Are Kilogram and Ampere (Coulomb) Fundamental Units?

In the current International System of Units (SI), the kilogram and the ampere are defined as base units. However, this classification reflects a historically contingent, human-centered choice made for measurement convenience, not a necessity imposed by nature. In this note, We argue that mass and electric charge are not fundamental units but constructed quantities derived from deeper spacetime relations.

Furthermore, We show that the gravitational constant \(G\), the vacuum permittivity \(\varepsilon_0\), and the vacuum permeability \(\mu_0\) function as proportional constants introduced to maintain consistency within the human-defined unit system of kilograms and coulombs, rather than intrinsic constants of nature.

To state the conclusion first: the kilogram is redefined through the \(\delta\)-transformation and expressed as a purely spacetime dimension \(\mathrm{m^3/s^2}\).

Likewise, the coulomb (electric charge unit) is redefined via the \(\varepsilon\)-transformation, reducing charge to a spacetime dimension as well.

Here, \(c\) is the speed of light, \(e\) is the elementary charge, \(m_e\) is the electron mass, and \(\mu_0\) is the vacuum permeability.

As a result, an extremely simple relation emerges—reminiscent of Einstein’s rest-mass energy relation:

We call this transformation framework the Space-Time Unit (ST unit). In the ST unit system, the unit structure necessarily collapses onto the electron scale, and the classical electron radius is defined as the fundamental length.

The fundamental time is then defined as the time required for light to traverse this classical electron radius. From this fundamental length and fundamental time, the elementary charge, the electron mass, and the electron rest-mass energy are consistently defined.

Consequently, by setting this fundamental length and fundamental time equal to unity, a natural unit system necessarily emerges—distinct from the Planck natural units.

In this way, simply redefining mass and charge—historically introduced as independent quantities— leads to a remarkable simplification of physical formulas, restoring a more intuitive structure to fundamental physics. For detailed derivations and the full theoretical framework, please refer to:

Note: This page is intended as an entry-point summary. Please see the reference above for full derivations and a systematic discussion.