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

By P. W Bridgman

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This differential equation is mathematically of the “elliptic” type for which changes propagate instantaneously. Thus, a change in ρ in the example described above, as the removal of mass density from one location (along the sides of your body) and relocating it to a new position (perpendicular to your body), would instantaneously alter φ throughout the universe and the acceleration experienced at all points in the universe would change without any delay whatsoever. This would contradict Special Relativity, the theory which has been remarkably successful in experiment after experiment.

31) s 2 = c2 t 2 − vs2 t 2 = (c2 − vs2 )t 2 . Now the speed of sound is less than the speed of light so we see that s 2 is positive and therefore s is a real number. Events separated by a real number spacetime interval are said to be “timelike separated” events. Note also that the shattering of the goblet occurred after Alicia’s scream. Now we know that Relativity can produce some surprising effects so it is well to ask whether Beatrice, moving relative to Alicia, could ever see the events occur in reverse order.

E. 1 m = x2 − x1 . In physics, we call the length that is read in the rest frame of an object, its “proper length”. Thus Alicia’s length of 1 m that she measures is the rod’s proper length. We wish to find the length of the rod that Beatrice perceives. 10), first for the right end position x2 and then for the left end position x1 : x2 = (x2∗ + vt2∗ ) 1 − v 2 /c2 , x1 = (x1∗ + vt1∗ ) 1 − v 2 /c2 . 11) Now we have to consider an issue that we might easily take for granted. It is well to ask: which times t2∗ and t1∗ are we to choose?

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