In his 1638 work Discourses and Mathematical Demonstrations Relating to Two New Sciences, a treatise on the motion of objects and the strength of materials, Galileo laid the foundation for classical mechanics that would be continued by the likes of Newton, Euler, Lagrange, and Hamilton. In it he formulated the Law of Inertia which we often call Newton’s First Law given its place in his work, the Principia. Simply stated, it maintains that an object at rest or at a uniform velocity in a straight line will continue as such unless acted upon by a external force.
With this, one can construct what is called, appropriately, a Galilean transformation where the laws of mechanics will hold in either a stationary reference frame or a uniformly linearly translating reference frame. The origin of a set of coordinates can either be at rest relative to a system under consideration, or moving in a straight line with constant speed passed the system. One way to think about this analytically is that since the laws of mechanics are based on the second derivative of position with respect to time, any constant change in velocity will be made superfluous.
Later on, in the 18th and 19th centuries, work on the phenomenon of electric charge and magnetism were ongoing. The number of contributing experimentalists and theorists are really too numerous to adequately name: Franklin, Volta, Coulomb, Ampere, Ohm, Cavendish, Faraday, etc. Ultimately, these disparate phenomenon were unified into a single, coherent theoretical picture by James Clerk Maxwell in his 1861 paper On Physical Lines of Force. As an aside, his original formulation of what are now called Maxwell’s equations were rather verbose and cumbersome, and were not reformulated using more modern vector notation until several decades later in 1884 by Oliver Heaviside.
One interesting result from Maxwell’s equations was a prediction for the velocity of electromagnetic waves, which when calculated seemed to agree very closely with the speed of light. This suggested that visible light was but one part of a broader electromagnetic spectrum, which we now know contains things like radio waves, microwaves, infrared, visible light, ultraviolet, x-rays, and gamma rays. There was a problem however: when the Galilean transformation is applied to Maxwell’s equations, it modifies the speed of light by the velocity of the observer (in the same way that if somebody throws a ball toward you, it appears to be moving either faster or slower depending on if you run towards it or away from it respectively). Trouble was, the equations predicted a baseline speed of light and it was thought that all reference frames were equivalent. This gave rise to the idea of a standard universal reference frame — the luminiferous aether.
Long story short, experiments such as the famous Michelson-Morley experiment provided strong evidence showing there was no aether, no standard frame of reference. Meanwhile, others had come up with a valid transformation that were invariant (the laws of electromagnetism remained the same) when applied to Maxwell’s equations, notably by Lorentz and hence the use of the term Lorentz transformations. These transformations had the notable characteristic that for speeds much less than the speed of light (v << c) the Lorentz transformation could be approximated by the Galilean transformation.
Finally, along comes Albert Einstein with his 1905 paper “On the Electrodynamics of Moving Bodies” where he had the intellectual courage to make the great leap from the past. Einstein was deeply unsatisfied with the idea that the laws of mechanics and electromagnetism should change for different inertial reference frames, so he established two fundamental postulates in his presentation of special relativity:
- The Principle of Relativity – If two systems are moving relative to one another in uniform translatory motion (with includes being at rest with respect to one another), the laws that govern changes in their state are unchanged (they are governed by the same laws of physics.
- The Law of the Constancy of the Speed of Light – Observers undergoing uniform translatory motion (what we call inertial reference frames) will agree on a constant value of the speed of light. No matter how fast an observer moves relative to another, they will both measure the same speed of light.
From these seemingly innocuous postulates all the bizarre effects of observers measuring different rates of time and objects being contracted in their direction of motion follow by logical construction. But that’s another post. As stated before, for v << c the Lorentz transform becomes the Galilean transformation, so special relativity is an extension, not a replacement, of Newtonian mechanics. Newton is still perfectly valid for hum-drum things that humans care about, because the speed of light is so huge relative to our usual experience. The morale of this story is that Einstein successfully resolved a problem in physics by making its foundations more universal and elegant while still preserving all the hard work and perfectly valid laws of mechanics that predated him, all in line with the evidence.