Michelson’s analysis of errors in his 1881/87 experiments of the two swimmers contest; Necessity of correcting college textbooks

The Paper highlights discovery from 2000 of two Errors (ERM81/87) by Michelson in analysis of his experiments ME81/87. ERM81/87 has also been addressed in series of previous articles by the authors. ERM81/87 consisted of assuming the transverse path of light ray 2 or of SW2 swimmer, to be an isosceles triangle (Error 1) inclined with angle β’ in referential frame (RF) ether/water (E/W), or a double orthogonal path (in RF device/bank (D/B)), thus calculating the wrong result, t2 < t1, or Δt = t1-t2 > 0, (Error 2), states SW2 wins the contest. In ERM81/87 it is proven firstly, by Demonstration 1, based on logic, starting from the non-observance in Michelson’s analysis, of rules of correctness and fair play, in development of the two swimmers contest (TSC). Rresulted in correct transversal path as a right triangle, with t2 = t1 (in RF, E/W), the correct contest result is a draw. Demonstration 2 consists, in correction of SW2 route, resulting under fair play conditions, for transversal path, a right triangle with hypotenuse inclined at angle 2β (in RF, E/W) and t2 = t1 or Δt = 0, with the contest result in a tie. Demonstration 3 is based on a new Generalised Case (GC) of the TSC where the orientation of the starting path of SW1 can be inclined at any angle α, always one obtains, t1 = t2, the correct result. Evidence provided shows Michelson designed his interferometer by analogy with TSC, Michelson considered SW2 the winner. Evidence provided in 1892 by Lorenz expressed doubts about the correctness of Michelson’s analysis of ME81/87, without finding errors. We show, an initial error (ERM81) was committed by Michelson in ME81analysis, erroneously superposing paths for SW2 (in RF, D/B), and in incorrect calculations of t2 and Δt obtaining t2 < t1, an error communicated to him by Potier, which also mentioned the correct result Δt = 0, without any demonstration. In analysis of ME87, Michelson acknowledged the error, modified the path of SW2 to isosceles triangle (in RF, E/W), and made new t2 calculation. But he reduced by only half, the Δt compared to Δt in ME81, meaning the basic error in Δt (ERM87) has persisted, until today. We emphasize that errors ERM81/87 in TSC are repeatedly printed, and appear in all college physics textbooks around the world, exemplifying by presenting four such excerpts from college textbooks from the US and Canada. Thus, a correction of ERM81/87 is required, starting with the correction of the TSC, by admitting the correct result of equality of SW1 and SW2, in all college physics textbooks. As result the ether can be reintroduced into physics with multiple consequences including re-evaluation of the Special Relativity Theory.