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Relativity: The General Theory
Viral Titan
Introduction
This is an introductory article that overviews general relativity to those with little experience in the field of physics. A little background knowledge on special relativity will be required to fully understand these concepts. Please read this link before reading this article.
Special relativity, the first work of the famous scientist Albert Einstein, changed how we view time. It changed many of our perspectives on the universe as well, such as matter-energy interchangeableness and how strangely things act when moving at high velocities. special relativity, however, dealt only with bodies moving at constant velocity. General relativity now deals with bodies undergoing acceleration. Once the concepts of special relativity are applied to accelerating bodies, we gather now even more significant implications that change how we view space and time, and even alters Newton's laws of gravity.
Equivalence Principle
In special relativity, there exists a certain indistinguishably between a body moving at a constant velocity, and one that is at rest. One of the fundamental postulates put forth by that theory is that there is no experiment that one can preform while in a frame of reference that is moving at a constant velocity that can prove that the person is not at rest. This is the equivalence principle of special relativity. Now consider a new experiment. There is a box out in space with no possible way of viewing what is outside the box. There is a person in this box. Also, consider an identical box with a person sitting on the surface of the earth. The person in the box on earth can tell he is on earth because of the gravity pulling him to the bottom of the box. Now consider the box in space is accelerating upward. That person would also be pulled to the bottom of the box. In fact, if the box accelerates upward at just the right speed, he would be pulled to the bottom of the box exactly as if he were standing on earth. So how can either of these two men claim they are on earth in the first place?
Here we see the equivalence principle of general relativity. It shows that there is way to distinguish by experiment that one is accelerating or in the presence of a gravitational field. This may seem like a trivial point now, but it will have some much stronger implications later.
Curving Space
To properly examine general relativity, we must view bodies that are accelerating. For this, we will examine a race car going around a perfectly circular track. When a body is moving in a circle, it can move a constant velocity (say the car is moving at fifty miles-per-hour the entire time). It is also, however, accelerating. It is constantly accelerating toward the center of the circle it is moving in. Acceleration is defined as a change in velocity, and since velocity does not only mean a speed, but a direction, the constant change in direction as the car travels around is a form of acceleration. This will be the stage to solve the mysteries of accelerating bodies.
Consider the track on which the car is going has a tower places exactly at the center of the circle track for the announcers to sit in. This will be our center point that will come in handy later. So now we have our car going around the track at a relatively low speed, only fifty miles-per-hour. If the driver were to measure the distance he is traveling around the circle using a ruler and then divide by the distance between himself and the tower (the radius of the track), he would get a number close to two pi. This is expected as this is the geometrically accepted definition of circumference. Now take this to the extreme. Consider his race car is traveling extremely close to the speed of light; within a percent. Special relativity now states that his car will become shorter to and observer as a result of length contraction. The other thing that will become shorter is his ruler that is being used to measure the distance he travels. Now, as he travels around the track, he measures the distance he travels to be much longer than it previously was since his ruler is shorter. However, when he measures the distance between himself and the center tower, there is no change since length is only variant in the direction of travel. So now when he divides the circumference of the circle he is traveling in by the radius, he gets a number much greater than two pi. How can this be? The circumference of a circle divided by its radius is always two pi in Euclidean geometry (that is geometry all in a flat plane). This means that he was not traveling in a flat plane, but in a curved surface. If a circle is drawn on the surface of a sphere, the circumference will be much less than the radius times two pi, due to the nature of a sphere's surface. Placing this circle on a more hyperbolic surface gives us a situation in which the circumference is greater than two pi times the radius. So by measuring the track at a near-light speed, it is revealed that the driver is now traveling in a curved area rather than flat land that normally is expected.
Lets dig even deeper. The driver, who was undergoing an acceleration, now claims that he was never driving in a circle, but rather under the influence of a gravitational field (as the equivalence principle fully justifies him doing so). Since the area he was driving in must be curved according to his measurements, that must mean that space itself is curved around him. This is the main principle of general relativity. Unlike Newton's laws, which merely describe a universal attraction between all bodies of mass, this new theory states that all bodies of mass bend space around them, and that bodies being pulled together are a result of this curving in space. As physicist John Wheeler summed it up, "Matter tells space how to curve, and space tells matter how to move." Space can no longer being thought of just this empty collection of nothingness, it is now this fabric that fills our universe that matter distorts and curves.
Bending Light
According to Newton's law of gravitation, only particles that have mass are attracted by gravity. But what happens when we apply our new views of gravity to light? Lets go back to the box floating out in space. Consider a laser is mounted inside this box and it shines on an "x" mark on the wall while the box is at rest. It will also still shine on this mark if the box is going at a constant velocity (special relativity equivalence principle). Now consider the box accelerating upward again very rapidly. The beam of the laser no longer hits the mark on the other side of the box, but hits slightly below it. This is because light, traveling at a fixed speed, must travel across the box, and in that time, the box has moved slightly upward thus making the beam strike a different point. The person in the box watching this light beam will notice it bending slightly downward. Now we can exploit the general relativity equivalence principle to claim that the box is not accelerating at all, but is just in a gravitational field. This now implies that light bends due to gravity, something forbidden by Newton's law.
Einstein's new theory generously accepts the fact that gravity now bends light, even though it has no mass. This is easy to see as it is a well-known fact that light always travels in a straight line. Einstein elaborated on this fact by saying light always travels in a straight geodesic line (that is, a line following a curve, such as a line drawn on a ball). So now that space is curved in our view, that means light just travels along those curves. This is the prediction that ultimately validated Einstein's theory in the 1940's. During a solar eclipse, pictures were taken of the stars near the sun. They were then compared to pictures of the same stars at a later time in the night without the sun. The measurements clearly shown the presence of the sun's massive gravitational field bent the light from the stars, shifting their apparent position. This phenomenon is known as gravitational lensing.
Bending Time
Recall the race car situation in which the car traveling near light speed measures a longer distance than expected because the driver's ruler is shortened by special relativity. We forgot to measure one other key element of the environment that changes as a result of special relativity: time. As the car approaches the speed of light, the driver will measure time to be much shorter than an observer outside the race track. Since the equivalence principle again allows the driver to claim he is just in a gravitational field, we notice that time will slow down in a gravitational field. This is known as gravitational time dilation. The stronger the field, the slow time will occur. This feature has been extensively tested with atomic clocks on satellites in space showing differences in measured time.
Conclusion
These ideas have revolutionized how space and time appear to exist. Not only are they woven together as special relativity shown, but now they can be curved and warped by mass like a bowling ball on a trampoline. This view of space and time have helped us explain some of the most complicated phenomenon witnessed in the universe from planets to quasars, as well as suggesting new unknown phenomenon such as black holes (I will write a separate article on these). Is this the final answer to how gravity and time work, or will there be another refinement on top of Einstein's yet to come? The world will have to wait and see.
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Thread: relativity: the general theory
- 28 Jun. 2010 05:57am #1
relativity: the general theory
- 28 Jun. 2010 06:02am #2
im gonna lay it flat.
i did not read more than 7 words of this.
good job
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