Notes: I have used a variation of Brian Greene's example of the warping of space from his book "The Elegant Universe", for it is the best and easiest explanation I can think of.

Have you ever heard of Relativity and Quantum Mechanics, and the conflict between them? Well, it is one of the biggest problems in science! These are two greatest theories in science, yet they cannot go together. Relativity is on a huge scale and is gentle, but Quantum Mechanics is on the smallest scale and is chaotic.

General and Special Relativity is, as you probably know, are Albert Einstein's great theories of gravity, light, time, and energy. It replaced Isaac Newton's theory of gravity. Einstein published his first theory of Special Relativity in 1905 in the German physics journal, Allenen Der Physik. At the time, he was a young man, only 26 years old, working at the Patent Office in Bern, Switzerland. Einstein's work in Special Relativity publicly began an amazing career which resulted in Albert Einstein being widely recognized as the greatest scientist of the last millennium, and certainly the driving force behind the tremendous advances in physics that occurred in the 20th century. In reviewing his theories we will see, that Einstein's influence continues in the work that followed and in the way we see our universe.

Special Relativity

Special Relativity is most probably one of science's best known theories. It solved a paradox of light which Einstein had been wondering ever since he was sixteen. His question was - if the speed of light is constant, what happens if you chase after a light beam at light speed? The sixteen year old Einstein did not know that many of the world's leading scientists were trying to solve this problem. According to old theory of Isaac Newton, the light wave was stationary and you would catch up with the light wave. The prevailing theory of the early 20th century was presented by Maxwell, who stated that there is no such thing as stationary light, hence the problem. Albert Einstein himself eventually did solve this problem with Special Relativity. At the same time, our ideas of space and time were forever changed.

Probably it is surprising that Special Relativity only essential concern is to know precisely what the world looks like to "observers" who are traveling relative to one another. Special Relativity states that observations between two individuals are more subtle and thoughtful based on the perspective of the observer. Relativity claims that observers who are relative have different views of distance and time. For example, pretend the year is 1970 and big, fast cars are the thing. Slim has just bought a shiny new Trans Am and wants to see how fast it goes. He goes to the local motor raceway. After getting the car up to speed, he goes around the track once at 120 miles per hour. Slim's friend Jim times him from the sideline. Wanting a second opinion, Slim also times himself. Common sense tells us that they will measure the same time, but according to Special Relativity this is not true. Jim might measure a flat 30 seconds, but the moving Slim will measure 29.99999999999952 seconds- a tiny bit less. Even with the most accurate watches this would be so. It is not the watches that cause the difference, it is the relative time. Based on this example it is no astonishment that this has almost no effect on everyday live.

The perception of distance is the same as Slim and Jim will show us. During another run, Jim, still on the sideline, uses a trick to find the length of the car. He starts his watch as the front of the car passes him and stops just as the back passes him. Then, all he has to do is multiply the speed of the car by the time he measured to determine that Slim is driving at 120 miles per hour. But to check himself he measures the car when it is not moving. Again common sense tells us that if Jim measures the car standing still it will be the same moving, but again this is not true. Say Jim measured the car standing still to be 16 feet long, but when the car is moving it will be 15.999999999999974 feet long- again a tiny bit less.

These are very small differences, but if we were to travel much faster, say, 580 million mile per hour, Jim, using his stopwatch way of finding length would find that the car "shrunk" to only eight feet. Slim would find that his time measured when he was driving would be only half of what Jim would time. As we begin to think of the speeds and distances of the universe, we come to see that relativity could have quite a significant impact.

But that is just one aspect; there is also the principle of relativity. This is that whenever we talk about speed or velocity we must specify who or what is measuring.

For instance, Ron is floating in absolute darkness with only a small flashing red light, from his perspective he is stationary. After awhile he sees a green light in the distance, this flashing light belongs to Rachel, who eventually passes by and waves. Now from Rachel's point of view, feeling completely stationary, a flashing red light comes towards her and she sees Ron, and while he passes by she waves.

