The Relationship Between Electric and Magnetic Fields

In the 19th century, Maxwell realized that there was a fundamental symmetry between electric fields and magnetic fields. This relationship is critical because it means that you can have a self-sustaining, propagating electromagnetic field even in empty space. The speed at which these waves will travel through a vacuum is equal to 1 over the square root of 2 numbers part of Maxwell's equations. So, what does this indicate? Well, it seems pretty clear that these electromagnetic waves that we predicted just by looking at Maxwell's equations must actually be light, you know, which travels at the speed of light.