The Need for Special Relativity
At the end of the nineteenth century, all the important questions of science seemed to have been answered. The were only a few puzzles and anomalies that did not fit into the scheme. The Michelson – Morley experiment for example, showed that the speed of light is the same in all inertial frames. This contradicts the assumption that speeds in different inertial frames are related by the Galilean transformation. In the nineteenth century, scientists proposed the existence of a substance called the ether, which pervaded all of space and acted as a medium for the transmission of light in the same way that air acts as a medium for the transmission of sound. Scientists thought that light would travel at a speedrelative to the ether, so any moving observer would see light travelling faster or slower thandepending on whether the were moving in the same direction or not not as the light.
The speed of light was also predicted to be a constant because of physics consideration. The value ofarises naturally out of Maxwell's equations. From them we can construct a wave equation for electromagnetic waves:
The speed of lightis constructed from known physics constantandconstants of electromagnetism, which do not vary at all, implying thatshould not vary. In fact
Another problem arose out of the Lorentz force law,This supposed law of physics contained a velocity termThe Galilean transformation implied the same acceleration and the same force in different inertial frames. The velocity of an object is not the same in different inertial frames, hence by applying the Galilean transformation to both sides we obtain a contradiction, since the right hand side will be changed but the left hand side will not. Either the Principle of Relativity – that the Laws of Physics can be written in the same form in all inertial frames – or the Galilean transformation must be modified or discarded.
The Galilean transformation was in fact modified, and became the Lorentz transformation. The Principle of Relativity survived unscathed, and by surviving, became much more of a bedrock of physics. Becoming also one of the two postulates of the theory.