Hendrik Lorentz, Oliver Heaviside, Joseph Larmor, and Henri Poincare introduced almost all the ideas of special relativity in the late 19th century in various ether theories.
Light is transverse waves in the ether. Light is described by the ordinary wave equation (= the massless Klein-Gordon equation). Massive particles might be described with the massive Klein-Gordon equation.
Let us consider the special theory of relativity. We define the inertial frame of our laboratory as the frame where the "ether" is static. It might be possible to reproduce all phenomena of special relativity in that ether, with suitable waves.
_________ mirror
/ \
/ \ bouncing light
/ \
_________ mirror
● v ------>
our laboratory moving laboratory
For example, time slows down for a moving observer because if he measures time by looking at light bouncing between two mirrors, normal to his direction of movement, the light will travel a longer path in the ether.
Should we claim that special relativity is just an illusion and that newtonian wave mechanics in the ether, which is static in our frame, is the "true physics"?
The claim is somewhat awkward because it requires us to declare that all matter is waves, and requires us to pick one inertial frame as the ether frame. In newtonian mechanics, all inertial frames are created equal. Why pick some specific one as the ether frame?
What about our claim that the Minkowski metric is the "true physics" and curved spacetime is just an illusion?
The ether theory on top of newtonian mechanics requires us to break the Galilei symmetry by picking one inertial frame over others. Also, the wave theory of matter is a serious complication.
Special relativity retains the galilean symmetry of inertial frames. If we have any frames which are moving at a constant velocity v relative to each other, the frames have the same status.
General relativity is an attempt to establish equality among all freely falling laboratories. Does that make sense?
A laboratory falling freely under the gravitation of any celestial body will observe tidal effects. The laboratories cannot be strictly equal.
In special relativity, inertial frames extend over the whole universe. In general relativity we cannot extend the frame of the laboratory over the whole universe. The symmetry between freely falling laboratories is much weaker than between inertial frames in special relativity.
Moreover, general relativity breaks the symmetry of forces by picking one force, gravity, as the paramount force which determines the "spacetime geometry". Yesterday we showed that for a complex system S, we cannot split apart the effect of various forces. Lifting gravity above other forces cannot succeed cleanly.
Thus, the case for general relativity is much weaker than for special relativity.
The equivalence principle of general relativity is a local, approximate, symmetry while the equivalence of inertial frames in special relativity is a global symmetry.
In newtonian mechanics, an accelerating frame is not equal to an inertial frame. Locally, we can fool people in a freely falling laboratory to think that their accelerating frame is equal to an inertial frame. That does not mean that the "true physics" in that laboratory is the physics of an inertial frame.
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