Relativity did not start with Einstein. Newton's Principia deals with the restricted principle of relativity, the idea that simple motions in straight lines can be considered cases of purely relative motion, because an observer inside a moving system cannot tell whether or not they are moving. If they look out of their window, they can see relative motion with respect to their environment, but cannot tell whether it's the environment that's moving or whether it's them.
If they accelerate then they feel gee-forces but the outside onlookers don't, making Newtonian acceleration absolute -- we can tell who is "really" accelerating. Ernst Mach pointed out that we could remove this distinction between absolute and relative motion if we claimed that the relative motion of matter caused not just apparent gravitational fields but real gravitational fields, of an unfamiliar type. If you sit on a spinning roundabout, said Mach, the forces that you feel pulling you outward can be considered an odd glass of gravitational field produced inside a spinning massed sphere (the rotating background starfield). Rotation and acceleration were now relative, because the effects of complex motion were now apparent to anyone. Somebody alongside a spinning roundabout would feel an increased inward attraction (gravitational effect of kinetic energy), and a sideways drag in the same sense as the structure's rotation.
The general principle of relativity was also argued for by the politically powerful George Berkeley, and Principia has a short passage describing how a rotating shell of matter should cause rotation of its contents (a result of modern general relativity!), which is presumably there to prevent Berkeley opposing the book's publication. We also have the relativity of inertia, the relativity of space, the relativity of time, the relativity of refractive index (Augustin-Jean Fresnel), the relativity of spacetime orientation, and doubtless a few others.
Since there have been multiple theories of relativity, and some of them disagree, they can't all be right .. we need to specify which theory of relativity we are talking about. Newton's 1704 model was wrong because it generated the wrong sort of gravitational shifts, C19th "ballistic emission theory" was wrong because it couldn't describe light as a wave, and Einstein's 1916 general theory is wrong because it is built on incompatible components. These were all relativistic theories.
The practice of referring to "THE theory of relativity" as if it was a single entity is partly Einstein's fault, as he was keen for people to think that his way of doing things was the only one possible. What Einstein told us relativity "said" also varied: the equations for "the general theory" had a tendency to change, as did the theory's predictions for things like cosmology, and sometimes the relativity of inertia was supposed to be a cornerstone of general relativity, but sometimes it wasn't.
In terms of relativising the properties of light, there were logical-philosophical reasons for believing that an atom couldn't move faster than its own light: if its internal processes were kept in equilibrium by forces moving at the speed of light, and different parts of the atom lost informational contact, then the atom might simply disintegrate. We wanted the speed in the vicinity of every atom to have the same value, and there were two ways of doing this, depending on whether we agreed with Hendrik Antoon Lorentz or Heinrich Rudolf Hertz .
| - | Hertz | Lorentz |
|---|---|---|
| geometry | curved | simple, flat |
| metric | interactive, dynamic, acoustic |
fixed Minkowski, Schwarzschild |
| c-constancy | local | global |
| - | all objects drag their own light | distances, times and velocities redefined using Lorentz factors |
| gives gravitomagnetism | flat spacetime only | |
| supports | relativistic gravitation general relativity |
not extensible |
| recession redshift | E'/E = (c-v)/c | E'/E = sqrt[ (c-v)/(c+v) ] |
| transverse redshift | E'/E = 1- v2/c2 | E'/E = sqrt[ 1- v2/c2 ] |
| horizon type | relative horizon | absolute event horizon |
| classical Hawking radiation? | yes | no |
| Hubble expansion? | yes | no |
| arrow of time? | yes | no |
Of the two systems, the Hertz concept was far simpler to visualise (moving matter drags light), but because it involved moving matter warping a region's lightbeam geometry, it was more difficult to implement mathematically. By the time you'd addressed all the little quirks, you essentially had a full general theory of relativity. By contrast, the Lorentz approach broke relativity into two more digestible-looking stages ... which turned out to be incompatible.
Working backwards from the general principle of relativity gives us gravitomagnetic dragging and a Hertz-style system, rather than the Lorentz-Einstein Minkowski ("LEM") system.
Hertz died in 1894. The success of the Lorentz system illustrates the importance, if you want your arguments to be treated fairly in a scientific debate, or Not Being Dead. The dominance of the Lorentz system is shown by the fact that the mathematical formulation of a Hertzian acoustic metric didn't happen until 1999. So for almost the entire Twentieth Century, we didn't even really know what the competitor math to Einstein's system looked like.