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PhysicsPhysics
Special RelativitySpecial Relativity
Michelson MorleyMichelson Morley
Time Dilation JokeTime Dilation Joke
Quantum MechanicsQuantum Mechanics
1D Schrödinger Applet1D Schrödinger Applet
Introduction
 

In 1095, Einstein released his Special Theory of Relativity. In this theory, our ideas about what space and time were had to be changed. Say you're on a stationary space station in deep space, nothing around you. A spaceship coasts toward you with no rockets on at a velocity of 9/10 the speed of light. In order to confirm the identity of the ship, you carefully measure its lengh (by say bouncing lasers off the front and back and measuring their return times) and you find that the ship is shorter than it was a week ago when it was docked at your station. You look at the top of the ship, which happens to have a giant clock on it, and you notice that the clock is running slower than your clocks. Then you get a message from the ship's captain saying, "Your station's a little flat today, commander. Maybe it's because you're all takin' it easy and movin' real slow today." You laugh at the captain's joke, but aren't surprised that each of you measures the same thing about the other, because ever since the 1900s, people had heard of these phenomena and some, like you, even knew the cause and could accurately calculate the effect. What your encounter reminds you most of is that these things happen not because something changes about their rulers or clocks, but because space and time themselves are different than people used to think.


Brief History
 

Newton's Laws look the same to any observer in any inertial reference frame. This is the principle of Gallilean Invariance or Gallilean Relativity. After Maxell's Equations were formulated to describe electrisity and magnetism, people noticed that these equations do not look the same to observers in different reference frames. It seemed like there was only one frame where they would be valid, and in every other frame, they would have to be modified slightly. Since one of the predictions of Maxell's Equations is the radiation of electromagnetic waves, it seemed like there was some medium throughout space that was doing the waving, which the called the aether. Just like sound waves propogate through air, and they are best analysed in the special frame where the air is, on average, standing still, it was thought that Maxell's Equations were only perfectly valid in the frame of the aether. Experiments were done to measure the movement of Earth through this aether, the most famous being the Michelson Morley Experiment that used light (an electromagnetic wave) to measure the difference between propogation in the direction of the moving Earth and perpendicular to the direction. What Michelson and Morley found was that their experiment wasn't moving through the aether at all. People tried to explain this result by saying the earth was dragging along the aether, and just like like a car drags along the air inside of it so that sound from a radio acts the same within the car as it does in within a house, the experiment is in a local bubble of aether being dragged along.

Einstein came up with a radically different solution. He got rid of the concept of the aether by extending Gallilean Relativity to include electromagnetic phenomena. He claimed that all laws of physics, including the laws of electromagnetism are the same for observers in any inertial reference frame. One of the predictions of Maxell's Equations is that the speed of light is a constant . Einstein's proposal meant that this speed would be measured to be the same in all reference frames -- a very strange prediction given that our intuition and the laws of Gallilean Relativity would predict that if you fire a burst of light from a space station and chase after it with a rocket moving at half the speed of light, people in the rocket would see it moving away from them at only half the speed of light. These two principles -- that the laws of physics and the speed of light are the same in all reference frames -- mean that Newton's Laws of Mechanics and our very ideas of space and time need modification, most drastically in cases where things are moving near the speed of light.


Explaining Relativity
 

Taking the historical approach and motivating relativity by Maxell's Equations the way Einstein was motivated would require knowledge of electromagnetism and some vector calculus. The modern approach, and the approach that's best to take as a beginner, is to start with the two basic principles of special relativity and use only simple thought experiments and simple algebra to derive the classic and unintuitive effects of Non-Simultineity, Time Dialation, and Length Contraction. Then sum these up in Lorentz Transformations and the Invarient Interval. After that, discuss Relivistic Kinematics, and the Relativity of Electromagnetism. In fact, one approach to electromagnetism is to combine the laws of electrostatics and magnetostatics with the laws of special relativity to get the laws of electrodynamics.


Axiom: Principle of Relitivity
 

The laws of physics are the same for any observer moving at a constant velocity (i.e. no forces or acceleration.)

This means that the results of any experiment you perform will be the same if you're moving with respect to another observer or not. There is no experiment you can do and no way you can tell if you're moving at a constant velocity or standing still.


Axiom: Speed of Light is Constant
 

There is a maximum speed called , which is the same for all observers and is also the speed of light in a vaccuum.


Discussion
 

These seemingly reasonable assumptions lead to some amazing results. For example, a ruler moving with respect to you will be shorter along the direction it's moving, which is called Length Contraction. A clock moving with respect to you will run slower, which is called Time Dialation. Also, events that are simultanious to one observer are not simultanious to another observer moving with respect to the first, which is referred to as Non-Simultaneity


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