相关论文: Categorical Foundations for Physics - I: Program a…

Category theory plays a special character in mathematics - it unifies distinct branches under the same formalism. Despite this integrative power in math, it also seems to provide the proper foundations to the experimental physicist. In this…

Category theory has become central to certain aspects of theoretical physics. Bain [Synthese, 190:1621--1635 (2013)] has recently argued that this has significance for ontic structural realism. We argue against this claim. In so doing, we…

A general information-theoretic framework for deriving physical laws is presented and a principle of informational physics is enunciated within its context. Existing approaches intended to derive physical laws from information-theoretic…

The growing complexity of modern practical problems puts high demands on the mathematical modelling. Given that various models can be used for modelling one physical phenomenon, the role of model comparison and model choice becomes…

The recent trend in mathematics is towards a framework of abstract mathematical objects, rather than the more concrete approach of explicitly defining elements which objects were thought to consist of. A natural question to raise is whether…

There exists a dispute in philosophy, going back at least to Leibniz, whether is it possible to view the world as a network of relations and relations between relations with the role of objects, between which these relations hold, entirely…

In this paper we develope a categorical theory of relations and use this formulation to define the notion of quantization for relations. Categories of relations are defined in the context of symmetric monoidal categories. They are shown to…

Underlying any theory of physics is a layer of conceptual frames. They connect the mathematical structures used in theoretical models with physical phenomena, but they also constitute our fundamental assumptions about reality. Many of the…

The theory of measurement is employed to elucidate the physical basis of general relativity. For measurements involving phenomena with intrinsic length or time scales, such scales must in general be negligible compared to the (translational…

The study of complex systems through the lens of category theory consistently proves to be a powerful approach. We propose that cognition deserves the same category-theoretic treatment. We show that by considering a highly-compact cognitive…

Along with weaving together observations, experiments, and theoretical constructs into a coherent mesh of understanding of the world around us, physics over its past five centuries has continuously refined the base concepts on which the…

We discuss the nature and a general formulation of the relativity principle and we show that it can be justified starting from a strictly operational point of view. We give some remark on the connection with the spacetime symmetry groups.…

In this note, we discuss the significance of the general principle of relativity for a physical theory that abandons the newtonian concept of force and, hence, uses an entirely different conception for the ``cause'' behind motions of…

Every physical theory has (at least) two different forms of mathematical equations to represent its target systems: the dynamical (equations of motion) and the kinematical (kinematical constraints). Kinematical constraints are…

We argue that category theory should become a part of the daily practice of the physicist, and more specific, the quantum physicist and/or informatician. The reason for this is not that category theory is a better way of doing mathematics,…

General relativity and quantum mechanics have both revealed the relativity of certain notions that were previously thought to be absolute. I clarify the precise sense in which these theories are relational, and I argue that the various…

The paper discusses from a metaphysical standpoint the nature of the dependence relation underpinning the talk of mutual action between material and spatiotemporal structures in general relativity. It is shown that the standard analyses of…

Questions of set-theoretic size play an essential role in category theory, especially the distinction between sets and proper classes (or small sets and large sets). There are many different ways to formalize this, and which choice is made…

In this paper we give a contribution to the taxonomy of physical theories. We provide here a thorough description of the axiomatic foundations of the most relevant physical theories, Mechanics, Special Relativity, General Relativity,…

The distinction between a theory's kinematics and its dynamics, that is, between the space of physical states it posits and its law of evolution, is central to the conceptual framework of many physicists. A change to the kinematics of a…