Related papers: Univalent foundations and the equivalence principl…
A question is proposed whether or not set theory is consistent.
Persistent homology is a popular and useful tool for analysing finite metric spaces, revealing features that can be used to distinguish sets of unlabeled points and as input into machine learning pipelines. The famous stability theorem of…
We challenge the view that there is a basic conflict between the fundamental principles of Quantum Theory and General Relativity, and in particular the fact that a superposition of massive bodies would lead to a violation of the Equivalence…
This thesis deals with General Probabilistic Theories (GPTs) and Entanglement Structures (ESs). An ES is a possible structure of a quantum composite system in GPTs, which is not uniquely determined as the Standard Entanglement Structure…
The equivalence principle (EP), as well as Schiff's conjecture, are discussed (en passant), and the connection between the EP and quantum mechanics is then briefly analyzed. Two semiclassical violations of the classical equivalence…
The Equivalence Principle is considered in the framework of metric-affine gravity. We show that it naturally emerges as a Noether symmetry starting from a general non-metric theory. In particular, we discuss the Einstein Equivalence…
Einstein Equivalence Principle (EEP) requires all matter components to universally couple to gravity via a single common geometry: that of spacetime. This relates quantum theory with geometry as soon as interactions with gravity are…
Statistical physics aims to describe properties of macroscale systems in terms of distributions of their microscale agents. Its central tool is the maximization of entropy, a variational principle. We review the history of this principle,…
It is demonstrated that, unless the meaning of conformal transformations for the underlying geometrical structure is discussed on a same footing as it is done for the equations of the given gravity theory, the notion of "conformal…
The quantum lens spaces form a natural and well-studied class of noncommutative spaces which can be subjected to classification using algebraic invariants by drawing on the fully developed classification theory of unital graph…
The equivalence test is a main part in any classification problem. It helps to prove bounds for the main parameters of the considered combinatorial structures and to study their properties. In this paper, we present algorithms for…
A chameleonic solution to the cosmological constant problem and the non-equivalence of different conformal frames at the quantum level have been recently suggested [Phys. Rev. D82 (2010) 044006]. In this article we further discuss the…
For a compact group G, we give a sufficient condition for embedding one G-equivariant vector bundle into another one and for a stable isomorphism between two such bundles to imply an isomorphism. Our criteria involve multiplicities of…
Being mathematics a natural language to Mankind and to physics, it must be constantly adapted to our necessities and our natural perception. Then, mathematical concepts are not absolute to reality. Although mathematical theories are…
We investigate two constructive approaches to defining quasi-compact and quasi-separated schemes (qcqs-schemes), namely qcqs-schemes as locally ringed lattices and as functors from rings to sets. We work in Homotopy Type Theory and…
There are two distinct definitions of 'P-value' for evaluating a proposed hypothesis or model for the process generating an observed dataset. The original definition starts with a measure of the divergence of the dataset from what was…
We show that a class of optimized e-value combinations, arising from a standard construction of e-processes, remains valid even when the tuning parameter is optimized based on the data. This result holds for independent e-values, and, more…
There have been various claims that the Equivalence Principle, as originally formulated by Einstein, presents several difficulties when extended to the quantum domain, even in the regime of weak gravity. Here we point out that by following…
Einstein's equivalence principle in classical physics is a rule stating that the effect of gravitation is locally equivalent to the acceleration of an observer. The principle determines the motion of test particles uniquely (modulo very…
An interesting test of Einstein's equivalence principle (EEP) relies on the observed lag in arrival times of photons emitted from extragalactic transient sources. Attributing the lag between photons of different energies to the…