Einstein's Theory of Relativity
by Paul Marmet
checked 2012/07/02 - The estate of Paul Marmet
The Deflection of Light by the Sun's
An Analysis of the 1919 Solar Eclipse
After the publication of this book, a much more
complete study of the observations of the deflection of light and
radio waves by the Sun has been published under the title:
Using Radio Signals and Visible Light.
This paper can be read direcly on the Web.
According to Einstein's general theory of relativity published
in 1916, light coming from a star far away from the Earth and
passing near the Sun will be deviated by the Sun’s gravitational
field by an amount that is inversely proportional to the star’s
radial distance from the Sun (1.745'' at the Sun's limb). This
amount (dubbed the full deflection) is twice the one predicted
by Einstein in 1911, using Newton's gravitational law (half
deflection). In order to test which theory is right (if any), an
expedition led by Eddington was sent to Sobral and Principe for
the eclipse of May 29, 1919 . The
purpose was to determine whether or not there is a deflection of
light by the Sun's gravitational field and if there is, which of
the two theories mentioned above it follows.
expedition was claimed to be successful in proving Einstein's
full deflection [1,2]. This test was
crucial to the general approval that Einstein's general theory
of relativity enjoys nowadays.
However, this experimental result is obviously not in accordance
with the result found in chapter ten. This is not a problem, as
we will show that the deflection was certainly not measurable.
We will see that the effect of the atmospheric turbulence was
larger than the full deflection, just like the Airy disk. We
will also see how the instruments could not give such a precise
measurement and how the stars distribution was not good enough
for such a measurement to be convincing. Finally, we will
discuss how Eddington's influence worked for Einstein's full
displacement and against any other possible result.
ABOUT THE EXPERIMENTAL RESULTS -
Atmospheric turbulence is a phenomenon due to the atmosphere
which causes images of stars as seen by an observer on Earth to
jump, quiver, wobble or simply be fuzzy. This is a well-known
phenomenon to any astronomer, amateur or professional. In fact  (page 40),
Rare is the night (at most sites)
when any telescope, no matter how large its aperture or
perfect its optics, can resolve details finer than 1 arc
second. More typical at ordinary locations is 2- or
3-arc-second seeing, or worse.
The problem becomes even worse during the afternoon
due to the heat of the ground. Tentative solutions to this seeing
problem have only recently been experimented .
anyone unacquainted with atmospheric turbulence, an easy way to
observe a similar phenomenon is by looking over a hot barbecue. In
this case, the distortion of the images (of the order of 10') is
due to the heat coming from the barbecue.
Eddington, an astronomer, was certainly aware of this problem. If
it was difficult in 1995 , to see
details finer that 1'', how much more difficult was it in the
jungle in 1919? The supposed effect (full and half deflection)
decreases with the distance of the star from the Sun. During the
1919 eclipse, the stars closest to the Sun's limb were drowned in
the corona and could not be observed .
Of the stars that were not drowned in the corona, Einstein’s
theory predicts that k2
Tauri should have the largest displacement, with 0.88''. In
Sobral, the displacement for that star was reported to be 1.00'' . How could Eddington and Dyson claim
to observe that if at best, their precision due to atmospheric
turbulence in daytime heat was several seconds? And they were not
at best, near noon at Sobral and 2 p.m. at Principe, when the
seeing is the worst, with small telescopes that were less than
caused by the atmospheric turbulence is large enough to refute any
measurement of the so-called Einstein effect. However, there are
object glasses were used during the expedition at Sobral, a 4-inch
object glass and an astrographic object glass. Assuming a perfect
optical shape, which means perfect correction for sphericity and
chromaticity, for the 4-inch telescope, the size of the central
spot (which is surrounded by the ring system of the diffraction
pattern) can never be smaller than 1.25''. This central spot is
called the Airy disk. Since some of the results were presented
with a claimed accuracy of the order of 0.01''  (page 391), that relatively big
diffraction ring pattern (125 times the claimed accuracy) should
have been easily seen. Since no mention is made of it, we must
understand that it was not observable because various aberrations
(chromatic of spheric) were larger than 1.25'' and/or because, as
expected, the atmospheric turbulence was larger than 1.25'', which
is the theoretical limit of resolution of that telescope when
there is no aberration and no turbulence.
of the telescopes was determined and fixed many days before the
eclipse  (page 141). But the
elements of a telescope are very sensitive to temperature  (page 153):
"when the [astrographic] object
glass is mounted in a steel tube, the change of scale over a
range of temperature of 10° F. should be insignificant,
and the definition should be very good".
