Related papers: Cutkosky Rules and Outer Space
A new varying-$c$ cosmological model constructed using two additional assumptions, which was introduced in our previous work, is briefly reviewed and the dynamic equation of the model is derived distinctly from a semi-Newtonian approach.…
We propose uncertainty relations for the different coordinates of spacetime events, motivated by Heisenberg's principle and by Einstein's theory of classical gravity. A model of Quantum Spacetime is then discussed where the commutation…
In this paper we introduce a new kind of topological space, called 'structured space', which locally resembles various kinds of algebraic structures. This can be useful, for instance, to locally study a space that cannot be globally endowed…
The definitions of gravitational work as well as work done by the total external force on a massive probe particle moving in generic spacetime backgrounds are proposed. These definitions are given in the form of scalar integrals and thus,…
We have already shown how a modified Friedmann equation, originating from a model of the Universe built from a certain $W_3$ algebra, is able to explainthe difference between the Hubble constants extracted from CMB data and from local…
Old and new puzzles of cosmology are reexamined from the point of view of quantum theory of the universe developed here. It is shown that in proposed approach the difficulties of the standard cosmology do not arise. The theory predicts the…
We start from classical general relativity coupled to matter fields. Each configuration variable and its conjugate momentum, as also space-time points, are raised to the status of matrices [equivalently operators]. These matrices obey a…
This paper discusses an ordinary homogeneous differential equation of the second order with constant real-valued coefficients. The solution of this equation has to satisfy additional conditions. The first of the conditions stems from the…
The cosmological models in the frame of the Newtonian and general relativistic treatments are considered. The centrifugal forces acting between particles rotating randomly around each other are shown to be able to reverse gravitational…
We discuss two topics that are usually considered to be exclusively "quantum": the Schroedinger equation, and the uncertainty principle. We show (or rather recall) that the Schroedinger equation can be derived from Hamilton's equations…
A literature review of related articles, either by affinity or by contrast, to a fundamental theory of time and space - time previously developed. It shows how from a primitive concept of preparticle and membership relation of set theory,…
We compare classical and quantum dynamics of a particle in the de Sitter spacetimes with different topologies to show that the result of quantization strongly depends on global properties of a classical system. We present essentially…
We prove that, under suitable assumptions, operationally motivated data completely determine a space-time in which the quantum systems can be interpreted as evolving. At the same time, the dynamics of the quantum system is also determined.…
We regard the background of space-time as a physical system composed of discrete volume elements at the Planck scale and get the internal energy of space-time by Debye model. A temperature-dependent minimum energy limit of the particles is…
We develop the spectral point of view on geometry based on the formalism of quantum physics. We start from the simple physical question of specifying our position in space and explain how the spectral geometric point of view provides a new…
The aim of this article is to promote the use of probabilistic methods in the study of problems in mathematical general relativity. Two new and simple singularity theorems, whose features are different from the classical singularity…
General relativity and quantum mechanics provide a natural explanation for the existence of dark energy with its observed value and predict its dynamics. Dark energy proves to be necessary for the existence of space-time itself and…
We investigate structure that describes physical data in gravitational systems that is, to one degree or another, independent of the metric and affine structure. We dub such structure surplus structure and seek to incorporate it into our…
We show how the Minkowskian space-time emerges from a topologically homogeneous causal network, presenting a simple analytical derivation of the Lorentz transformations, with metric as pure event-counting. The derivation holds generally for…
A notion of local algebras is introduced in the theory of causal fermion systems. Their properties are studied in the example of the regularized Dirac sea vacuum in Minkowski space. The commutation relations are worked out, and the…