Related papers: Universal constants and natural systems of units i…
We consider an inverse variational problem for the lines of constant curvature in (pseudo-)Euclidean two-, three-, and four-dimensional spaces. The accumulated results are physically meaningful in the case of relativistic mechanics of…
We consider a two-dimensional model of gravity with the cosmological constant as a dynamical variable. The effective cosmological constant is derived when the universe has no initial boundary. It turns out to be extremely small if the…
Four-dimensional spacetime, together with a natural generalisation to extra dimensions, is obtained through an analysis of the structures and symmetries deriving from possible arithmetic expressions for one-dimensional time. On taking the…
We propose that the constants of Nature we observe (which appear as parameters in the classical action) are quantum observables in a kinematical Hilbert space. When all of these observables commute, our proposal differs little from the…
The quest to understand better the nature of the initial cosmological singularity is with us since the discovery of the expanding universe. Here, we propose several non-flat models, among them the standard cosmological scenario with a…
Anomalous diffusion phenomena have been observed in many complex physical and biological systems. One significant advance recently is the physical extension of particle's motion in static medium to uniformly (and even nonuniformly)…
One unusual property of dynamic systems, whose state is characterized by a set of scalar dynamic variables satisfying a system of differential equations of a general form, is considered. This property is related to the behavior of equations…
We describe here, for the first time, a lower bound on the total number of fundamental constants required for a mathematical description of our physical universe to be complete. The answer is shown to be one. The formal arithmetized…
Introducing a general class of one-dimensional single-file systems (meaning that particle crossings are prohibited) of interacting hardcore particles with internal degrees of freedom (called charge), we exhibit a novel type of dynamical…
Theoretical and observational arguments are listed in favor of a new principle of relativity of units of measurements as the basis of a conformal-invariant unification of General Relativity and Standard Model by replacement of all masses…
A new proof of the impossibility of a universal quantum-classical dynamics is given. It has at least two consequences. The standard paradigm ``quantum system is measured by a classical apparatus" is untenable, while a quantum matter can be…
We discuss here the significance of the generalization of the newtonian concept of force by that of a transformation of a certain Standard Borel Space of cardinality $\mathbf{c}$ of the continuum as the ``cause'' behind motions of material…
I give metrics and equations of motion in 5D general relativity, and use the conservation of momentum and conformal transformations to study the possible variability of particle masses and the cosmological 'constant'. It is feasible that…
We prove a general multidimensional invariance principle for a family of U-statistics based on freely independent non-commutative random variables of the type $U_n(S)$, where $U_n(x)$ is the $n$-th Chebyshev polynomial and $S$ is a standard…
Recent cosmological observations suggest the existence of a positive cosmological constant $\Lambda$ with the magnitude $\Lambda(G\hbar/c^3) \approx 10^{-123}$. This review discusses several aspects of the cosmological constant both from…
This article describes the various experimental bounds on the variation of the fundamental constants of nature. After a discussion on the role of fundamental constants, of their definition and link with metrology, the various constraints on…
In the late 1990s, observations of type Ia supernovae led to the astounding discovery that the universe is expanding at an accelerating rate. The explanation of this anomalous acceleration has been one of the great problems in physics since…
We set up a framework for a model-independent analysis of the time variation of $e$, $\hbar$, and $c$ indiviually. It is shown that the time-evolution of each constant can be determined uniquely from the time evolution of the fine structure…
A classical solution is called universal if the quantum correction is a multiple of the metric. Universal solutions consequently play an important role in the quantum theory. We show that in a spacetime which is universal all of the scalar…
We describe a MOND-related approach to natural scales of distance and mass, viewing it as a logical step following Planck's modification of the Stoney system of units. The MOND-induced scales are not based on the strength of any physical…