TITLE:
A Reanalysis of the Two Swimmers Problem, as Frequent Model of Michelson’s Interferometric Experiment Demonstrating that Transversal Path Is Not an Isosceles but a Right Triangle and the Race Will End in a Tie
AUTHORS:
Ioan Has, Simona Miclaus, Aurelian Has
KEYWORDS:
Michelson Experiment, Two Swimmers Model, Swimming Times Calculation, Right Triangle Correct Transversal Path, Error of Isosceles Triangle for Transversal Path
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.6 No.7,
July
27,
2018
ABSTRACT: The article initially reviews various works
describing the physical model (PM) of Michelson’s interferometric experiment
(ME), represented by the race between two swimmers Sw1, Sw2 (or boats, or
planes, or sound signals, etc.). The two swimmers must each swim the same
distance, but Sw1 will swim along the river flow, and Sw2 will swim
perpendicularly to this direction. In all such works, it is considered that
Sw2’s path will require less time and that it will reach the start point first.
However, in this work, it has been determined that in order to make this
possible, Sw2 must not observe the orthogonality rule of his start direction.
This action would be deceitful to the arbiters and thus considered as
non-fair-play towards Sw1. The article proves by swimming times calculus, that
if the fair-play rules are observed, then the correct crosswise path (in water
reference frame) is a right triangle instead of the isosceles triangle
considered by Michelson. Consequently, the two times shall be perfectly equal and
the race ends in a tie, and the myth of Sw2 as the race winner shall be
debunked. Note that the same result shall also be applicable to Michelson’s
interferometric experiment (ME) as well as to any similar experiment.
Therefore, utilising the isosceles triangle as the transversal path in PM and
also in ME is an erroneous act.