condensation of infinite number of microscopic quanta responsible for symmetry breakdown, which implements the basic essence of "Quantum-Classical Correpondense" and of the forcing method in physical and mathematical contexts, respectively. From this viewpoint, the space(-time) dependence of physical quantities arises from the "logical extension" OjiOza to change "constant objects" into "variable objects" by tagging the order parameters associated with the condensation onto "constant objects"; the logical direction here from a value y to a domain variable x (to materialize the basic mechanism behind the Gel'fand isomorphism) is just opposite to that common in the usual definition of a function f:x->f(x) from its domain variable x to a value y=f(x).

physics.gen-ph↗
arXiv2011

Who has seen a free photon?

While the notion of the position of photons is indispensable in the quantum optical situations, it has been known in mathematical physics that any position operator cannot be defined for a massless free particle with a non-zero finite spin. This dilemma is resolved by introducing the "effective mass" of a photon due to the interaction with matter. The validity of this interpretation is confirmed in reference to the picture of "polariton", a basic notion in optical and solid physics. In this connection, we discuss the long-standing controversy between Minkowski's and Abraham's definitions of the momenta of a photon in media from the general viewpoint adopted in the appendix.

physics.gen-ph↗
arXiv2008

A Unified Scheme of Measurement and Amplification Processes based on Micro-Macro Duality -- Stern-Gerlach experiment as a typical example

A unified scheme for quantum measurement processes is formulated on the basis of Micro-Macro duality as a mathematical expression of the general idea of quantum-classical correspondence. In this formulation, we can naturally accommodate the amplification processes necessary for magnifying quantum state changes at the microscopic end of the probe system into the macroscopically visible motion of the measuring pointer. Its essence is exemplified and examined in the concrete model of the Stern-Gerlach experiment for spin measurement, where the Helgason duality controlling the Radon transform is seen to play essential roles.

math-ph↗
arXiv2007

Micro-Macro Duality and Emergence of Macroscopic Levels

The mutual relation between quantum Micro and classical Macro is clarified by a unified formulation of instruments describing measurement processes and the associated amplification processes, from which some perspective towards a description of emergence processes of spacetime structure is suggested.

math-ph↗
arXiv2006

How to Observe Quantum Fields and Recover Them from Observational Data? -- Takesaki Duality as a Micro-Macro Duality --

After the mathematical notion of "Micro-Macro Duality" for understanding mutual relations between microsopic quantum systems (Micro) and their macroscopic manifestations (Macro) is explained on the basis of the notion of sectors and order parameters, a general mathematical scheme is proposed for detecting the state-structure inside of a sector through measurement processes of a maximal abelian subalgebra of the algebra of observables. For this purpose, the Kac-Takesaki operators controlling group duality play essential roles, which naturally leads to the composite system of the observed system and the measuring system formulated by a crossed product. This construction of composite systems will be shown to make it possible for the Micro to be reconstructed from its observational data as Macro in the light of the Takesaki duality for crossed products.

math-ph↗