arXiv subjects

M. I. Kalinin

Publications and source records attributed to M. I. Kalinin.

8 recordsLinked to original sources

arXiv2026

On the dual nature of a plane angle

For decades, metrologists have debated heatedly whether a plane angle is a dimensional or dimensionless quantity; whether it is a base quantity in the International System of Units (SI) or a derived quantity. Two main points of view have emerged in the international metrology community. Those who hold the first view believe that a plane angle is a dimensionless derived quantity equal to the ratio of two lengths, and its unit, the radian, is the dimensionless number one (1 rad = 1 m/m = 1). Those who hold the second view believe that a plane angle is a dimensional quantity with its own independent dimension, and its unit, the radian, is not the dimensionless number one, as is currently accepted in the SI. This article demonstrates that, depending on the physical situation, a plane angle is described by either a dimensional or a dimensionless quantity. When measuring, expressing, and communicating an angle's size, physicists use the dimensional quantity plane angle. Its dimension and unit are independent of the dimensions of other quantities and their units. This quantity, plane angle, should be classified as a base quantity, and its unit, radian, should be included in the class of base SI units. In theoretical studies of physical systems with angular quantities, the latter always enter into equations as a dimensionless combination of dimensional plane angles. This dimensionless combination, in turn, is also a physical quantity characterizing the plane angle in question. This new quantity is a dimensionless derived quantity, which physicists also call an angle.

physics.class-ph↗

arXiv2023

On the heat evolution of the early Universe

We discuss the heat history of the early Universe and its further evolution in the framework of modern cosmological models of general relativity (GR) and alternative theories of gravity. Of great importance are the new puzzling forms of matter comprising parts of our Universe, namely, dark energy and dark matter that crucially affect the Universe structure and evolution.

gr-qc↗

arXiv2018

On the status of plane and solid angles in the International System of Units (SI)

The article analyzes the arguments that became the basis for declaring in 1995, at the 20th General Conference on Weights and Measures that the plane and solid angles are dimensionless derived quantities in the International System of Units. The inconsistency of these arguments is shown. It is found that a plane angle is not a derived quantity in the SI, and its unit, the radian, is not a derived unit. A solid angle is the derived quantity of a plane angle, but not a length. Its unit, the steradian, is a coherent derived unit of the radian.

physics.class-ph↗

arXiv2014

On new definitions of SI base units. Why is the "atomic" kilogram preferable

We discuss the role of fundamental constants and measurement data for the Planck, Avogadro and Boltzmann constants and the elementary electric charge in connection with the planned transition to new definitions of four base SI units (the kilogram, mole, ampere and kelvin) in terms of fixed values of these constants. It is proposed to choose a new definition of any base SI unit in terms of a particular fundamental physical constant using a number of criteria, or principles, such as succession relative to the current SI, a sufficient stability of the new unit standards, and concordance between physical dimensions of the unit and the corresponding fundamental constant. It is argued that a redefinition of the kilogram and mole by fixing the values of the atomic mass unit and the Avogadro constant satisfies all these criteria and bears some more advantages against the version with fixed Planck constant: a well founded approach to definition of the ampere and the opportunity to preserve the current relationship between definitions of the mole and the kilogram. It is also argued that the kelvin can be redefined independently of the other three units.

physics.ins-det↗

arXiv2008

On completeness of description of an equilibrium canonical ensemble by reduced s-particle distribution function

In this article it is shown that in a classical equilibrium canonical ensemble of molecules with $s$-body interaction full Gibbs distribution can be uniquely expressed in terms of a reduced s-particle distribution function. This means that whenever a number of particles $N$ and a volume $V$ are fixed the reduced $s$-particle distribution function contains as much information about the equilibrium system as the whole canonical Gibbs distribution. The latter is represented as an absolutely convergent power series relative to the reduced $s$-particle distribution function. As an example a linear term of this expansion is calculated. It is also shown that reduced distribution functions of order less than $s$ don't possess such property and, to all appearance, contain not all information about the system under consideration.

cond-mat.stat-mech↗

arXiv2008

On one-to-one correspondence of Gibbs distribution and reduced two-particle distribution function

In this article it is shown that in an equilibrium classical canonical ensemble of molecules with two-body interaction and external field full Gibbs distribution can be uniquely expressed in terms of a reduced two-particle distribution function. This means that while a number of particles $N$ and a volume $V$ are fixed the reduced two-particle distribution function contains as much information about the equilibrium system as the whole canonical distribution. The latter is represented as an absolutely convergent power series relative to the reduced two-particle distribution function. As an example a linear term of this expansion is calculated. It is also shown that Gibbs distribution function can de expressed in terms of reduced distribution function of the first order and pair correlation function.That is the later two functions contain the whole information about system under consideration.

cond-mat.stat-mech↗

arXiv2006

On the cosmological constant in quantum cosmology

Quantization of a dust-like closed isotropic cosmological model with a cosmological constant is realized by the method of B. DeWitt \cite{1}. It is shown that such quantization leads to interesting results, in particular, to a finite lifetime of the system, and appearance of the Universe in our world as penetration via the barrier. These purely quantum effects appear when $Λ>0$.

gr-qc↗

arXiv2004

On the completeness of describing an equilibrium canonical ensemble using a pair distribution function

It is shown that in equilibrium a canonical ensemble of particles with two-particle interaction the Gibbs distribution function may be expressed uniquely through a pair distribution function. It means, that for given values of the particle number $N$, volume $V$, and temperature $T$, the pair distribution function contains as many information about the system as a full Gibbs distribution. The latter is represented as a series expansion in the pair distribution function. A recurrence relation system is constructed, which allows all terms of this expansion to be calculated successively.

cond-mat.stat-mech↗