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Lenses, optics and dependent lenses (or equivalently morphisms of containers, or equivalently natural transformations of polynomial functors) are all widely used in applied category theory as models of bidirectional processes. From the…

We present an overview on relational observables in gravity mainly from a loop quantum gravity perspective. The gauge group of general relativity is the diffeomorphism group of the underlying manifold. Consequently, general relativity is a…

Our notions of what is physically 'real' have long been based on the idea that the real is what is immediately apprehended, that is the local or observable, the physically tangible, though there has always been an alternative philosophical…

There is a deeply entrenched view in philosophy and physics, the closed systems view, according to which isolated systems are conceived of as fundamental. On this view, when a system is under the influence of its environment this is…

This paper addresses the following main question: Do we have a theoretical understanding of entanglement applicable to a full variety of physical settings? It is clear that not only the assumption of distinguishability, but also the…

This paper has been withdrawn by the author. In this short paper I present a new approach to the problem of measurement, based on the difference between language (reality) and meta-language (meta-reality). This way, it will be shown as the…

This paper explores how a pluralist view can arise in a natural way out of the day-to-day practice of modern set theory. By contrast, the widely accepted orthodox view is that there is an ultimate universe of sets $V$, and it is in this…

I show that, by the same criteria that led to Galilean and Special Relativity and gauge symmetries, there is no way to identify a unique set of observables that give the structure of space or spacetime. In some sense, space is lost in the…

Human beings do not observe the world from the outside, but rather are fully embedded in it. The sciences, however, often give the observer both a "god's eye" perspective and substantial a~priori knowledge. Motivated by W. Ross Ashby's…

We study the relationship between assumptions of state separability and both preparation and measurement contextuality, and the relationship of both of these to the frame problem, the problem of predicting what does not change in…

We consider two concepts often discussed as significant features of general relativity (particularly when contrasted with the other forces of the Standard Model): background independence and diffeomorphism invariance. We remind the reader…

Machine learning models increasingly function as representational systems, yet the philosoph- ical assumptions underlying their internal structures remain largely unexamined. This paper develops a structuralist decision framework for…

In this paper the notion of the rigid frame of reference within special relativity is analysed. Three definitions of rigidity are formulated. By using several examples of non-inertial frames, it is shown that these definitions are not…

We make a critical comparison of relativistic and non-relativistic classical and quantum mechanics of particles in inertial frames and of the open problems in particle localization at the two levels. The solution of the problems of the…

There are several first-order logic (FOL) axiomatizations of special relativity theory in the literature, all looking essentially different but claiming to axiomatize the same physical theory. In this paper, we elaborate a comparison, in…

We propose a distinction between the physical and the mathematical parts of gauge field theories. The main problem we face is to uphold a strong and meaningful criterion of what is physical. We like to call it "Field's dilemma", referring…

The problem of comparing concepts of dependence in general rough sets with those in probability theory had been initiated by the present author in some of her recent papers. This problem relates to the identification of the limitations of…

I defend algebraicism, according to which physical fields can be understood in terms of their structural relations without reference to a spacetime manifold, as a genuine relationalist view against the conventional wisdom that it is…

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…

Physics is a model of nature able to both describe and predict the results of measurements made with respect to reference systems. These reference systems, in turn, are themselves physical and thus subject to the laws of physics. The…