Length Contraction: Measuring a Difference of 55 Nanometers

[Foppe Hoekstra]

TL;DR Summary

If the table (with the mirrors, beamsplitter, etc.) is rotated 90 degrees, one arm will get shorter (due to lengthcontraction) because its longitudinal speed goes from zero to 30 km/s (our speed around the sun) and the other arm will get longer as its speed goes from 30 km/s to zero. So with a total 'armlength' of 11 meter, the difference in lenghts of the lightpaths will be around 55 nanometer, to be messured as appr. 0,1 wavelength. They messured no differences more than 0,02 wavelength.

If the table (with the mirrors, beamsplitter, etc.) is rotated 90 degrees, one arm will get shorter (due to lengthcontraction) because its longitudinal speed goes from zero to 30 km/s (our speed around the sun) and the other arm will get longer as its speed goes from 30 km/s to zero. So with a total 'armlength' of 11 meter, the difference in lenghts of the lightpaths will be around 55 nanometer, to be messured as appr. 0,1 wavelength. They messured no differences more than 0,02 wavelength.

 

[Ibix]

If you regard the apparatus as moving then light doesn't travel a distance equal to the length of the arm, because the ends of the arm are moving while the light travels along it. If you factor in length contraction of one arm and the motion of the mirrors in both arms then the flight time is the same. Length contraction alone is not enough to analyse this.

 

[Nugatory]

If the table (with the mirrors, beamsplitter, etc.) is rotated 90 degrees, one arm will get shorter (due to lengthcontraction) because its longitudinal speed goes from zero to 30 km/s (our speed around the sun) and the other arm will get longer as its speed goes from 30 km/s to zero.

You’ve just described how the lengths of the arms would behave according to an observer who is moving at 30 km/s relative to the apparatus. But the lab and the experimenters are at rest relative to the apparatus, so they find no length contraction - as far as they are concerned nothing is moving. (If you’re still not clear on how you’ve gone wrong here, ask yourself why you’re considering the 30 km/s from the earth’s movement around the sun, but not the additional contributions from the sun’s moving around in the galaxy, the galaxy drifting through the local group, and so forth).

So we have two equal-length arms and we’re testing whether light takes the same amount of time to traverse both arms - if it does the speed of light is the same in both arms and if it does not the speed of light is not the same in both arms.

 

[Foppe Hoekstra]

You’ve just described how the lengths of the arms would behave according to an observer who is moving at 30 km/s relative to the apparatus. But the lab and the experimenters are at rest relative to the apparatus, so they find no length contraction - as far as they are concerned nothing is moving. (If you’re still not clear on how you’ve gone wrong here, ask yourself why you’re considering the 30 km/s from the earth’s movement around the sun, but not the additional contributions from the sun’s moving around in the galaxy, the galaxy drifting through the local group, and so forth).

So we have two equal-length arms and we’re testing whether light takes the same amount of time to traverse both arms - if it does the speed of light is the same in both arms and if it does not the speed of light is not the same in both arms.

I see now that I missed the point that in RT c is considered to be constant to every moving frame. So whatever the speed, and the contraction that goes with it, may be, the light (or the situation) is 'not aware' of any chances.