36.3 Einstein’s Principle of Relativity

The 19th century was an era of optics and electromagnetism. Thomas Young demonstrated in 1801 that light is a wave, and by midcentury scientists had devised techniques for measuring the speed of light. Faraday discovered electromagnetic induction in 1831, setting in motion a series of events leading to Maxwell’s prediction, in 1864, that light waves travel with speed

c = \frac{1}{\sqrt{ϵ_{0} μ_{0}}} = 3.00 \times 10^{8} m / s

This is a quite specific prediction with no wiggle room. But in what reference frame is this the speed of light? And, if light travels with speed c in some inertial reference frame S, then surely, as FIGURE 36.7 shows, the light speed must be more or less than c in a reference frame $S'$ that moves with respect to S. There could even be reference frames in which light is frozen and doesn’t move at all!

The figure illustrates two light waves moving toward the right in two different reference frame.

FIGURE 36.7 Full Alternative Text

It was in this muddled state of affairs that a young Albert Einstein made his mark on the world. Even as a teenager, Einstein had wondered how a light wave would look to someone “surfing” the wave, traveling alongside the wave at the wave speed. You can do that with a water wave or a sound wave, but light waves seemed to present a logical difficulty. An electromagnetic wave sustains itself by virtue of the fact that a changing magnetic field induces an electric field and a changing electric field induces a magnetic field. But to someone moving with the wave, the fields would not change. How could there be an electromagnetic wave under these circumstances?

Several years of thinking about the connection between electromagnetism and reference frames led Einstein to the conclusion that all the laws of physics, not just the laws of mechanics, should obey the principle of relativity. In other words, the principle of relativity is a fundamental statement about the nature of the physical universe. Thus we can remove the restriction in the Galilean principle of relativity and state a much more general principle:

All the results of Einstein’s theory of relativity flow from this one simple statement.