This repository contains a mathematical essay on the foundations of SR.
- Final chapter needs improvement. More detail required for Fizeau spinning wheel experiment with variable regular sawtooth patterns. This is our form of Ralph Sansbury's proposed experiment.
Let us give a preview of some issues in the SR theory. There is an extremely subtle error in the foundations of special relativity, especially as treated by Einstein himself in his own accounts. Admittedly, an apparent incompatibility arises between the two basic assumptions of the theory, namely
(A1) the principle of restricted relativity, that the laws of physics have the same form (what this means is not well defined by AE himself); and
(A2) the so-called Law of Propagation of Light along straight lines at a constant velocity in vacuum of about one foot per nanosecond.
Apparently the conjunction (A12) := (A1) AND (A2) is a contradiction, at least according to classical mechanics, e.g. Fizeau's law of addition of velocities, additivity of energy, etc.. The reconciliation of this apparent incompatibility is achieved -- according to Einstein's reasoning -- by postulating the Lorentz-Fitzgerald formulae relating the coordinates (x,y,z,t) of inertial frame K, and (ξ,η,ζ,τ) of inertial frame K'. These formulae are one explanation for the observed null effect in the Michelson-Morley interferometer fringe experiment.
It is observed, as Einstein argues, that substitution of the Lorentz formulae leaves invariant the Minkowski form, and the equation x^2+y^2+z^2=c^2 t^2 is satisfied whenever ξ^2+η^2+ζ^2= c^2 τ^2 is satisfied. But here comes the error: this does not imply that the conjunction (A12) is resolved, because the equation ξ^2+η^2+ζ^2= c^2 τ^2 is not the equation of a sphere! More specifically we should say, not the equation of a round sphere.
There are further difficulties when we examine the Lorentz transformations more closely.
For example, the above reasoning can be reformulated in terms of the homogeneous wave equation. Then the error in Einstein's alleged proof can be thus summarized: radius is not a Lorentz invariant variable. Equivalently the class of radial solutions of the homogeneous wave equation is not a Lorentz invariant class.
We welcome critical comments and responses.
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