Light Waves in a Vacuum

A light wave is a transverse disturbance of electric and magnetic fields that is able to propagate through a vacuum (unlike a sound wave), and does so at the fixed speed

$$c = \frac{1}{\sqrt{\epsilon_0\,\mu_0}},$$ (3.10)

where $\epsilon_0= 8.854\times 10^{-12}\,{\rm F\,m^{-1}}$ is the electrical permittivity of free space, and $\mu_0 =4\pi\,\times 10^{-7}\,{\rm H\,m^{-1}}$ the magnetic permeability of free space. (See Section 2.4.4.) It follows that

$$c = \frac{1}{[(8.854\times 10^{-12})\,(4\pi\,\times 10^{-7})]^{1/2}}= 2.998\times 10^8\,{\rm m\,s^{-1}}.$$ (3.11)

Note that $\epsilon_0$ and $\mu_0$ can be determined from simple experiments involving measurements of the forces exerted by electric charges and current loops on one another.

The classical theory of electromagnetism (i.e., Maxwell's equations) does not explicitly mention a medium through which electromagnetic disturbances propagate. (See Section 2.4.2.) Nevertheless, prior to the 20th century, most physicists assumed that such a medium existed, because they could not conceive of a wave that propagated in the absence of a medium. The medium in question was known as the aether (from the ancient Greek

, which is the fifth element of Aristotelian philosophy), and was thought to permeate all space, including vacuums. Thus, by analogy with a sound wave, the phase velocity of a light wave in a frame of reference moving at fixed velocity ${\bf v}$ with respect to the rest frame of the aether was assumed to be

$${\bf c}' = {\bf c}- {\bf v},$$ (3.12)

where ${\bf c}$ is the phase velocity of the light wave in the rest frame of the aether, and $\vert{\bf c}\vert=c$ is the speed of light, (3.10).