On Dimensions

Physicists deal with two frameworks when discussing fundamental constants: unit-based dimensions and unitless (dimensionless) formulations. Each approach offers different insights into the nature of physical laws and the structure of reality.

In the unit-based system, constants like the speed of light c, Planck’s constant h, and Newton’s gravitational constant G carry dimensions—Meters per second (c), Joule-seconds (h) and Newtons X meters squared per kilogram squared (G).  These dimensional constants serve as conversion factors between different physical quantities. For example, c links space and time, h connects energy and frequency, and G relates mass to gravitational force. This framework is essential for engineering, measurement, and communication across disciplines, as

By contrast, the unitless or dimensionless approach seeks to express physical laws in terms of pure numbers, stripping away human-imposed units. This is often achieved by adopting natural units: setting c = h = G = 1— simplifies equations and reveals deeper symmetries. 
In this system, quantities are measured relative to fundamental scales (e.g., Planck length, Planck time), and constants like the fine-structure constant (~1/137) are dimensionless indicators of physical relationships. These numbers are considered more “fundamental” by some because they are invariant across unit systems and potentially across other universes if they exist.

The tension between these approaches reflects a philosophical divide: unit-based constants are practical and context-dependent, while dimensionless constants are abstract and considered universal. When physicists ask whether a constant is truly fundamental, they often mean: “Can it be expressed without reference to arbitrary units?” This distinction becomes crucial in fields like cosmology and quantum gravity, where the goal is to uncover laws that transcend human conventions and reveal the architecture of nature itself. 

That said, the considerations of fundamental constants on this website use unit-based based dimensions. Why? Because they are more concrete and tied to the physical measurement of the parameter. These are also called SI Units. The International System of Units, internationally known by the abbreviation SI (from French Système international d'unités), is the world's most widely used system of parameter measurement (Wikipedia).  

Some argue that true fundamental constants should use dimensionless units. However, the whole point here is that if these constants could vary then what may be the side effects. Unitless measurements would always force c = h = G = 1 (for example) and this becomes counterproductive for understanding the fine tuning of nature's "constants".