First, I believe that the problem has not been previously discovered because, in general, the current methods of teaching SR (at the undergraduate level) do not use the derivations as contained in Einstein’s original manuscripts. This means that many are not actually reviewing Einstein’s original derivations, but some other author’s alternative derivation. These alternatives are often based on assumptions that are only valid if Einstein’s equations are themselves valid or are based on assumptions that are later lifted.
Consider the following simplified derivation of Einstein’s equations:
- ξ=β(x-vt), where β=1/sqrt(1-v^2/c^2).
- Since Einstein derives ξ from the equation ξ=cτ, then τ=ξ/c must be true such that we divide by c to produce τ=β(x-vt)/c.
- This equation can be rewritten as τ=β(x/c-vt/c).
- This equation is simplified, using an implicit assumption, as τ=β(t-vx/c^2).
We use this example to reveal why the problem is hard to detect. There is an implicit assumption between step 3 and 4 that x=ct can be used to further simplify the equations. When this occurs, we introduce a constraint that must also be true in the usage of the equations. To reveal the problem we simply need to show that τ=β(x-vt)/c does not generally equal τ=β(t-vx/c^2) for the same input values. Consider the case where x=50, v=5, and t=10. The first equation produces τ=0*β, or τ=0, while the second equation produces approximately τ=10*β. If the assumption used in simplifying the equations, specifically that x=ct, is lifted in the use of the equations, then Einstein’s time equation will yield incorrect results since τ will not equal ξ/c.
Because the number of alternative derivations is too great to address each one individually, I have limited my discussion to Einstein’s original works.
Lastly, my findings are not only theoretical, but experimental since experiments such as Michelson-Morley and Ives-Stillwell produce results that are closer to the predictions of the CICS model than to the predictions of SRT.
