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An Introduction to Einstein's Theory of Relativity
Yes, it's all relative.
No, I'm not talking family. I'm just preparing myself to write an essay on Relativity, and I'm wondering how to begin.
Before Albert Einstein, there was Isaac Newton. Newton's Universe is the universe of common sense. Before I can discuss Einstein's Universe I need to describe what existed before. The Newtonian Universe makes the following assumptions.
The problem with Relativity is that it violates all of the above common-sense ideas. Because of that, many people have problems believing Relativity rather than understanding it.
Newton's mechanics served well until around the middle of the 19th Century. It was observed that Mercury's orbit was not quite as it should be. People thought that another planet was tugging at Mercury and causing it to deviate from its predicted (Newtonian) path. This hypothetical planet (originally called Vulcan) was never seen. Newton's theories worked with all other known phenomena so the tiny discrepancy in Mercury's orbit was forgotten.
Then came James Maxwell. He produced the theories of electricity and magnetism that are still current today. He proved that light was a wave travelling at 300,000 km/s. Some people said 'waves in what?' Water waves travel in water; sound waves travel in air. What is it that light waves travel in? There was no logical answer so an ancient idea was revived: the aether.
The aether was postulated to be a medium that vibrated the light wave along. This aether had never been observed. If it was made of matter it would slow down objects like the Earth and cause them to spiral into the Sun! The aether was thus solid enough to let light vibrate in but light enough to let the Earth travel in space without hindrance.
Two physicists decided to try and observe the aether. Albert Michelson and Edward Morley set up an experiment to try and measure the drag of the aether on the Earth. They measured the speed of a light beam travelling parallel to the direction of the Earth's motion and compared that to a light beam travelling perpendicular to the Earth's motion. The aether idea predicted that light would have a slightly different speed in the two directions. They would, in fact, be measuring the Earth's speed against the aether. Their equipment would have been accurate enough to have measured this difference if the Earth had been travelling at a speed of 5km/s around the Sun. The Earth actually travels around the Sun at nearly 30km/s. Michelson and Morley found no difference in the speed of light in two perpendicular directions. This meant one of three things:
Michelson and Morley thought that (1) was the problem since there was overwhelming evidence that the Earth was going around the Sun. They improved their equipment and made it more sensitive. Try as they might, they could not find any difference in the speed of light. Eventually they gave up and published their experiments describing them as a failure.
Einstein read about the experiment. It actually confirmed an idea that had been germinating in his mind since he was a teenager. At the time (1905), Einstein was working as a patent clerk in Switzerland. Einstein took the Michleson and Morley experiment at face value. He made two assumptions about the Universe and proceeded to use these assumptions to completely rebuild physics.
His two assumptions were:
The first assumption is not too tricky. The aether was postulated to explain something that really did not need explaining. Light is an oscillation of magnetic and electric fields. That is what the wave is, not a vibration in a medium.
The second assumption, however, is against all common sense. Light travels at 300,000 km/s. If an object travelling at 100 km/s sends out a beam of light to us and we measure its speed, common sense tells us that we should measure the speed of light to be 300,100 km/s. Similarly, if the light source is moving away from us at 100 km/s, we should measure the speed of light at 299,900 km/s. But no, Einstein says it will be measured at 300,000 km/s regardless of how the source or the observer is moving. This assumption violates common sense but has since been tested with equipment of such accuracy that if it wasn't valid, the discrepancy would have shown up.
The first assumption actually means that you cannot measure absolute speed. Speed is relative.
You can measure your speed relative to the Earth, the Earth's speed relative to the Sun, the Sun's speed relative to the centre of the Galaxy, etc. What you cannot measure is your speed absolutely. The second assumption means that many quantities that we thought of as constant and unchanging actually vary for different observers. These are the predictions that Einstein made.
The mass of an object increases with its velocity. At low speeds this effect is very difficult to observe. As a body approaches the speed of light its mass approaches infinity. This is where the dictum that nothing can travel faster than light came from. It has been tested with sub-atomic particles and close binary stars. In both cases the mass change has been observed and agrees with Einstein's predictions. In fact, because Mercury is the closest planet to the Sun, it's velocity is high enough to increase its mass enough to cause the discrepancy with its orbit observed over half a century before!
The length of an object decreases with its velocity. Again, Einstein's equations predict that an object's length would become zero at the speed of light. This has been tested indirectly by an experiment depending on something called the Mossbauer Effect.
Time slows down for a body that is moving and for one in a gravitational field. This is one of Einstein's most fascinating predictions. Again, it has been tested many times. Sub-atomic particles last longer before decaying when they are moving close to the speed of light. Energy from Pulsars and White Dwarfs (stars with huge gravitational fields) slow down the vibration of atoms which can be detected. Using Atomic clocks it is possible now to measure these effects on the Earth. At the speed of light all time slows down to zero. The speed of light seems to be forever unattainable if Einstein is correct.
Light should bend around a gravitational field. This one is difficult to explain but is to do with time varying near a strong gravitational field. This was first measured during a total eclipse of the sun in 1919. The effect is similar to refraction where a stick appears to bend where it enters water. These so-called gravitational lenses have since been observed amongst distant galaxies.
For Cosmology, if there is enough matter in the Universe, a beam of light will eventually return to its starting point.
Matter and Energy are the same phenomenon. This is the famous equation,
It means that matter, m, can be converted into a very large amount of energy, E, if it is multiplied by the speed of light (c) squared. This equation explains the source of energy of stars as well as atom bombs!
The Universe is not static. This prediction indicates that if the Universe were static it would be unstable. A few years after this prediction was made, the Universe was found to be expanding.
The Theory of Relativity does two things that any good theory should do. Firstly, it explained existing observations using only a few assumptions (the Michelson and Morley experiment, Mercury's orbit, the energy of the Sun). Secondly it made predictions that could be tested. In this case the predictions were ridiculously at odds with common sense (time slows down, light is bent by gravity, mass increases for a moving body) and yet the theory has passed every test.
Modern laser techniques cannot measure any difference in the speed of light no matter what speed the source or observer have. Many observations and inventions would not work unless relativistic effects are taken into account. The study of Cosmology would not make sense without Relativity.
As such, Relativity is one of the two great theories of the 20th Century. The other being Quantum Mechanics.
© 1997, 2011 KryssTal
Albert Einstein Online
A site full of interesting links for the man his theory and his ideas.
A good site about General Relativity.