Introduction To Special Relativity - Classical Physics and Electromagnetism

Classical Physics and Electromagnetism

Through the era between Newton and around the start of the 20th century, the development of classical physics had made great strides. Newton's application of the inverse square law to gravity was the key to unlocking a wide variety of physical events, from heat to light, and calculus made the direct calculation of these effects tractable. Over time, new mathematical techniques, notably the Lagrangian, greatly simplified the application of these physical laws to more complex problems.

As electricity and magnetism were better explored, it became clear that the two concepts were related. Over time, this work culminated in Maxwell's equations, a set of four equations that could be used to calculate the entirety of electromagnetism. One of the most interesting results of the application of these equations was that it was possible to construct a self-sustaining wave of electrical and magnetic fields that could propagate through space. When reduced, the math demonstrated that the speed of propagation was dependent on two universal constants, and their ratio was the speed of light. Light was an electromagnetic wave.

Under the classic model, waves are displacements within a medium. In the case of light, the waves were thought to be displacements of a special medium known as the luminiferous aether, which extended through all space. This being the case, light travels in its own frame of reference, the frame of the aether. According to the Galilean transform, we should be able to measure the difference in velocities between the aether's frame and any other – a universal frame at last.

Designing an experiment to actually carry out this measurement proved very difficult, however, as the speeds and timing involved made accurate measurement difficult. The measurement problem was eventually solved with the Michelson–Morley experiment. To everyone's surprise, no relative motion was seen. Either the aether was travelling at the same velocity as the Earth, difficult to imagine given the Earth's complex motion, or there was no aether. Follow-up experiments tested various possibilities, and by the start of the 20th century it was becoming increasingly difficult to escape the conclusion that the aether did not exist.

These experiments all showed that light simply did not follow the Galilean transformation. And yet it was clear that physical objects emitted light, which led to unsolved problems. If one were to carry out the experiment on the train by "throwing light" instead of balls, if light does not follow the Galilean transformation then the observers should not agree on the results. Yet it was apparent that the universe disagreed; physical systems known to be at great speeds, like distant stars, had physics that were as similar to our own as measurements allowed. Some sort of transformation had to be acting on light, or better, a single transformation for both light and matter.

The development of a suitable transformation to replace the Galilean transformation is the basis of special relativity.