S5. Birth of Special Relativity

We talked about the concept of Galilean transformation in the previous section. Here we talk about inconsistencies of the transformation with the theory of electricity and magnetism.

In between the time period of the 18^th  and 19^th century there was a significant development in the field of mechanics due to remarkable contribution of Sir Isaac Newton and many other following the path laid down by him. Mechanics was then already both very analytical and abstract. Classical mechanics was at its height of serene beauty.

However, there were other new generation of scientists doing the study on the newly discovered phenomenon so called Electric and Magnetic field. Michael Faraday followed the lead on the very subject matter. Although Faraday’s work on the electricity and magnetism was highly insightful, electric and magnetic field were considered to be entirely different concept. Maxwell from his analysis on the Ampere’s contribution found a loop hole, this led him to develop a set of equation which we now call the Maxwell’s Equation.

                                                        

What’s more interesting is that he found a wave equation associated with the electric and magnetic theory which propagated with the speed$(c)$, which was a pure constant.

But since Galilean transformation points us to the fact that that velocity is a relative concept. We could state in principle  that the light should have different speeds in different frame due to the velocity addition rule. We have just found that the light had a constant speed with no indication to any particular frames of reference. How could that be? Was there a universal frame of reference that light moved on?? 

To put it in plain words, we found that Velocity of light was a constant $c$, but the question remained, to whom? Someone sitting inside the bus, or someone standing still on the surface of the earth. Trying to figure out a way out of it, scientists began speculating about illusive substance permeating all over space called aether. The detailed history can be found here.

In this point of time physicists had apparently three possible direction;

1. The first one was that there was an absolute standard of rest. Galilean relativity in mechanics was just a coincidence. The “relativity” coincidences in electrodynamics are nothing deep. Or
2. There was no absolute standard of rest. Galilean relativity applies to all of physics. Maxwell's equations are wrong. Seek new laws of electrodynamics consistent with Galilean relativity.
3. There was no absolute standard of rest. There exists a relativity principle that applies to all of physics, but it's not Galilean relativity. Laws of mechanics must be revised. Perhaps laws of electrodynamics can survive intact.

Which path did Einstein follow?  The third one..