Special Relativity |
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The purpose of the essay is not to cover Einstein’s theory of special relativity in even a qualitatively thorough manner. Rather its purpose in to present some key results that have philosophical implications. The special theory of relativity applies to fast moving objects. It was developed before the general theory of relativity, which applies to gravity. The special theory of relativity is far less mathematically complicated. A special relativity course is generally taken early in an undergraduate physics program, while a full general relativity course is taken towards the end of a Ph.D. physics program at a good university, and then only by students interested in that area of specialization. The key observation that leads to the special theory of relativity is that light has the same speed, c, for all observers. For example, suppose you are standing on a railway platform, and a train is passing at 60mph. Someone on the train throws a ball forward at 10mph, within the train. Now, from your point of view, the ball is moving forward at 70 mph. This is simple addition of velocity. Now suppose a train is passing at half the speed of light, or .5c . Now, someone on the train shines a flashlight forward. The light moves forward at the speed of light, c, for the observer on the train. If we use simple addition of velocities the light should be moving forward at 1.5 c from the point of view of the observer on the platform. However, this is not the case. The observer on the platform sees the light moving forward at the speed of light c. This is counter-intuitive, but it has been verified in a number of ways. Initially it was predicted by Maxwell’s equations of electromagnetism. These equations were based on basic observations of magnets and electric currents. They predicted that electromagnetic waves could exists, and that they would have a constant speed c. Later other experiments showed that electromagnetic radiation, like light, did indeed behave this way. This is where Einstein came into the picture. He took the observations at face value. If two observers can disagree about velocities, as described, he realized that they must also disagree about distance and time, since velocity is just distance/time. His conclusion was that different observers can disagree about how much time had passed between events.This time-dilation effect has since been confirmed in a number of ways. One consequence of this is that no object with mass can ever reach the speed of light. It can get close, from an external point of view, but it will never get there. And from the point of view of the accelerating object, it will never gain anything on a passing beam of light. No matter how much the object accelerates, it will always see the beam of light as still passing it by at the speed of light. Now we get to a point that will be important here. If two events take place in space-time in such a way that a beam of light could travel between them, then all observers will agree on the order of the events. For example, suppose event A takes place at 1:00, and event B takes place at 2:00, according to an observer half way between. And suppose only a short distance in space separates the events, (at least less that 1 light-hour). All observers will agree that event A took place before event B. Events A and B could be causally related. That is A could have caused B. All observes will agree on the order of causally related events. Now suppose events A and B both occur at exactly 1:00 from the point of view of an observer in the middle. A light beam that starts at event A, could not reach the point in space where event B takes place, before the time event B takes place. Since nothing can travel faster than light, A and B can not be causally related. Now however, different observers can disagree about the order of events. Some observers can say A happened before B, and others that B happened before A.The key point going forward is that, in these circumstances, different observer can disagree about the order of events, and no observer is more “correct” than any other. In the language of special relativity, A and B have a space-like separation as opposed to a time-like separation. We could also say that they are not in each other's past or future light cones. The clock employed could be the aging of the body, atomic decay, or any other clock. But no matter what clock is used, the passages of time is not independent of position in space, and velocity in space. |
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For more information |
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http://casa.colorado.edu/~ajsh/sr/sr.shtml | ||||||||||||||

http://www.teach12.com/ttc/assets/coursedescriptions/153.asp | ||||||||||||||

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