Chapter 9a: The Special Theory of Relativity

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The Special Theory of Relativity is a tight logical structure, like a mathematical proof. You need to be able to identify and differentiate among: the postulates of the theory, the predictions of the theory (length contraction, time dilation, mass increase) and real experiments that are used as tests of Special Relativity. You must also be able to differentiate between thought experiments and real experiments. It is important to understand that when writers for a nonspecialist audience (including our text) write about relativity, they use words like "the observer sees," "it appears to him,", "she observes," and "it looks like." Thus relativity might be incorrectly interpreted as a kind of "optical illusion." This is dead wrong! Technically, all of these expressions mean that an observer something. "Space" and "time" are given meaning by objective measurements and Special Relativity is about the surprising disagreement in measurements by observers in different frames of reference. A "frame of reference" means an observer with and which move with him/her and are used to make measurements of separations in space and time. "Events" are things that happen. Events happen at a place and at a time. They are the "points" in a four-dimensional "space-time." Two events are "simultaneous" if an observer located exactly between where the events occur receives light signals coincidentally from both events that were generated when the two events occur. Where and when are determined by the observer's own rulers and clocks. The two postulates of Special Relativity are these: 1. The Special Principle of Relativity (also known as symmetry), i.e., "the laws of nature are the same for all observers who are in relative motion." 2. "The speed of light in empty space is the for all observers, regardless of their motion or the motion of the sources of light." (The second postulate seems to point to light as something mysterious, but it is the speed of light that is the mysterious thing. The speed of light is a speed limit in nature that people before Einstein did not realize was there. Measurement has verified time and again that this speed limit exists, but no one yet understands why our world possesses such a speed limit nor why it has the value that it does. Light (and some other things) travel in empty space at precisely this speed limit.) SURPRISE #1: Two events that are observed (measured) to be simultaneous to one observer (are, are not?) simultaneous to another observer in uniform motion relative to the first. We are forced to conclude that both observers are right! SURPRISE #2: If the postulates are true and simultaneity is indeed relative, then observers (do, do not?) agree on measured lengths and, hence give a relative meaning to space. The discrepancy in measured length is called "length " and is summarized as "Moving objects are measured to be (longer, shorter?) than when measured at rest. It (does, does not?) matter whether the object is moving toward you or away." We conclude that both observers are exactly right, though they disagree!

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