Relativity Calculator
suggested source of diagram: Richard Feynmann's " Lectures on Physics - Vol. I "
I. By the addition of velocities of light thru the aether, longitudinal time is:
II. Now for some other arbitrary time the Michelson-Morley Interferometer moves a longitudinal distance
and hence
.
Solving for transverse time:
IIa. Another derivation of solving for transverse time:
Each one of these right triangles is similar [ or proportional ] to each other and hence the following ratios are true:
III. Also the following relationships are rather interesting and will be used shortly:
A.
B.
IV. Michelson-Morley Interferometer is rotated 90º and final interference fringe calculations taken:
That is, the interference displacement fringe ratio must be at least 0.37 when the Michelson-Morley Interferometer is rotated 90º and given the fact that the instrument itself was itself sensitive to within 1/100th of a fringe ratio.
Rather what the Michelson-Morley Interferometer produced for all degree turns of the instrument was
An ad-hoc assumption provides a partial solution:
The continuing conundrum of adhering to a luminiferous aether hypothesis - which by definition should be producing fringe interferences - while repeated interference experiments were still producing
,
was tentatively solved in 1889 by George Francis Fitzgerald ( 1851-1901 ), born Dublin, Ireland, and later elaborated upon in 1892 by Hendrik Antoon Lorentz ( 1853-1928 ), born Arnheim, Holland, when together they conjectured that there existed a sort of "aether drag" causing all bodies ( including an observer's eyeballs! ) to be "squashed" or contracted in the rectilinear direction of motion thru the luminiferous aether by a so-called Lorentz factor:
G. F. FitzGerald - brilliant mathematical physicist H. A. Lorentz - Noble Prize in Physics 1902,
FitzGerald's ad hoc solution relied upon his understanding of Maxwell's Electromagnetic Wave Equations and how rectilinear motion effected these waves, in particular the Doppler Effect, whereas Lorentz more fully developed a "contraction theory" based upon his theory of electrons.
The FitzGerald-Lorentz Contraction Hypothesis:
Ok, so how does the FitzGerald-Lorentz Contraction Equation solve the Michelson-Morley null result?
Remember, at this stage of physics understanding ( 1895 ) the idea of the hypothetical luminiferous aether is still being maintained and that the FitzGerald-Lorentz Contraction Equation is being utilized in an ad-hoc fashion in order to rescue the concept of the aether! That is, the interpretation given by Lorentz for this "contraction effect" was wrong, nevertheless the equation was correct and it would shortly enter into a pantheon of other equations developed by Poincaré and others leading ultimately to the tensor mathematics of Special Relativity.
In truth the FitzGerald-Lorentz Contraction Equation only temporarily postponed the eventual abandonment of the concept of an invisible luminiferous aether. It will be Albert Einstein's publication in 1905 of the tensor mathematics of Special Relativity and Einstein's concept of space-time with the Lorentz Transformation Equations ( as the FitzGerald-Lorentz Contraction Equation came to be known ) at its core foundation to have finally "solved" the Michelson-Morley null result.
In the meantime, go to "Albert Michelson & the Aether - Part III - The FitzGerald-Lorentz Solution" to view the full solution to the null result of the Michelson-Morley Experiment.
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