What happens at the origin in the Michelson-Morley experiment.
Frank Russo - December 26, 2012.
A pair of photons that split their itinerary at the origin with one heading to the orbital mirror whilst travelling with the velocity of the earth, whilst the other heads perpendicularly towards the perpendicular mirror across the velocity of the earth: end up at their respective mirrors at different times... the perpendicular one reaches its mirror first.
However whilst the orbital photon had the longer initial segment, it actually has a somewhat shorter return leg... so much so that both of the photons end up back at the origin beam-splitter - where they were originally split up - at the same time so that no interference is detected in the resultant fringe pattern!
However, the question that comes to mind in reference to my very recent writings is, where does the 'unknown' photon (that actually reaches the perpendicular mirror at the same time as the original photon reaches the orbital one), fit into the scheme of things especially in reference to the origin?
Well this is what this page is about... a slight elaboration of yesterday's ideas. The perpendicular photon at the mirror has originated from the beam-splitter, after the beam-splitter has advanced some 0.335799009 m beyond the position from which the original pair emanated... whilst the original orbital photon has advanced some 1.921923284 m beyond the said original origin (beam-splitter).
Let us now retrogress both of these photons that end up at the mirrors together, to and before the beam-splitter's original position. The orbital mirror's photon is the easy one... you just grab it and go back 1.921923284 m from the 'timing' starting point of the perpendicular mirror's photon, and you're back at the original beam-splitter: this photon thus has backed-up through the equivalent earth motion that the apparatus travels orbitally in an 11 m length. As for the perpendicular mirror's photon, you likewise bring the beam-splitter back by 0.335799009 m and it's back at the original origin... thus the beam-splitter has back-tracked the equivalent apparatus length that equates to 1.921923284 m of light travel!
However, we've only backtracked the beam-splitter... its dependant photon in the same amount of time, has to be back-tracked by 1.921923284 m to keep things even: this brings it back through the original beam-splitter position... actually to precede the origin by 1.586124275 m !
To some, this might appear contradictory because the orbital original path has an extra 1.921923284 m to be travelled, rather than simply 1.586124275 m ! However, one must not forget that at the end of the said path, one has to cross the advancing apparatus gap, and this apparatus gap has an increasing ratio of 12.921923284/10.66420099 or namely 1.211710403 and it is this factor that converts the 1.586124275 m into 1.921923284 m !
In conclusion then, I hope that I've exposed some more of the intricate goings-on of the Michelson-Morley, and thus shed some more light on the actual motion of light itself! I trust that everybody can share in the satisfaction that knowledge brings to all of us!