On 10/31/16 10/31/16 - 4:21 PM, Dono, wrote:
> On Monday, October 31, 2016 at 1:14:19 PM UTC-7, tjrob137 wrote:
[... Skinner's example, which I'll not discuss until I get the book]
>> In fact,
>> for a Michelson interferometer with arms of different lengths (within the
>> coherence length of the source), SR predicts ZERO fringe shift as the
>> interferometer is rotated, independent of the lengths of the arms.
>
> Let's check this claim:
To do that, you must explain your notation and actually USE SR.
> In the frame of the lab, the time difference is
> [tex]t_0=\frac{2L_1}{c}-\frac{2L_2}{c}[/tex]
WHAT "time difference"????? I am not clairvoyant. You must describe the physical
situation and the meanings of symbols.
Your use of TeX is obfuscatory. Please use the usual ASCII
notation everyone else uses around here:
t_0 = 2 L_1/c - 2 L_2/c
We can all read this MUCH more easily than what you wrote.
> [tex]L_1=L_2+\epsilon[/tex]
> So
> [tex]t_0=\frac{2 \epsilon}{c}[/tex]
> When you rotate the interferometer 90 degrees, the difference doubles and the
> fringes travel about the zero point by a total excursion of [tex]4
> \epsilon[/tex]
More undefined nonsense. When you don't explain your physical situation, your
terms, and your notation, all you can write is NONSENSE.
Using SR the analysis of the MMX is simple and straightforward:
The interferometer is at rest in an inertial frame [#]. Light propagates
isotropically in this frame, and with equal-length arms the optical axis has
equal-length paths, and thus has reinforcing interference and a white fringe
(the light source is white). A fringe pattern extends left-and-right from the
central fringe, with "rainbows" at the edges that uniquely identify the central
fringe.
[#] Not strictly true, but as I have explained several times
before, the non-inertial motions of the lab have negligible
effects on this measurement. So I neglect them.
Note I did not need to specify the orientation of the instrument -- this is a
GREAT BIG HINT that the result is independent of orientation: when the
instrument is rotated [@], NOTHING in the previous paragraph changes, and the
fringe pattern visible in the eyepiece remains in the same place -- NO FRINGE SHIFT.
[@] This is the MMX, and the entire instrument is rotated rigidly,
including both arms, the beam splitter, the light source, the
telescope, and the observer (who walks around the rotating
instrument). Dono seems to have some other notions about what
rotates.
Note there is no "aether frame", because THIS IS SR. In SR I can choose any
inertial frame for the analysis, and the inertial frame of the lab and
instrument makes everything simple. As light propagates isotropically in this
inertial frame, the fringe position is completely independent of orientation. NO
FRINGE SHIFT.
Now consider changing the length of one arm [%]. The fringes move as its length
is changed, but once its length is fixed they stop moving. As before, rotating
the instrument changes NOTHING and the fringe pattern visible in the eyepiece
remains in the same place -- NO FRINGE SHIFT.
[%] Keeping the path-length difference within the
coherence length of the source. For a white source this
is not possible, so we must switch to a different source
with longer coherence length. But nothing else changes.
Yes, as one changes the length of one arm, the fringes move. This is the basis
of using a Michelson interferometer to measure distance with an accuracy of a
fraction of a wavelength. But this is NOT the MMX (in particular, no rotation is
involved -- one arm is kept aligned with the distance to be measured).
Tom Roberts