Related papers: Angles are inherently neither length ratios nor di…
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…
We address the issue of angular measure, which is a contested issue for the International System of Units (SI). We provide a mathematically rigorous and axiomatic presentation of angular measure that leads to the traditional way of…
The concept of an angle is one that often causes difficulties in metrology. These are partly caused by a confusing mixture of several mathematical terms, partly by real mathematical difficulties and finally by imprecise terminology. The…
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…
In the paper by P. Quincey (2020) [1], the author claims that angles are not dimensionless quantities and that the radian should be a new independent base unit. However, the claim is not supported and the proposed redefinition will cause…
The recent paper by Mohr and Phillips (arXiv:1409.2794) describes several problems relating to the treatment of angle measurement within SI, the unit hertz, and quantities that can be considered countable (rather than measureable). However,…
We examine implications of angles having their own dimension, in the same sense as do lengths, masses, {\it etc.} The conventional practice in scientific applications involving trigonometric or exponential functions of angles is to assume…
The treatment of angles within the SI is anomalous compared with other quantities, and there is a case for removing this anomaly by declaring plane angle to be an additional base quantity within the system. It is shown that this could bring…
The International System of Units (SI) is supposed to be coherent. That is, when a combination of units is replaced by an equivalent unit, there is no additional numerical factor. Here we consider dimensionless units as defined in the SI,…
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…
We consider the angle in mathematics and arrive at a conclusion that there are two concepts on the issue. One is a descriptive geometrical one, while the other is from functional analysis. They are somewhat different, allow for different…
A recent Letter proposed changing the dimensionless status of the radian and steradian within the SI, while allowing the continued use of the convention to set the angle 1 radian equal to the number 1 within equations, providing this is…
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…
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…
We review the current status of dimensions, as the result of a long and controversial history that includes input from philosophy and physics. Our conclusion is that they are subjective but essential concepts which provide a kind of…
Have our fundamental theories got time right? Does size really matter? Or is physics all in the eyes of the beholder? In this essay, we question the origin of time and scale by reevaluating the nature of measurement. We then argue for a…
Some recent papers have argued that frequency should have the dimensions of angle/time, with the consequences that 1 Hz = $2\pi$ rad/s instead of 1 s$^{-1}$, and also that $\nu = \omega$ and $h = \hbar$. This letter puts the case that this…
We briefly review the various contexts within which one might address the issue of ``why'' the dimensionless constants of Nature have the particular values that they are observed to have. Both the general historical trend, in physics, of…
Angular equivalence is introduced and shown to be an equivalence relation among the norms on a fixed real vector space. It is a finer notion than the usual (topological) notion of norm equivalence. Angularly equivalent norms share certain…
Formal definitions of quantities, quantity spaces, dimensions and dimension groups are introduced. Based on these concepts, a theoretical framework and a practical algorithm for dimensional analysis are developed, and examples of…