Harvey and Schucking reply: Roy Bishop is right to mention the 1957 paper by Banesh Hoffman. We are not entirely happy with Bishop’s derivation of the null effect: Einstein’s equivalence principle of 1907 refers to a constant field of acceleration, with the pole and equator points accelerating in different directions. However, we are also not pleased with the “derivations” we gave in our paper, derivations that used the crutches of Newtonian gravity and special relativity. In Einstein’s theory, the exact derivation using a stationary Killing vector is very simple but deemed to be beyond the comprehension of physics undergraduates. It is a scandal that, despite this year’s monumental Einstein lip service, his greatest achievement of 80 years ago, his theory of gravitation, has not become a regular part of the undergraduate physics curriculum.
David Taylor contends that clock rates do not increase with gravitational potential. We understand clock rates to be the number of ticks per second. An increased clock rate means a “blueshifted” clock. We also define the gravitational potential as increasing with distance from Earth. Thus, our clock rates increase with gravitational potential.
However, the gravitational potential introduced by Joseph Louis Lagrange was defined with the opposite sign, so that its gradient gave the acceleration. After the conservation of energy was discovered, physicists redefined the gravitational potential with the opposite sign while astronomers and geophysicists often stayed with the old definition.
We are grateful to Jeremy Bernstein for pointing to the work of professor Carroll O. Alley. Unfortunately, we did not know that he had experimentally confirmed Einstein’s theory of gravitation by studying clock rates at different latitudes. In addition to the reference Bernstein quotes, a talk by Alley appears in the Proceedings of the Thirteenth Annual Precise Time and Time Interval Application and Planning Meeting, 1982 (NASA Conference Publication 2220). Referring to that talk, Alley writes in a letter to Bernstein: “When I told the audience of physicists about the required understanding of relativistic time in the engineering of modern timekeeping systems, Eugene Wigner was so pleased that he interrupted my talk to beat his hands on the table in front of him in the European fashion!”
We do not agree with the views of Bill Shields on the history of science. Although they may be valid for a history of religion, science—unlike religion—can be tested against experiment and observation of nature. Mismatches between theory and observation are the germs for exciting new developments. To keep historians of science from discussing the truth seems absurd to us. If they discuss a flat-earth theory, are they not allowed to mention that the theory has a problem?
