Rotating through the full 360 degrees in the Michelson-Morley.

Frank Russo - May 20, 2010.

In the usual Michelson-Morley experiment rendition, the orbital arm which is contrasted to the perpendicular has the away orbital arm travelling with the 'orbital' velocity. So naturally if the set-up is rotated through 90 degrees, the original perpendicular would end up travelling with the 'orbital' velocity in the away arm. However, to have the full functioning experiment, one must be able to rotate through the full 360 degrees, taking readings at every 90 degree interval.

This means that at the 270 degrees readings, the original perpendicular will be in the orbital position with the away arm travelling into the 'orbital' velocity. This scenario is of course different to the one we've considered so far! Obviously the away orbital will be the full 10.830,799,18 m with an actual  9.219,896,171 m travelled with the mirror travelling  1.610,903,011 m to meet the beam... the origin would of course move in the same direction as the mirror leaving the return arm (hollow) as still  10.830,799,18 m. However we do know that the total away and return trip, is a total of  22.00000000 m... hence when taking into account the effect of the motion of the apparatus, we are dealing with a total return arm of  22 minus 9.219896171 metres giving us  12.780,103,83 m.

In view of the foregoing we can actually work out the unexpanded length which would give us this latter length by dividing this 12.780,103,83 by the contacting factor of   [C absolute / C absolute-Vabsolute] ,  this factor being 1.211,710,403 .

The resultant actual length becomes  10.547,160,28 m and this is  0.2836389 m less than the full  10.83079918 m - with this  0.2836389 actually being equal to two lots of   0.14181945 m. So in other words the situation which we saw at the 90 degree rotation the other day, is actually somewhat reversed!

Instead of the longer arm being even longer and the shorter arm being even shorter, at the 270 degrees slot the short arm is made a bit longer and the long arm made a bit shorter. This rearrangement is of course understandable seeing that the 'orbital' speed is now "reoriented" as coming from the opposite direction subjectively speaking!

Of course as previously outlined the other day, when rotating the starting away arm, you are rotating the full  10.830,799,18 metres! The rotation therefore actually works very well!

In conclusion then, one would have expected what worked at 90 degrees to also work at 270 degrees regardless of the fact that I have not studied these recent figures as much!

Frank Russo.