If Maxwell’s equations of electromagnetism are laws of physics, and there’s every reason to think they are, then, according to the principle of relativity, Maxwell’s equations must be true in every inertial reference frame. On the surface this seems to be an innocuous statement, equivalent to saying that the law of conservation of momentum is true in every inertial reference frame. But follow the logic:

1. Maxwell’s equations are true in all inertial reference frames.

2. Maxwell’s equations predict that electromagnetic waves, including light, travel at speed $c=3.00\times {10}^8\text{m}/\text{s}$.

3. Therefore, light travels at speed c in all inertial reference frames.

FIGURE 36.8 shows the implications of this conclusion. All experimenters, regardless of how they move with respect to each other, find that all light waves, regardless of the source, travel in their reference frame with the same speed c. If Cathy’s velocity toward Jaylon and away from Yang is $v=0.9c$, Cathy finds, by making measurements in her reference frame, that the light from Jaylon approaches her at speed c, not at $c+v=1.9c$. And the light from Yang, which left Yang at speed c, catches up from behind at speed c relative to Cathy, not the $c-v=0.1c$ you would have expected.

FIGURE 36.8 Light travels at speed $c$ in all inertial reference frames, regardless of how the reference frames are moving with respect to the light source.

Although this prediction goes against all shreds of common sense, the experimental evidence for it is strong. Laboratory experiments are difficult because even the highest laboratory speed is insignificant in comparison to c. In the 1930s, however, physicists R. J. Kennedy and E. M. Thorndike realized that they could use the earth itself as a laboratory. The earth’s speed as it circles the sun is about $30\text{,}000\text{m}/\text{s}$. The relative velocity of the earth in January differs by $60\text{,}000\text{m}/\text{s}$ from its velocity in July, when the earth is moving in the opposite direction. Kennedy and Thorndike were able to use a very sensitive and stable interferometer to show that the numerical values of the speed of light in January and July differ by less than $2\text{m}/\text{s}$.

More recent experiments have used unstable elementary particles, called $\pi$ mesons, that decay into high-energy photons of light. The $\pi$ mesons, created in a particle accelerator, move through the laboratory at 99.975% the speed of light, or $v=0.99975c$, as they emit photons at speed c in the $\pi$ meson’s reference frame. As FIGURE 36.9 shows, you would expect the photons to travel through the laboratory with speed $c+v=1.99975c$. Instead, the measured speed of the photons in the laboratory was, within experimental error, $3.00\times {10}^8\text{m}/\text{s}$.

FIGURE 36.9 Experiments find that the photons travel through the laboratory with speed $c$, not the speed $1.99975c$ that you might expect.

In summary, every experiment designed to compare the speed of light in different reference frames has found that light travels at $3.00\times {10}^8\text{m}/\text{s}$ in every inertial reference frame, regardless of how the reference frames are moving with respect to each other.