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Pentcho Valev wrote:
http://www.physicstoday.org/vol-58/iss-9/p12.html
Pentcho Valev
Pieces of Einstein's 1905 Puzzle
LETTERS
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
Harvey and Schucking describe the similar rates of a polar clock and an
equatorial clock in two ways:
o The gravitational blueshift of a clock on the equator precisely
cancels the time dilation associated with its motion.
o 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.
Reference
1. B. Hoffman, Phys. Rev. 106, 358 (1957) [SPIN].
Roy Bishop
(rg@ns.sympatico.ca)
Acadia University
Wolfville, Nova Scotia, Canada
_________________________________
There is a small error in "A Small Puzzle from 1905" about Einstein's
prediction error regarding time dilation: The caption under the
illustration on page 36 says clock rates increase with gravitational
potential. Of course the authors meant "decrease."
David L. Taylor
(taylors1327@att.net)
Webster Groves, Missouri
_________________________________
Although I am flattered by the refrence to me in Alex Harvey and
Engelbert Schucking's article, I need to correct the record. Sometime
in the late 1970s, while giving a lecture at the University of
Maryland, I innocently stated Einstein's prediction about the polar and
equatorial clocks. It had not occurred to me that the prediction was
wrong. After the lecture Carroll O. Alley came up to me and pointed out
the error. He also gave me some reprints in which he presents the
correct theory and gives results that prove it with atomic clocks flown
in airplanes.1 Alley is the hero of this tale and should be credited.
Reference
1. C. O. Alley, in Quantum Optics, Experimental Gravity, and
Measurement Theory, P. Meystre, M. O. Scully, eds., Plenum Press, New
York (1983), p.363.
Jeremy Bernstein
Aspen, Colorado
_________________________________
Alex Harvey and Engelbert Schucking make repeated references in their
article to the "erroneous prediction" in Albert Einstein's 1905 paper
on electrodynamics. The point of the article seems to be amazement that
neither Einstein nor "numerous historians of science" have focused
attention on the "erroneous" calculation of time dilation, which did
not take into account gravitational effects. However, historians of
science do not, in general, attempt to judge the work of scientists by
the standard of later developments.
In the case at hand, Einstein himself found a theory of greater
generality than special relativity, on which the 1905 calculation was
based. But that later discovery does not ex post facto make the earlier
calculation an error. In fact, it was a correct calculation based
solely on special relativistic ideas. How would Einstein's
contemporaries have reacted if he had scattered throughout the 1905
paper numerous references to Isaac Newton's "errors"? Einstein
recognized that special relativity modified Newton's ideas, and of
course general relativity was an even greater modification. Einstein
did not go back to correct his 1905 mistake, because he had made none.
The history of science is endless and fascinating, but it should not be
told in terms of errors and wrong predictions. That approach suggests
that science is a progression of correcting errors from the past rather
than the acquisition of deeper understanding. Some day decades or more
in the future, much of what we believe today of quantum theory and
gravitation will be regarded as special cases of a broader, more
comprehensive theory. Let us hope that the historians of that day will
not reflect on the inexplicable errors of those who paved the way.
Bill Shields
(highc.king@verizon.net)
Virginia Polytechnic Institute and State University
Blacksburg, Virginia
_________________________________
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\u2014unlike religion\u2014can 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?
Alex Harvey
Engelbert Schucking
New York University
New York City
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