the team’s stay at Sobral, the temperature ranged from 75°F
during the night to 97°F in the afternoon. This change in
temperature must have affected the astrograph, but what about the
the mirrors and the 4-inch telescope?
photographs of the eclipse taken with the astrograph were very
disappointing  (page 153). It
appears that the focus had changed from the night of May 27 to the
moment of the eclipse. After the eclipse, the team left Sobral and
came back in July to take comparison plates. They discovered that
the astrograph had returned to focus! They blamed this change of
focus on the effect of the Sun’s heat on the mirror, but they
could not say whether this effect caused a change of scale or if
it only blurred the images.
about the 4-inch telescope? The Sun’s heat could have affected its
scale without blurring the images. We know that there is a zone
around the focal length where the image will look as if it were in
focus but where the scale will be changed. To the best of our
knowledge, nothing has ever been said about that possible problem.
plot the value of Einstein's deflection against the angular
distance of the star from the Sun (as done in  page 50), we see that the part of the
hyperbola where the slope changes the most lies under a distance
of two solar radii from the Sun's center. That part is thus
crucial to a good interpretation of the results. Looking at page
60 of the same article, we see that only two of the stars used by
the teams at Principe and Sobral are in this area. It is thus very
difficult to fit a hyperbola when only two of the stars are in
that zone. These observations (and most of the others studied in
von Klüber's article which reviews all observations done
before 1960) could easily be fitted by a straight line instead of
Einstein's deflection equation. Therefore they do not prove any of
Einstein's deflections (full or half).
In one of
the meetings of the Royal Astronomical Society  (page 41), Ludwik Silberstein pointed
out that the displacements found were not radial, as Einstein's
theory states, but sometimes deviated from the radial direction by
as much as 35°! Nothing was said about that in Dyson's
article. According to Silberstein:
"If we had not the prejudice of
Einstein’s theory we should not say that the figures
strongly indicated a radial law of displacement."
brings us to our next point, which is to what degree social
circumstances influenced the acceptation of Einstein's theory.
ABOUT EDDINGTON’S INFLUENCE -
results from the 1919 expedition were quickly accepted by the
scientific community. When preliminary results were announced,
Joseph Thomson (from the Chair) said 
"It is difficult for the audience
to weigh fully the meaning of the figures that have been put
before us, but the Astronomer Royal [Dyson] and Prof.
Eddington have studied the material carefully, and they
regard the evidence as decisively in favor of the larger
value for the displacement."
makes it look like only Eddington and Dyson are able to understand
the results. It seems that they have such a reputation that the
general and the scientific public should blindly believe them.
Dyson who presented the results of the Sobral expedition at a
meeting of the Royal Astronomical Society 
(page 391). Some of the displacements presented were very small,
sometimes of the order of 0.01''. In another meeting  (page 40), Oliver Lodge asked if it
were possible to measure a deviation of 1/60'' (approximately
0.02'') to which Dyson responded:
"I do not think that it would be
possible to measure so small a quantity."
clearly see that Dyson contradicted himself.
Furthermore, Eddington said himself he was in favour of the full
deflection before doing the experiment. Writing about the results
of the expedition, he said  (page
"Although the material was very
meager compared with what had been hoped for, the writer
(who it must be admitted was not altogether unbiased)
believed it convincing."
according to Chandrasekhar  (page
"had he been left to himself, he
would not have planned the expeditions since he was fully
convinced of the truth of the general theory of relativity!"
was a Quaker and like other Quakers, he did not want to go to war
(WWI). In England, Quakers were sent to camps during the war, but
because of Dyson's intervention 
"Eddington was deferred with the
express stipulation that if the war should end by May 1919,
then Eddington should undertake to lead an expedition for
the purpose of verifying Einstein’s predictions! "
circumstances of the war forced Eddington to do an experiment that
he would have never done had he had a choice because he was so
convinced of its outcome.
the theory so quickly, widely and easily accepted? After all, it
was radically changing the common view of the universe, curving
space and dilating time. Furthermore, the British were accepting a
theory from a German man, right after a bitter war with Germany.
that the theory was widely accepted only after the eclipse
expedition  (page 50). According to
Earman and Glymour, Dyson and Eddington played a great influential
role in the acceptation of the general theory of relativity by the
British. In fact, it is Eddington who, convinced of the truth of
the theory, convinced Dyson. In the few years before 1919, they
made the measurement of the "Einstein effect" a challenge and
after the expeditions of May 1919, they helped give the impression
that the data had confirmed Einstein’s theory.
from the fact that Eddington was convinced that the theory was
right, another reason pushed him to advocate it  (page 85). He hoped that a British
verification of a German theory might reopen the lines of
communication and collaboration between the scientists of both
countries, lines that had been closed during World War One.
before 1919, no one had claimed to have observed shifts of the
size required by Einstein's theory. Probably because the theory
was thought to be proved by the 1919 eclipse observations, a lot
of scientists, maybe throwing out some of their data, reported
finding the right shift  (page 85).