Both are valid and true, but who was moving? Each feels completely stationary, and sees the other pass by them. Neither is "right" or "wrong.

This is an excellent example of the principal of relativity. Motion is relative, at least to comparison to other seen objects. This example has no "absolute" motion, only relative ("Rachel passes by Ron at 10 mph, in the opposite direction). But it is important to remember that there are no forces, it is "force-free" motion.

Another key in Special Relativity has to do with light and its motion. After a almost a century of dedicated scientists, light travels at 670 miles per hour regardless of other objects for comparison.

So say someone throws a baseball to you at 20 feet a second, and you run away, then the baseball will no longer be heading to you at 20 feet per second, say you run away at 12 feet per second, you would find that the baseball will travel to you at 8 feet per second (20-12=6). But the same would not happen to light, no matter how fast you try to run from light it always moves towards you at 670 million miles per hour. (Maxwell)

To explain the effect of time warping, let's use a "light clock", the simplest and most impractical clock ever. It is two mirrors suspended by a metal rod, and facing each other, with a light beam bouncing between the two mirrors and a "tick" is the light beam taking a round trip between the two mirrors, that's about one billionth of a second. Now imagine a stationary light clock, and then a light clock moving by the other, from our perspective in the picture the one moving has to go along a zig zag path, therefore taking longer to "tick".

This also applies to everything else, in motion will "live" longer than something at rest. This has been proven directly to be true, with muons, which disintegrate after two millionths of a second, when sitting at rest, but when put into a particle accelerator and made to go up to speeds of 99.5% of that of light, which is 667 million miles per hour, a muon's life will increase by a factor of ten, a lot compared to two millionths of a second. These traveling muons though fell like the do only live two millionths of a second, so if humans would go as fast as 99.5% of the speed of light we would live not just 70 years, but 700 years. But since the time feels that same, we would be living in "slow motion". For instance if you read a book a day in one year, but if you kept moving at 99.5% the speed of light it would take you 10 years to read the books you read in one "normal" year.

So you might ask, "Well why don't we just speed up the muon some more, like maybe to 99.999%?" The answer is simple; we can't because the muon will have an increased mass, if we did get a muon to go 99.999% the speed of light its weight would increase by a factor of 224. So therefore it we would need an infinite amount of energy to get to the speed of light, so nothing can go the speed of light. But if you know a way I bet a lot of scientist will want to know!

General Relativity: The Downfall of Newtonian Physics

Since nothing can go the speed of light and light is always going 670 million miles per hour, no matter how fast you chase after it, this could only mean, NEWTON WAS WRONG! So Einstein needed a new idea of the universe to have his new theory work, so thus we get General Relativity.

Since there is no way to go the speed of light, and this applies to everything, even gravity. He needed a new universe to have his theory work because of one reason. This reason is this simple problem, according to Newton if the sun exploded we would feel it's gravity go away at once, then we would find out that the sun exploded after the gravity from the sun went away. But in Einstein's theory it is not possible that anything goes faster than light, so we would feel the effect, and the aftermath of the sun exploding at the same time.

Newtonian gravity states that something big, like the sun, instantaneously grabs hold of the earth and sends it into orbit around itself. But according to Einstein's theory gravity is like a huge 3D grid, making cubes "stacked up on top of each other. This "fabric of space" is the 3 dimensions we see, and the fourth dimension of time. Something very large, like the sun, would warp the fabric of space to create a curve. Something smaller would go into orbit by rolling along the curved path the sun makes. So if the sun was to explode the sudden disappearance of it would make a "ripple" in the space fabric. And it would travel with the explosion, most probably at light speed, so we would see and feel the aftermath of the sun exploding. (If your having trouble visualizing that think of a huge sheet of rubber and a bowling ball as the sun then for the "earth" think of a marble rolling along the curve the bowling ball makes, the only drawback to this example is that it is a flat, not 3D, vision of space.)

