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In physics, every observation is made with respect to a frame of reference. Although reference frames are usually not considered as degrees of freedom, in all practical situations it is a physical system which constitutes a reference frame.…
Historically, appearance of the quantum theory led to a prevailing view that Nature is indeterministic. The arguments for the indeterminism and proposals for indeterministic and deterministic approaches are reviewed. These include collapse…
We comment on the fact that certain mathematical models that have been proposed in the quantum gravity literature, may not be subject to experimental checks, even if they turn out to be mathematically well defined. This means that they…
In quantum gravity there is no notion of absolute time. Like all other quantities in the theory, the notion of time has to be introduced "relationally", by studying the behavior of some physical quantities in terms of others chosen as a…
How the objective everyday world emerges from the underlying quantum behaviour of its microscopic constituents is an open question at the heart of the foundations of quantum mechanics. Quantum Darwinism and spectrum broadcast structure are…
We study the expressive power of fragments of inclusion and independence logic defined either by restricting the number of universal quantifiers or the arity of inclusion and independence atoms in formulas. Assuming the so-called lax…
The notion of a macroscopic quantum state must be pinned down in order to assess how well experiments probe the large-scale limits of quantum mechanics. However, the issue of quantifying so-called quantum macroscopicity is fraught with…
Determining the physical Hilbert space is often considered the most difficult but crucial part of completing the quantization of a constrained system. In such a situation it can be more economical to use effective constraint methods, which…
Relativistic positioning systems are interesting {\em technical objects} for applications around the Earth and in the Solar system. But above all else, they are basic {\em scientific objects} allowing developing relativity from its own…
We extend the treatment of functional dependence, the basic concept of dependence logic, to include the possibility of dependence with a limited number of exceptions. We call this approximate dependence. The main result of the paper is a…
Quantum reference frames provide a relational description of multipartite quantum systems in which physical states and observables are defined relative to quantum observers. Yet different observers can assign different entropies to the same…
Let $R$ denote a 2-fir. The notions of F-independence and algebraic subsets of R are defined. The decomposition of an algebraic subset into similarity classes gives a simple way of translating the F-independence in terms of dimension of…
Set-theoretical, physical, and intuitive notions of continuum are compared. It is shown that the independence of the continuum hypothesis determines status and properties of the set of intermediate cardinality. The intermediate set is a…
The possibility of a quantum system to exhibit properties that are akin to both the classically held notions of being a particle and a wave, is one of the most intriguing aspects of the quantum description of nature. These aspects have been…
It is argued that in the description of macroscopic systems inside quantum mechanics the study of the dynamics of selected degrees of freedom slowly varying on a suitable time scale, corresponding to relevant observables for the given…
We claim that both multipartiteness and localization of subsystems of compound quantum systems are of an essentially relative nature crucially depending on the set of operationalistically available states. In a more general setting, to…
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…
Some physical consequences of the negation of the continuum hypothesis are considered. It is shown that quantum and classical mechanics are component parts of the multicomponent description of the set of variable infinite cardinality.…
The ontology proposed in this paper is aimed at demonstrating that it is possible to understand the counter-intuitive predictions of quantum mechanics while still retaining much of the framework underlying classical physics, the implication…
We introduce an algebraic framework for interacting quantum systems that enables studying complex phenomena, characterized by the coexistence and competition of various broken symmetry states of matter. The approach unveils the hidden unity…