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PhysicsPhysics
Special RelativitySpecial Relativity
Michelson MorleyMichelson Morley
Time Dilation JokeTime Dilation Joke
Overview
 

In 1887 Michelson and Morley built an interferometer which is shown below. In this interferometer, you shoot a beam of light at a beam splitter. The beamsplitter splits the light into two parts, which each bounce off of their own mirror. The light is then recombined by the beam splitter and goes to a detector. Light is a wave, so when the path lengths are equal, the waves add to produce a bright spot at the detector. When the path length changes by only half a wavelength (which for visible light comes out to be about 250nm) the waves cancel each other to produce a dark spot. For more information about this, see Interference. Even though this instrument can be a few meters big, it can detect changes in distance of hundreds of nanometers.

PICTURE of INTERFEROMETER

Discussion: The Earth Moving Through the Aether
 

The idea was to use this interferometer to measure the movement of the Earth through the Eather. As we'll see, if the concept of the aether was correct, light would take different amounts of time to go through the arm facing in the direction of motion as it would through the arm perpendicular to it.

EARTH INTERFEROMETER PICTURE HERE

Why didn't they just think the Eather was being dragged along with the earth like air inside of a plane?
Discussion: Stationary Interferometer
 

Here is what they thought the interferometer would look like if it was standing still in the eather. Think of the sphere as a photon or a wavefront traveling at the speed of light when you first turn on the light source. Each arrow is an equal distance from the previous one and since the speed of light is constant, one arrow turns on for every clock tick.

Movie: AVI

Michelson Morley Interferometer, stationary in the Aether


Discussion: Interferometer Moving Through the Aether
 

If the interferometer is moving through the aether, the light that is going in the direction of motion takes longer to get to the detector. They thought that by rotating the whole interferometer, one arm would go from being in the direction of motion to being perpendicular to it and the light traveling down this arm would at first have a longer distance to travel and then a shorter distance. They should have been able to detect this change by seing bright and dark fringes pass by their detector.

Movie: AVI

Michelson Morley Interferometer, moving Through the Aether

What they saw was absolutely no change in the interference fringes.

Analysis
  Where was their reasoning flawed? It took 18 years before Einstein came up with a satisfactory explanation. He said that there was no eather. The electromagnetic waves predicted by Maxwell's Equations travel at the speed of light regardless of the reference frame you're observing them in. This is the major break from Galeleo's relativity where if you were traeling with velocity in the direction of light, you were supposed to measure the light's velocity as ----------- c --- v ------- v-c How does Einstein's new postulate solve the mystery of the MM interferometer? First let's see how it's inconsistent with our analysis of the moving interferometer. In our analysis, the speed of light was a constant relative to the eather (the grid underneath.) According to Einstein, if we travel with the interferomter, the speed of light should also be c. TRAVELING WITH INTERFEROMETER 2 Whereas before the light would always cover equal distances in equal times, now it's speeding up or slowing down when it changes directions. Constant speed of light would look like the first picture where both wavefronts get to the detector after traveling the same distance. No matter how you rotate the interferometer, as you travel with it, you would see that both wavefronts will cover the same distance. So what assumptions did we make in our analysis that was false? It turns out that even though the two arms of the interferometer were at equal distances at rest, when moving, space itself is contracted along the direction of motion. This shortens the journey for the light along that arm exactly enough to allow it to catch up with the light in the top arm. This is called . LORENTZ CONTRACTED INTERFEROMETER 2

Discussion: Why not Expanded?
 

Wouldn't the two paths also be the same length of the top arm gets bigger and the side arm stays the same? What about some combination?

If space gets expanded perpendiclar to the direction of motion to compensate by making the top arm longer, it would violate the Principle of Relativity -- you could tell if you were the one moving or standing still. For the example shown below, the peg perfectly fits into the hole when both are at rest. If the peg was "at rest" and the hole moved toward it and got expanced, it would be bigger than the peg. On the other hand if the hole was "at rest" and the peg was zooming toward it, it would be expanded and be too big to fit through the hole. The Principle of Relativity is violated since you would know who was moving faster even though all constant velocity motion should be indistinguishable.

CYLENDARS

Discussion: Couldn't You Measure Contraction?
 

So isn't be squished something that you could measure too? It turns out that when you combine Lorentz Contraction with other Special Relativity effect known as and , there is no way to tell that you are squashed. In fact, since things are equally good from your perspective, everything you're wizzing by looks squashed too.


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