# Expected result of vertical Michelson-Morley Experiment [duplicate]

What would the result of a vertical variation of the Michelson-Morley experiment be? I.e., if one were to compare light traveling along a horizontal arm with light traveling along a vertical arm (perpendicular to the surface of the Earth), what would the result be?

My understanding is that light traveling along each arm will both travel at c and consequently the result of such a variation of the experiment will be exactly as all of the previous (fully horizontal) versions of the experiment. Namely, that there is no directional dependence in the speed of light.

Is this understanding correct?

## marked as duplicate by ACuriousMind♦, Kyle Kanos, John Rennie, user10851, SofiaMar 15 '15 at 9:35

Leaving aside for a moment the comments made by dmckee et al, what matters is the angle of the measurement to the direction of motion. If an ether exists and you make a measurement along the direction of motion then you would get a different result to a measurement made at right angles to the direction of motion. It doesn't matter whether the right angle measurement is horizontal or vertical as long as it's at right angles to the velocity vector. For obvious practical reasons it's a lot easier to make the measurements horizontally, but you are correct that it shouldn't matter whether the equipment is horzontal or vertical.

Well, not quite.

As dmckee says in his comment, the Earth's gravitational field causes a (very, very small) shift in the frequency of light that doesn't travel horizontally. The M&M equipment was too small and had too poor resolution to detect this change, so it wouldn't have mattered if they had done the experiment vertically. However it is possoble to measure the effect and as Kyle mentions this was first done in the Pound-Rebka experiment.

There are a couple of Einstein's papers that talk about the constancy of the velocity of light, the most important of them, in my opinion, is the one called On the Influence of Gravitation on the Propagation of Light. In this paper he notices that the velocity of the light depends on the potential gravitation, yes!

The velocity of light shall be regarded as constant only in a space where the potential gravitation is constant, e.g. imaginary spherical surface over a celestial body. So, if you observe the pattern of interference from a Michelson-Morley interferometer in different phases of the moon, you will see different patterns of interference, because the potential gravitation on the Earth surface has changed due to different phases of the moon. Or if you play the Michelson-Morley experiment in vertical plane, you will see the changing in the interference pattern as well. Search for "Michelson-Morley experiment vertical" on Youtube and you will see.

Yes. The speed of light is independent from the direction and the reference system. In fact Michelson and Morley did their experiment in different directions and periods of the year in order to work in different earth revolution period, and they found always c.

• Did MM do it vertically? I thought that they had only rotated it horizontally. – Kyle Kanos Mar 2 '14 at 18:11
• Honestly i don't know that. I only know that they prove it in different periods of the year and different direction. There are a lot of "light-experiments" more complicated (surely someone reproduce MM vertically too). – LC7 Mar 2 '14 at 18:13
• M&M did not do it vertically, and doing so introduces corrections related to GR as well as those related to SR. – dmckee Mar 2 '14 at 18:18
• To further dmckee's comment, see the Pound-Rebka experiment. – Kyle Kanos Mar 2 '14 at 18:20
• I dont know GR but i think that SR dont modify c. – LC7 Mar 2 '14 at 19:56

I believe that the vertical leg could differ from the horizontal leg. If the vertical leg is long enough, then the difference in air pressure would change the time the beam took to complete the path.