By Robert Geroch
ISBN-10: 0226288633
ISBN-13: 9780226288635
"An inventive and convincing new presentation of Einstein's concept of basic relativity. . . . The remedy is masterful, continuous emphasis being put on cautious dialogue and motivation, with the purpose of unveiling how physicists imagine and enhance their ideas."—Choice
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Example text
20 THE EXPERIMENTAL BACKGROUND OF THE THEORY OF SPECIAL RELATIVITY The Michelson Morley Experiment The hypothesis advanced by Lorentz and by Fitzgerald was that all bodies are contractedin the direction of motion relative to the stationary ether by a factor VI — v2/c2. Again, let the ratio v/c be represented by the symbol /3, so that this factor may be written as V1 — /32. Now, if /° represents the length of a body at rest with respect to the ether (its rest length) and 1 its length when in motion with respect to the ether, then in the MichelsonMorley experiment - 11= /?
As for the origins of his special theory of relativity, Einstein was probably convinced, independently of the experimental background that we have presented, that Maxwell's equations had to have exactly the same form in all inertial * See Refs. 11-19 for some rewarding articles and books about Einstein. Q UESTIONS 31 frames of reference. He may have reached such a conclusion intuitively in his youth while meditating on how a light wave would look to an observer who was following it at speed c. The constancy of the velocity of light seemed to him indisputable, and his 1905 paper begins with the precise electrodynamical experimental situation described in a text on Maxwell's theory that he was studying at the time.
The "binumeral explosion" (one student's preference). (a) Use the binomial expansion theorem to verify each of the expansions displayed in the footnote on page 17. 30, what percent error is made in the first of these expansions if only two terms are kept? Only three terms? (c) Answer these same questions for the second of these expansions. * 18. Michelson Morley, generalized. Figure 1 11 shows a Michelson interferometer (compare Fig. 1-4) with a presumed ether wind whose uniform velocity v makes an - + 12) AN = /32(11 cos 20.