Interpretation of the Michelson-Morley experiment

[Daniil]

Dear Sirs,

I have a question regarding the interpretation of the Michelson-Morley experiment.

As I understand it, the special relativity theory implies that, say, if I were to watch another person in a n inertial reference frame (say a vehicle) moving relative to me send a light beam towards the front of the vehicle, we would both register the same speed of light. This would have to be compensated by the slowing of the clock of the person inside the vehicle relative to mine.

On the other hand, in the Michelson-Morley experiment, there is no external observer, since the whole experimental set-up is moving together with the Earth. There is thus no external observer relative to whose clock the time within the set-up would slow down. Yet, two light beams are said to arrive to the detector at the same time, even though one of them seems to have covered a longer distance.

How can this be explained, if the aether drag hypothesis is rejected?

 

[wabbit]

Why would it "have to be compensated" ? The invariance of the speed of light is a primary fact, a property of relative velocities and how they combine, it doesn't require compensation.

It does imply a lot of consequences, including that in some situations one clock appears to run slower than another in a certain frame, but if you are in a situation where you consider only one clock then you cannot even define a time dilation - but this says nothing about the speed of light.

Also I am not sure the aether drag hypothesis is necessarily rejected, my (admittedly limited) understanding is that is simply irrelevant and hence usually ignored.

 

[Dale]

two light beams are said to arrive to the detector at the same time, even though one of them seems to have covered a longer distance.

Therefore, they must have covered the same distance. This demonstrates length contraction.

 

[Daniil]

Therefore, they must have covered the same distance. This demonstrates length contraction.

But doesn't the special theory of relativity claim length contraction only for the moving objects?

 

[Dale]

But doesn't the special theory of relativity claim length contraction only for the moving objects?

Every object is moving in most frames. In the frame you described, where one path seems to have covered a longer distance, in that frame the interferometer is moving.

 

[Daniil]

Every object is moving in most frames. In the frame you described, where one path seems to have covered a longer distance, in that frame the interferometer is moving.

But the interferometer could in principle be not a single, uniform object but just several mirrors separated by distances. Or not? And would it matter if it could?

 

[Dale]

And would it matter if it could?

No. It would not matter.

 

[Janus]

But the interferometer could in principle be not a single, uniform object but just several mirrors separated by distances. Or not? And would it matter if it could?

To expand on DaleSpam's reponse:

Length contraction is not something that "acts" on physical objects. It is due to the difference in how inertial frames measure distance. If we are measuring a distance from two different inertial frames, we come up with different answers. It doesn't matter whether that distance is the length of a single solid object, the distance between two unconnected objects, or even just two points in space with no objects.

 

[harrylin]

Dear Sirs,

I have a question regarding the interpretation of the Michelson-Morley experiment.

As I understand it, the special relativity theory implies that, say, if I were to watch another person in a n inertial reference frame (say a vehicle) moving relative to me send a light beam towards the front of the vehicle, we would both register the same speed of light. This would have to be compensated by the slowing of the clock of the person inside the vehicle relative to mine.

On the other hand, in the Michelson-Morley experiment, there is no external observer, since the whole experimental set-up is moving together with the Earth. There is thus no external observer relative to whose clock the time within the set-up would slow down. Yet, two light beams are said to arrive to the detector at the same time, even though one of them seems to have covered a longer distance.

How can this be explained, if the aether drag hypothesis is rejected?

First of all, this is not quantum mechanics; "observer" is more abstract here, one can mean with that any reference system. You are putting yourself in the shoes of an observer relative to whom the interferometer is moving when you write that "two light beams are said to arrive to the detector at the same time, even though one of them seems to have covered a longer distance." The obvious conclusion is length contraction of the one arm relative to the other.

Note that the ether drag hypothesis was rejected by means of another experiment that Michelson and Morley repeated before the experiment that made them famous.

But the interferometer could in principle be not a single, uniform object but just several mirrors separated by distances. Or not? And would it matter if it could?

In the standard experiment that distance is controlled by the interferometer arms.
They performed not a complete series of experiments although they had in mind doing so; however others did. A complete experimental series consists of the following procedures:

1- do measurements while rotating the apparatus
2- wait several months in order to to slowly change the velocity of the apparatus.
3- repeat 1.

So, the answer may depend on how you determine or control the distances between the mirrors in those procedures. How do you want to change the velocity of the mirrors without some kind of arm or ruler? If you use a different arm or ruler or even the floor, or if you use light to compare with light, you should not expect to find any effect. However, if you would be able to accelerate the mirrors independently in an identical way for procedure number 2 (in practice that's hardly possible to do), then you would reproduce "Bell's spaceship paradox". As Bell explained with that "paradox", obviously the distance between the mirrors cannot contract by itself without atomic bonds to contract that distance.