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THESIS (INTRO): In Special Relativity, there exists a vagueness. It can be fixed with clever application of Einstein's 2nd Postulate of Special Relativity (invariance of c), but only at the cost of rejecting and replacing General Relativity as we know it.
POINT 1 - The train of logic is pretty undeniable. Before Einstein, Newton's Laws of Mechanics were very strong. Similarly, Maxwell's Electromagnetism represented a synthesis of earlier physical theories into a beautiful whole.
POINT 2 - The problem was that Maxwell's Electromagnetism was at odds with Newton's laws of mechanics, through electromagnetic radiation that was predicted to move at a speed that didn't seem relative to anything; the speed of light.
POINT 3 - Einstein felt that the key to unification was to keep the spirit of relativity alive under the constraints that the speed of light is a constant. Reflected in the postulates of Special Relativity.
POINT 4 - Using the postulates, Einstein uncovered a solution to the problem of making the theories connect, through the Lorentz transformation. Here is the Lorentz transformation, from (such and such source).
POINT 5 - However, there's a vagueness in his solution. Einstein built the theories with the Galilean Laboratory in mind. The Galilean Laboratory has extents.
POINT 6 - Here's what happens when we apply the same logic to a zero-dimensional point. Vagueness appears in whether or how fast a single particle (the Blain Laboratory) rotates in a Special Relativistic situation.
POINT 7 - Vagueness solved by Einstein's 2nd Postulate in the World Frame. Orient the particle towards the photon at all times, always.
Conclusion: This solution solves the vagueness but leads to a vastly different physical theory than Einstein's Special Relativity, and will require a new theory of gravity. However, it's worth the effort since it may offer a chance to connect Special Relativity and gravity (whatever it may be) with quantum mechanics. Please see more of my ideas for gravity, etc.