Related papers: Is G a conversion factor or a fundamental unit?
I argue that the laws of physics should be independent of one's choice of units or measuring apparatus. This is the case if they are framed in terms of dimensionless numbers such as the fine structure constant, alpha. For example, the…
It is possible that fundamental constants may not be constant at all. There is a generally accepted view that one can only talk about variations of dimensionless quantities, such as the fine structure constant $\alpha_{\rm e}\equiv…
There are some theoretical arguments about possible variations of fundamental constants with cosmic time. We review the fact that all conversion factors depend on these quantities and consider how their variations may affect transformations…
It is argued by Duff that only the time variation of dimensionless constants of nature is a legitimate subject of enquiry, and that dimensional constants such as c, h-bar and G... are merely human constructs whose value has no operational…
The natural unit system, in which the value of fundamental constants such as c and h are set equal to one and all quantities are expressed in terms of a single unit, is usually introduced as a calculational convenience. However, we…
We revisit, qualify, and objectively resolve the seemingly controversial question about what is the number of dimensional fundamental constants in Nature. For this purpose, we only assume that all we can directly measure are space and time…
A spacetime interval connecting two neighbouring points can be measured in different unit systems. For instance, it can be measured in atomic unit defined in terms of fundamental constants existing in quantum theories. It is also possible…
Significant research has been carried out in the past half-century on defining generalised determinants for transformations between (typically real) vector spaces of different dimensions. We review three different generalisations of the…
Planck units are natural physical scales of mass, length and time, built with the help of the fundamental constants $\hbar, c, G$. The functional role of the constants used for the construction of Planck units is different. If the first two…
The problem of fundamental units is discussed in the context of achievements of both theoretical physics and modern metrology. On one hand, due to fascinating accuracy of atomic clocks, the traditional macroscopic standards of metrology…
Conformal transformations are obtained by demanding that the form of the metric change by a conformal factor. Nevertheless, this transformation of the metric is not taken into account when a variation of the action is performed. The basic…
Let $p$ be a prime number. We consider diagonal $p$-permutation functors over a (commutative, unital) ring $\mathsf{R}$ in which all prime numbers different from $p$ are invertible. We first determine the finite groups $G$ for which the…
An (additive) functor F from an additive category A to an additive category B is said to be objective, provided any morphism f in A with F(f) = 0 factors through an object K with F(K) = 0. In this paper we concentrate on triangle functors…
An element $g$ of a group is called reversible if it is conjugate in the group to its inverse. An element is an involution if it is equal to its inverse. This paper is about factoring elements as products of reversibles in the group…
Here we discuss direct links of the number of fundamental dimensions to the fundamental natural constants using simple arguments of dimensional analysis \corr{based on Maxwell's dimensions length (L), time (T) and mass (M) as well as the…
We discuss the universal constants c, epsilon, and h in relation to the CPT symmetry. Because MKSA units (S.I. units) have no essential meaning, we should use the units where c^2=epsilon^2=h^2=1. When volume is negative in the left-handed…
We extend vector formalism by including it in the algebra of split octonions, which we treat as the universal algebra to describe physical signals. The new geometrical interpretation of the products of octonionic basis units is presented.…
The quantities of dimension one - known as the dimensionless quantities - are widely used in physics. However, the debate about some dimensionless units is still open. The paper brings new interrelated arguments that lead to the conclusion…
The question whether the invariant speed c, Planck constant h/, and gravitational constant G can be or should be put equal to 1 is analyzed. The discussion is based on fundamental considerations concerning the notion of physical quantity.…
In this paper we give explicit characterizations, based on the cutting and spacer parameters, of (a) which rank-one transformations factor onto a given finite cyclic permutation, (b) which rank-one transformations factor onto a given…