Physics
Vandebilt Catholic High School
W.Dupre
SPECIAL THEORY OF RELATIVITY
QUOTES BY EINSTEIN:
"Relativity teaches us the connection between the different descriptions of one and the same reality".
"I sometimes ask myself how it came about that I was the one to develop the theory of relativity. The reason, I think, is that a normal adult never stops to think about problems of space and time. These are things that he has thought about as a child. But my intellectual development was retarded, as a result of which I began to wonder about space and time only when I had already grown up."
"Put your hand on a hot stove for a minute, and it seems like an hour. Sit with a pretty girl for an hour, and it seems like a minute. THAT'S relativity."
Einstein developed this theory in 1905. It rests on two postulates.
1. The laws of physics have the same form in all inertial reference frames.
2. The speed of light through the vacuum is c, independent of the speed of the light source or observer.
Recall an inertial reference frame is one in which the law of inertia holds. This first postulate, the principle of relativity, dates from the time of Galileo. Einstein sought to extend its validity from mechanics to all of physics, especially electricity and magnetism. Note it says nothing about accelerating or rotating (non-inertial) frames. Einstein's special theory only applies to observers in inertial frames. In 1915 he would publish the general theory of relativity that applies to all observers and introduces new ideas about gravity.
The second postulate contradicts our common sense views on velocity addition based on our low velocity experience. Experiments have shown it is true, and we will now explore the logical outcomes of these two postulates.
Simultaneity
Two events that are simultaneous to one observer are not necessarily simultaneous to a second observer. Both observers are correct in their observations -- there is no best or preferred frame of reference.
Time Dilation
Einstein's theory of relativity predicts that time passes differently in one frame of reference than in another. If different observers measure the time interval between a pair of events, they will not agree about how long the time interval for the event was. The time dilation effect states that clocks moving relative to an observer are measured by that observer to run more slowly (as compared to clocks at rest). In other words, time is dilated (or stretched) for a moving object.
Dt = g Dt'
where Dt' is the proper time interval, or that recorded at rest relative to an inertial reference frame
Dt is the dilated time interval
g is the Lorentz factor
g = [1 - (v/c)2 ]-1/2
Since nothing can travel faster than light, g > 1 and it appears to the stationary observer that a clock in motion at velocity v takes longer to tick or runs slowly compared to his own clock. This is called time dilation and really is a property of time, not just an unusual clock.
Further Einstein claims that time dilation occurs for all mechanical, chemical, and biological processes.
Example
Albert, at rest on earth, watches Henry wave as he zooms by in a rocket ship at constant velocity v = 0.8c. How much time passes according to Albert when Henry claims 24 hours have passed since his wave? Albert sees time Dt elapse while Henry claims Dt' = 24 hours has passed. Thus since g = 5/3 for v = 0.8c we have Dt = 40 hours. Time flows at different rates for observers in relative motion.
Note: At normal speeds much less than c, these relativistic effects are so tiny we do not notice them.