SQUARE45

In the context of classical electrodynamics, the speed of light

c

in a vacuum is derived from the constitutive relations governing the electromagnetic field tensor

F^{\mu \nu}

. Specifically,

c

is defined by the relationship between the vacuum permittivity

\epsilon_0

and the vacuum permeability

\mu_0

, which are fundamental constants derived from the vacuum Maxwell equations. The magnitude of the propagation speed of any electromagnetic wave is given by:\n\n

c = \frac{1}{\sqrt{\epsilon_0 \mu_0}}

\n\nFurthermore, this speed dictates the dispersion relation for the wave vector

\vec{k}

and angular frequency

\omega

of a plane wave propagating in vacuum, satisfying:\n\n

\omega^2 = c^2 \vec{k}^2

\n\nThis relationship confirms that

c

represents the maximum signal velocity in the vacuum spacetime manifold, consistent with the structure of the Minkowski metric.

Speed of Light

The statement of the theorem