# Deriving Lorentz contraction from Michelson-Morley experiment

1. Aug 8, 2014

### dsoodak

In order for the light to take the same amount of time for both paths in the interferometer, simple geometry implies that the ratio between length and width will have to decrease. A straightforward derivation gives L/W=Sqrt(1-v^2/c^2) where the velocity v is in the direction of the length.

However, I can't figure out a way to show that the width remains constant using only this experimental result. Precise measurements of time dilation (example: every time a gps satellite is used) demonstrates that width is unchanging (as would 2 high speed spacecraft flying past each other and verifying that their wing tips touch exactly), but I thought that the MM result by itself was supposed to pretty much imply all of SR.

Dustin Soodak

2. Aug 8, 2014

### Staff: Mentor

Relativity can be deduced to within about .1% from three experiments:
Michelson Morely
Ives Stillwell
Kennedy Thorndike

I don't think one is enough.

3. Aug 8, 2014

Thanks!

4. Aug 9, 2014

### Staff: Mentor

Hi dsoodak,

I thought that it might be helpful to post a reference to the paper where they prove those three experiments are enough to deduce relativity, even without assuming the postulates.

http://authors.library.caltech.edu/11476/1/ROBrmp49.pdf

I hope it helps. If you have any questions, feel free to ask.

5. Aug 23, 2014

### losk

Question: has Michelson-Morley experiment ever performed in a setup moving relative to Earth? For example in an airplane, or a vehicle, or in some laboratory moving setup, or maybe aboard a satellite that is not geostationary?

6. Aug 23, 2014

### Staff: Mentor

Moving relative to which part of the earth? Because of the earth's rotation, every point on the earth's surface is moving relative to every other point.

7. Aug 23, 2014

### Staff: Mentor

The GPS system is like a continuous, world-wide Michelson-Morley experiment, much more precise than the original experiment.
And see the previous reply: it does not really add anything new.

8. Aug 23, 2014

### losk

moving relative to ECEF frame, the same one in which MM experiment was originally conducted.

9. Aug 23, 2014

### losk

I don't understand how is GPS system like MM experiment? MM is designed to measure the potential difference in times it takes light to move in different directions, in a two way trip. How is this like GPS, and what is the basis for saying so, like a paper with experimental data?

10. Aug 23, 2014

### Simon Bridge

i.e. in a paper examining a variation from the null result:
http://arxiv.org/pdf/physics/0605067.pdf
... should also give you a bigger picture.

GPS system assumes that SR is correct - and needs it to be correct to higher precision than MM measured - in order to work. If the speed of light postulate was even a little out, then GPS would drift off accuracy quite fast. You can work it out from the GPS literature.

11. Aug 24, 2014

### Staff: Mentor

The GPS system operates by precisely measuring the light travel time between various sources (the GPS satellites) in known positions and the receiver. The signals from the sources are traveling in different directions, and all the sources are moving at different speeds relative to one another and the receiver. If the speed of light were different on any of these paths, the computer in the receiver would calculate an incorrect distance from the source and hence an incorrect location for the receiver.

If Michelson and Morley had had access to the modern GPS system back then, they would have used it instead of building their interferometer

12. Aug 24, 2014

### Staff: Mentor

You may be misunderstanding what a "frame" is. Everything always happens in all frames, so it makes no sense to talk about an experiment being conducted "in a frame". All the frame does is give us a rule for assigning coordinates to events, and anyone is free to choose any frame, or multiple frames, for this purpose - you just have to be consistent.

Thus, your question about doing an MM experiment in a frame other than ECEF makes no sense. However, you might be asking a different question, namely whether anyone has ever done an MM experiment in a lab that is not at rest relative to the surface of the earth directly underneath it.

If that's your question, I don't know if it's been done, but I'd be surprised if anyone had tried it. It wouldn't make a lot of sense to loft a piece of 19th-century experimental equipment into earth orbit when we have lighter and more capable devices such as GPS satellites that work better for that purpose.