The reason that we still use Newtonian physics on a low speed scale (everyday speeds, e.g. cars, walking, running, etc..) is that it works perfectly fine, and it is a lot easier. What is the point of doing countless mathematical equations to see how dropping a piece of paper is going to change the universe? (Unless you want the exact answer, but that is not usually needed in that situation.)

Annotated Bibliography


Einstein, Albert, Letter 2 August 1939.

This is a letter signed by Albert Einstein and written by Leo Sziland to U. S. President Franklin D. Roosevelt. In it, Einstein warns Roosevelt of the danger of Germany developing an atomic weapon.

Einstein, Albert, Letter 7 March 1940.

This is a letter by Albert Einstein to U. S. President Franklin D. Roosevelt. In it, Einstein warns Roosevelt of specific work being done in Germany toward the development of an atomic weapon.

Einstein, Albert, Letter 25 April 1940.

This is a letter by Albert Einstein to U. S. President Franklin D. Roosevelt. In it, Einstein encourages more diligent work towards the United States being the first to understand and develop an atomic weapon.

Einstein, Albert, Letter 25 March 1945.

This is a letter signed by Albert Einstein and supposedly written by Leo Sziland to U. S. President Franklin D. Roosevelt. In it, Einstein introduces Dr. Sziland and recommends that Sziland be consulted on further work being done on nuclear fission.

Einstein, Albert , "The World as I See It", Essay. Originally published in "Forum and Century", volume 84, pp. 193-194, Simon Schuster, 1931.

Einstein Explains the Equivalence of Energy and Matter- from the soundtrack of the film "Atomic Physics" J. Arthurr Organization, Ltd. 1948- This is a soundtrack of Einstein explaining his equation E=mc2, in his own voice.


Brian, Denis; Einstein: A Life; New York; John Wiley and Sons Inc.; 1996- In this book I found a detailed biography of Albert Einstein's life.

Pais, Abraham; The Genius of Science; Princeton; Oxford University Press; 1999-

In this book I found information on Albert Einstein's predecessor. This would be useful for comparing him to them and find out what made him so notable for the general public.

Dukas, Helen and Benesh Hoffman; Albert Einstein: The Human Side; Princeton; Princeton University Press, 1979-

In this book I found many personal letters written by Einstein to be sent to his relatives and friends. This would be useful to see what his personal life was like.

Greene, Brian; The Elegant Universe; New York; W.W. Norton and Company Press; 1999-

In this book I found a great deal of information about General and Special Relativity. This would be very useful to understand how ingenious Einstein's ideas were, and how revolutionary his ideas were.

Parker, Barry; Einstein's Brainchild: Relativity Made Relatively Easy!; New York; Prometheus Books; 2000-

This book explains what General and Special Relativity states, and how it effects normal life, and some insight on how Einstein came up with these ideas.


Einstein Revealed, Nova Online 2004, available wgbh/nova/einstein/html-.

On this website I found an article comparing him to Isaac Newton by his works and effect on science and found that you cannot compare the two physicists. I also found animations and photos.

Albert Einstein: Image and Impact, American Institute of Physics, 2004, available online: history/einstein;

This website had a good collection of photos showing Einstein. It also had a good essay about Einstein. I found primary resources, an essay titled "The World As I See It" by Albert Einstein. I also found many photos at this website.

Pictures of Albert Einstein, Joachin Reinhardt, 2004, available online: . /~ ;

I found a good collection of photos here from the archives of the University of Frankfurt Germany.

The Caltech Institute Archives, Caltech Archives PhotoNet California Institute of Technology, 2004, available: . ;

PhotoNet is a very good site that has a large photo archive of historical significance.

Albert Einstein and the David and Fela Shapell Organization Project at the Jewish National University Library, The Hebrew University of Jerusalem, 2004, available: .info;

In Albert Einstein's will he wanted all of his records to go to The Hebrew University of Jerusalem, this is their archives. There are images available of notes and papers written in Einstein's own hand.