Pieces of Einstein’s 1905 Puzzle

Abstract

In their article “A Small Puzzle from 1905” in the March 2005 issue of Physics Today, (page 34), Alex Harvey and Engelbert Schucking express surprise that the relevant literature contains no commentary about Albert Einstein’s one erroneous prediction in his 1905 paper on relativity: He predicted a rate difference between Earth-based equatorial and polar clocks. The earliest reference given to demonstrate that the behavior of clocks on the geoid has been widely known among physicists is from 1975. The earliest account of which I am aware is from 1957. 1 1. B. Hoffman, Phys. Rev. 106, 358 (1957) https://doi.org/10.1103/PhysRev.106.358. Harvey and Schucking describe the similar rates of a polar clock and an equatorial clock in two ways: ▸ The gravitational blueshift of a clock on the equator precisely cancels the time dilation associated with its motion.▸ Relative to a frame attached to Earth, neither clock is moving and both are at the same effective gravitational potential; thus their rates are identical. A third way to view this situation is closely related to the second. By the principle of equivalence, a clock at rest in a gravitational field is equivalent to a clock being accelerated in a field-free space. As described by general relativity, gravitation is geometry, not a force, which is why no one has ever felt a force of gravity. The only force acting on the Earth-based clocks, or on any stationary Earth-based objects, is the electromagnetic contact force supporting them. Any two nearby clocks located on the same surface perpendicular to the direction of this contact force (the plumb-bob direction) will have identical rates. Thus all clocks on the geoid run at the same rate.A popular-level description of time that includes this elegant behavior of clocks on the geoid appears in the annual Observer’s Handbook of the Royal Astronomical Society of Canada. Although the handbook began publication in 1907, a description of this feature of Earth-based clocks first appeared in the 2003 edition.REFERENCESection:ChooseTop of pageREFERENCE <<1. B. Hoffman, Phys. Rev. 106, 358 (1957) https://doi.org/10.1103/PhysRev.106.358. Google ScholarCrossref, ISI© 2005 American Institute of Physics.