# michelson morley experiment construction

#### RossBlenkinsopPerth

If you built the MM experiment in a frame that was subject to an unknown velocity vector would the arms of the experiment be the same length ?

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a

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#### RossBlenkinsopPerth

see attached images PDF and text PDF

The bottom images is the analysis of the arm parallel to Vu. A photon would travel from the source (point a) to the end of the arm (point g), In that time the MM experiment would move a distance tag x Vu (tag is the time from point a to g) the direction Vu and then mutatis mutandis for the return trip point g to e

Vv is the velocity of the photon in the direction perpendicular to Vu I resolved the photon travelling at an angle to Vu into its horizontal component and perpendicular to Vu component

By my reckoning something in the experiment , when it was built, had to be askew for it to work, or alternatively Vu = 0 in which case the earth is miraculously absolutely stationary

Actually my analysis is not right as the MM experiment worked of the phase difference of the photon, so the length of the arms only has to be an integer multiple of the wavelength of the photons , not necessarily the same length ?

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#### RossBlenkinsopPerth

Actually my analysis is not right as the MM experiment worked of the phase difference of the photon, so the length of the arms only has to be an integer multiple of the wavelength of the photons , not necessarily the same length ?

#### RossBlenkinsopPerth

but that means by chance the arms could be the same length , so back to square 1, something was askew

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#### topsquark

Forum Staff
but that means by chance the arms could be the same length , so back to square 1, something was askew
As you pointed out it is the phase difference between the two beams which is important, not the actual length of the arms. For example, the experiment would be done over a several days and the phase difference tracked. If the aether thoery was correct there should be a detectable phase difference. (You could even potentially do it over the course of a year if you have the patience.) This is a very sensitive experiment and it clearly showed that there was no difference in the lengths of the bars.

-Dan

#### RossBlenkinsopPerth

As you pointed out it is the phase difference between the two beams which is important, not the actual length of the arms. For example, the experiment would be done over a several days and the phase difference tracked. If the aether thoery was correct there should be a detectable phase difference. (You could even potentially do it over the course of a year if you have the patience.) This is a very sensitive experiment and it clearly showed that there was no difference in the lengths of the bars.

-Dan
you have misunderstood what i am saying. The experiment itself would have been constructed in a frame subject to an unknown velocity vector Vu.

I did an analysis of that and found that, if the arms were the same length, then the round trip for each photon would be a different time.

Given your response the outcome is unclear as i will have to do the analysis for a photon of a given wavelength and see if the unknown velocity vector Vu has an impact on the result.

As it used the phase diff of the light I know it is super sensitive

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#### RossBlenkinsopPerth

Not sure what to make of this result

On the above analysis the return time on the vertical leg is different to the return time on the horizontal leg. That is ok as long as the difference is an integer multiple of the wavelength of the photons used, not allowing for possible Doppler effects

If Vu has no impact i should be able to rotate the MM experiment by 45 degrees, or some angle, and I should get the same result. If I rotate the MM experiment by 45 degrees then both paths are an identical length, so Vu does change the analysis or some other phenomena is at play. , see attached PDF image

So, not allowing for Doppler effects, MM should have been able to detect Vu, or Vu was zero which is extremely unlikely or doppler is causing the paradox

Can anyone show me how to do the Doppler analysis on this ?

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#### RossBlenkinsopPerth

the other possibility is when they were building the experiment Vu was influencing the build

#### HallsofIvy

When you write "subject to an unknown velocity vector" you seem to be under the impression that there is some absolute frame under which we could have such a velocity vector. Even in "Gallilean relativity" there is no such frame. Every object has 0 velocity relative to itself. If that is not what you mean, the "unknown velocity vector" is relative to what?