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By P. W Bridgman

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In the above example, L˜ is the proper length of the subway car. Note that since γ ≥ 1, the proper length of an object is always longer than the length measured in a frame in which the object is moving. The two seemingly simple postulates of Einstein have logical consequences that are very deep and amazing. To summarize: • • • Relativity of simultaneity Two events that happen at the same time but at different locations in space according to one set of observers do not happen at the same time to any other observers moving at constant velocity relative to the first set.

Length contraction The length of an object as measured by observers in a frame in which the object is at rest is always greater than the length of that same object as measured by observers for whom the object is in motion. 7 From light waves to spacetime geometry In Chapter 1 we entertained the possibility that there could be a distance function on a unified space and time that would be analogous to the Pythagorean rule in space. The Pythagorean rule on its face tells us how to calculate the length L of the hypotenuse of a right triangle, given the lengths X and Y of the two legs of the triangle, by the formula L2 = X2 + Y 2.

Keep doing this as many times as necessary to be able to draw what you see on the paper and answer the following questions: • • • • Does the wave have a definite location at any one moment in time? Does the wave have a definite direction as it propagates? Approximately how far does the wave travel in 1 s? Describe the motion of the water in which the wave moves. Throw your small projectile in the air at various angles, letting it drop down (not in the water). Keep doing this as many times as necessary to be able to draw what you see and answer the following questions: • • • • • Does the object have a definite location at any one moment in time?

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A sophisticate's primer of relativity by P. W Bridgman


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