Simple Nature - Light and Matter

self-check BTurn your book upside-down and reinterpret figure ag. ⊲ Answer, p.924A symmetry property of the Doppler effect example 12Suppose that A and B are at rest relative to one another, but C ismoving along the line between A and B. A transmits a signal to C,who then retransmits it to B. The signal accumulates two Dopplershifts, and the result is their product D(v)D(−v). But this productmust equal 1, so we must have D(−v)D(v) = 1, which can beverified directly from the equation.The Ives-Stilwell experiment example 13The result of example 12 was the basis of one of the earliest laboratorytests of special relativity, by Ives and Stilwell in 1938. Theyobserved the light emitted by excited by a beam of H + 2 and H + 3ions with speeds of a few tenths of a percent of c. Measuringthe light from both ahead of and behind the beams, they foundthat the product of the Doppler shifts D(v)D(−v) was equal to 1,as predicted by relativity. If relativity had been false, then onewould have expected the product to differ from 1 by an amountthat would have been detectable in their experiment. In 2003,Saathoff et al. carried out an extremely precise version of theIves-Stilwell technique with Li + ions moving at 6.4% of c. Thefrequencies observed, in units of MHz, were:f o = 546466918.8 ± 0.4(unshifted frequency)f o D(−v) = 582490203.44 ± .09(shifted frequency, forward)f o D(v) = 512671442.9 ± 0.5√fo D(−v) · f o D(v)(shifted frequency, backward)= 546466918.6 ± 0.3The results show incredibly precise agreement between f o and√fo D(−v) · f o D(v), as expected relativistically because D(v)D(−v)is supposed to equal 1. The agreement extends to 9 significantfigures, whereas if relativity had been false there should havebeen a relative disagreement of about v 2 = .004, i.e., a discrepancyin the third significant figure. The spectacular agreementwith theory has made this experiment a lightning rod for antirelativitykooks.We saw on p. 394 that relativistic velocities should not be expectedto be exactly additive, and problem 1 on p. 437 verifies thisin the special case where A moves relative to B at 0.6c and B relativeto C at 0.6c — the result not being 1.2c. The relativistic Dopplershift provides a simple way of deriving a general equation for therelativistic combination of velocities; problem 17 on p. 441 guidesyou through the steps of this derivation, and the result is given onp. 936.Section 7.2 Distortion of Space and Time 409