Core Principles of Special and General Relativity by James H. Luscombe

Author:James H. Luscombe
Language: eng
Format: epub
Publisher: CRC Press (CAM)
Published: 2018-11-08T16:00:00+00:00

One could measure the time to fall, , so that mg/mi = 2h/(gt2), from which .

Another experiment is to compare the oscillation periods of pendulums of the same length made of different materials. Galileo used a lead ball and a cork ball, with the lead ball approximately 100 times as heavy as the cork ball. He watched the two pendulums, released at the same time, and could observe no difference in their motion. The oscillation period and thus . Newton performed this experiment around 1680, and from his data one can estimate η ≈ 10−3. Friedrich Bessel repeated the experiment in 1832 and found η ≈ 2 × 10−5.

By far the most accurate experiment is that of Loránd Eötvös, who devised a torsion balance technique, starting in 1885 and repeated and refined by Eötvös and co-workers until 1920. Eötvös found η < 5 × 10−9. The Eötvös experiment has been repeated with ever-increasing precision. In 2008 a group reported η = (0.3 ± 1.8) × 10−13,[43] consistent with η = 0, or mi = mg. Einstein took the identity mi ≡ mg as a fact of experience and used it to far-reaching effect in establishing GR. The Eötvös experiment provides the foundation for GR, just as the Michelson-Morley experiment provides the foundation for SR. The classic Eötvös experiment uses Earth as a laboratory, which as a rotating object allows us to probe the difference between mg (associated with gravity), and the inertial mass mi (associated with inertial forces). The experiment consists of a balance suspended in gravity from a torsion fiber (dashed line in Fig. 11.1), having objects A and B at distances l and l′ from the fiber. The centrifugal force from Earth’s rotation has components in the z and x-directions (depending on one’s latitude on Earth).

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