1919, other expeditions were undertaken to measure the deflection
of light by the Sun. Most of them obtained results a bit higher
than Einstein's prediction, but it did not matter anymore since
the reputation of the theory had already been established.
Jamal Munshi in reference to his
² Weird but True² reports on the internet at:
Dr. F. Schmeidler of the Munich
University Observatory has published a paper  titled "The Einstein Shift An
Unsettled Problem," and a plot of shifts for 92 stars for
the 1922 eclipse shows shifts going in all directions, many
of them going the wrong way by as large a deflection as
those shifted in the predicted direction! Further
examination of the 1919 and 1922 data originally interpreted
as confirming relativity, tended to favor a larger shift,
the results depended very strongly on the manner for
reducing the measurements and the effect of omitting
individual stars. So now we find that the legend of Albert
Einstein as the world's greatest scientist was based on the
Mathematical Magic of Trimming and Cooking of the eclipse
data to present the illusion that Einstein's general
relativity theory was correct in order to prevent Cambridge
University from being disgraced because one of its
distinguished members was close to being declared a
the popularity of Einstein's general theory of relativity relies
on the observations done at Sobral and Principe. We see now that
these results were overemphasized and did certainly not consecrate
Einstein's theory. It is interesting to think of what would have
happened if the results had been deemed not good enough or if they
had clearly showed that there is no deviation of light by the Sun.
Einstein’s theory might not have enjoyed the popularity it now
does and a new more realistic theory might have been found years
 Dyson, F. W., A. S.
Eddington and C. Davidson, A Determination of the Deflection
of Light by the Sun's Gravitational Field, from Observations
Made at the Total Eclipse of May 29, 1919, in Philosophical
Transactions of the Royal Society of London, series A, 220,
p. 291-333, 1920. (See also: Annual Report of the Board of
Regents of the Smithsonian Institution Showing the Operations,
Expenditures, and Conditions of the Institution for the Year
Ending June 30 1919, Government Printing Office,
Washington, p. 133-176, 1921.
 Joint Eclipse
Meeting of the Royal Society and the Royal Astronomical
Society, 1919, November 6, The Observatory, 42,
545, p. 389-398, 1919.
 MacRobert, Alan M., Beating
the Seeing, Sky & Telescope, 89, 4, p.
 Fischer, Daniel, Optical
Interferometry: Breaking the Barriers, Sky &
Telescope, 92, 5, p. 36-41, 1996.
 von Klüber, H.,
The Determination of Einstein's Light-Deflection in the
Gravitational Field of the Sun, Vistas in Astronomy,
Pergamon Press, London, 3, p. 47-77, 1960.
 Meeting of the
Royal Astronomical Society, Friday, 1919, December 12, in
The Observatory, 43, 548, p. 33-45, Jan. 1920.
 Eddington, A., Space,
and Gravitation: An Outline of the General Relativity Theory,
Cambridge University Press, Cambridge, 218 pages, 1959.
 Chandrasekhar, S., Eddington:
Time, Cambridge University Press, Cambridge, 64 pages,
 Earman, J. and C.
Glymour, Relativity and Eclipses: The British Eclipse
Expeditions of 1919 and Their Predecessors, in Historical
Studies in the Physical Sciences, 11, p. 49-85,
1 Contents Appendix3
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by Paul Marmet
Bohr Radius ao = 5.29×10-11 m
Coulomb constant k =1/4pe0=8.988×109 N·m2/C2
Eccentricity of Mercury’s orbit e = 0.2056
Electronic charge e =1.602×10-19 C
Electron mass me = 9.109×10-31 kg
Gravitational acceleration on Earth g = 9.8 m/s2
Gravitational constant G = 6.6726×10-11 N·m2/kg2
Mass of the Earth M(E) = 5.9742×1024 kg
Mass of the hydrogen atom mo =
Mass of Mercury M(M) = 0.33022×1024 kg
Mass of the Sun M(S) = 1.9834×1030 kg
Muon mass mm =
207me = 1.886×10-28 kg
Planck constant h = 2p =
Semi-major axis of Mercury a = 5.791×1010 m
Sommerfeld fine structure constant a = 7.297×10-3 @ 1/137
Velocity of light c = 2.99792458×108 m/s
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