The article is here: https://en.wikipedia.org/wiki/Hafele...ing_experiment (the original two reports by Hafele and Keating may be found on this webpage: http://www.personal.psu.edu/rq9/HOW/...redictions.pdf [though the second one is incomplete on this page]).
The beginning of this article is good, explaining the kinematic (related to velocity) and gravitational (related to gravitational potential) components of relativistic time dilation. The gravitational time dilation is caused by the fact a clock is ticking at a slower rate
f = f0 (1 + Φ/c²) in a gravitational potential Φ = -GM/R (to first order in G). So, all clocks on an equipotential surface will tick at the same rate (as far as gravitational effects are concerned).
Yet, the wikipedia article states this:
(!)
I believe this is incorrect (or at best misleading and incomplete). The statement by Einstein was correct, and does not need to be corrected for gravity effects because, precisely because the Earth's surface is an approximate equipotential, there is no need for a gravitational correction (one could imagine a small gravitational correction if the potential Φ on a pole is somewhat different from Φ at the equator because of complicated quadrupole terms and the fact that distances from the center of the Earth are somewhat different, but clearly this is not what the wikipedia writer is talking about).
What do you think?
The beginning of this article is good, explaining the kinematic (related to velocity) and gravitational (related to gravitational potential) components of relativistic time dilation. The gravitational time dilation is caused by the fact a clock is ticking at a slower rate
f = f0 (1 + Φ/c²) in a gravitational potential Φ = -GM/R (to first order in G). So, all clocks on an equipotential surface will tick at the same rate (as far as gravitational effects are concerned).
Yet, the wikipedia article states this:
Quote:
|
Historical and scientific background In his original 1905 paper on special relativity,[6] Einstein suggested a possible test of the theory: "Thence we conclude that a spring-clock at the equator must go more slowly, by a very small amount, than a precisely similar clock situated at one of the poles under otherwise identical conditions." Because he had not yet developed the general theory, he did not realize that the results of such a test would in fact be null, since the surface of the earth is a gravitational equipotential, and therefore the effects of kinematic and gravitational time dilation would precisely cancel. |
I believe this is incorrect (or at best misleading and incomplete). The statement by Einstein was correct, and does not need to be corrected for gravity effects because, precisely because the Earth's surface is an approximate equipotential, there is no need for a gravitational correction (one could imagine a small gravitational correction if the potential Φ on a pole is somewhat different from Φ at the equator because of complicated quadrupole terms and the fact that distances from the center of the Earth are somewhat different, but clearly this is not what the wikipedia writer is talking about).
What do you think?
via International Skeptics Forum http://ift.tt/2FkkrEA
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