Related papers: Physics over a finite field and Wick rotation
A general formulation of classical relativistic particle mechanics is presented, with an emphasis on the fact that superluminal velocities and nonlocal interactions are compatible with relativity. Then a manifestly relativistic-covariant…
A quantum mechanics representation based on position ($\vec{r}$), linear momentum($\vec{p}$) and energy($E$) eigenvalues is presented here. A set of equations, explicitly independent on wave function, was derived relating these observables.…
The stipulation that no measurable quantity could have an infinite value is indispensable in physics. At the same time, in mathematics, the possibility of considering an infinite procedure as a whole is usually taken for granted. However,…
We combine the ideas of Dirac's orthonormal representation, Everett's relative state, and 't Hooft's ontological basis to define the notion of a world for quantum mechanics. Mathematically, for a quantum system $\mathcal{Q}$ with an…
We strengthen the case that the new logical perspective afforded by topos theory is suitable to the task of describing the physical world around us. In exploring some of the aspects of construction of a simple quantum-mechanical system in a…
The strong proper time dilation and radial contraction in the gravitational field of compact sources leads to a frozen state of matter. It is shown that the falling particles and photons can not cross the gravitational radius due to the…
The Friedman-Lemaitre-Robertson-Walker (FLRW) cosmological models are based on the assumptions of large-scale homogeneity and isotropy of the distribution of matter and energy. They are usually taken to have spatial sections that are simply…
What is the shape of the Universe? Is it curved or flat, finite or infinite ? Is space "wrapped around" to create ghost images of faraway cosmic sources? We review how tessellations allow to build multiply-connected 3D Riemannian spaces…
We provide an informal discussion of pattern formation in a finite universe. The global size and shape of the universe is revealed in the pattern of hot and cold spots in the cosmic microwave background. Topological pattern formation can be…
Active motion is a concept in complex systems theory and was successfully applied to various problems in nonlinear dynamics. Explicit studies for gravitational potentials were missing so far. We interpret the Friedmann equations with…
The hypothesis of a discrete fabric of the universe--the "Planck scale"--is always on stage, since it solves mathematical and conceptual problems in the infinitely small. However, it clashes with special relativity, which is designed for…
An oscillating universe cycles through a series of expansions and contractions. We propose a model in which ``phantom'' energy with a supernegative pressure ($p < - \rho$) grows rapidly and dominates the late-time expanding phase. The…
Much of the twentieth century physics has considered rigid laws-- even Quantum Mechanics and Statistical Mechanics were based on such laws. These laws operated in a smooth spacetime manifold. However more recent approaches as in Quantum…
{\it If gravity is a metric field by Einstein, it is a Higgs field.} Gravitation theory meets spontaneous symmetry breaking in accordance with the Equivalence Principle reformulated in the spirit of Klein-Chern geometries of invariants. In…
The dynamics of the expanding universe is analyzed in terms of the quantum geometrodynamical model. It is shown that the equations of quantum theory in the form of the eigenvalues equation similar to the stationary Schr\"{o}dinger equation…
I suggest that the Spin-Statistics connection is a consequence of the phase shifts on quantum scattering amplitudes due to the induced gravitomagnetic field of the whole Universe at critical density. This connection was recently brought out…
The universe media is considered as a non-perfect fluid with bulk viscosity and described by a more general equation of state. We assume the bulk viscosity is a linear combination of the two terms: one is constant, and the other is…
This is a broad and in places unconventional overview of the strengths and shortcomings of our standard models of fundamental physics and of cosmology. The emphasis is on ideas that have accessible experimental consequences. It becomes…
Is field space infinite? If not, it either loops back on itself or ends altogether. Periodic boundary conditions are of course familiar, but field space endpoints--which appear in real-world systems--are far less explored. In this paper we…
The universe we observe is homogeneous on super-horizon scales, leading to the ``cosmic homogeneity problem''. Inflation alleviates this problem but cannot solve it within the realm of conservative extrapolations of classical physics. A…