Einstein's Theory of Relativity


Classical Mechanics

by   Paul Marmet
( Last checked 2017/01/15 - The estate of Paul Marmet )
Appendix II

The Deflection of Light by the Sun's Gravitational Field:

An Analysis of the 1919 Solar Eclipse Expeditions.

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:
 Relativistic Deflection of Light Near the Sun 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 Sunís gravitational field by an amount that is inversely proportional to the starís 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 [1]. 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.
        The 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.

        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 [3] (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 [4].
        For 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 [3], 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 [1]. Of the stars that were not drowned in the corona, Einsteinís 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'' [2]. 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 ideal.
        The error caused by the atmospheric turbulence is large enough to refute any measurement of the so-called Einstein effect. However, there are other reasons.
        Two 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'' [2] (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.
        The focus of the telescopes was determined and fixed many days before the eclipse [1] (page 141). But the elements of a telescope are very sensitive to temperature [1] (page 153):
"when the [astrographic] object glass is mounted in a steel tube, the change of scale over a range of temperature of 10į F. should be insignificant, and the definition should be very good".
        During the teamís stay at Sobral, the temperature ranged from 75įF during the night to 97įF in the afternoon. This change in temperature must have affected the astrograph, but what about the the mirrors and the 4-inch telescope?
        The photographs of the eclipse taken with the astrograph were very disappointing [1] (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 Sunís heat on the mirror, but they could not say whether this effect caused a change of scale or if it only blurred the images.
        What about the 4-inch telescope? The Sunís 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.
        If we plot the value of Einstein's deflection against the angular distance of the star from the Sun (as done in [5] 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 KlŁber'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 [6] (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 35į! Nothing was said about that in Dyson's article. According to Silberstein:
"If we had not the prejudice of Einsteinís theory we should not say that the figures strongly indicated a radial law of displacement."
        This brings us to our next point, which is to what degree social circumstances influenced the acceptation of Einstein's theory.

        The results from the 1919 expedition were quickly accepted by the scientific community. When preliminary results were announced, Joseph Thomson (from the Chair) said [2] (page 394):

"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."
        Thomson 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.
        It is Dyson who presented the results of the Sobral expedition at a meeting of the Royal Astronomical Society [2] (page 391). Some of the displacements presented were very small, sometimes of the order of 0.01''. In another meeting [6] (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."
        We 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 [7] (page 116):
"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."
        Moreover, according to Chandrasekhar [8] (page 25),
"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!"
        Eddington 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 [8] (page 25),
"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 Einsteinís predictions! "
        The 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.
        Why was 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.
        It seems that the theory was widely accepted only after the eclipse expedition [9] (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 Einsteinís theory.
        Aside from the fact that Eddington was convinced that the theory was right, another reason pushed him to advocate it [9] (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.
        Finally, 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 [9] (page 85).
        After 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 Weird but True reports on the internet at:


Dr. F. Schmeidler of the Munich University Observatory has published a paper [49] 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 "conscientious objector"!
        Much of 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. Einsteinís theory might not have enjoyed the popularity it now does and a new more realistic theory might have been found years ago.


[1] 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.
[2] Joint Eclipse Meeting of the Royal Society and the Royal Astronomical Society, 1919, November 6, The Observatory, 42, 545, p. 389-398, 1919.
[3] MacRobert, Alan M., Beating the Seeing, Sky & Telescope, 89, 4, p. 40-43, 1995.
[4] Fischer, Daniel, Optical Interferometry: Breaking the Barriers, Sky & Telescope, 92, 5, p. 36-41, 1996.
[5] von KlŁber, 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.
[6] Meeting of the Royal Astronomical Society, Friday, 1919, December 12, in The Observatory, 43, 548, p. 33-45, Jan. 1920.
[7] Eddington, A., Space, Time and Gravitation: An Outline of the General Relativity Theory, Cambridge University Press, Cambridge, 218 pages, 1959.
[8] Chandrasekhar, S., Eddington: The Most Distinguished Astrophysicist of His Time, Cambridge University Press, Cambridge, 64 pages, 1983.
[9] 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, 1980.

Appendix 1        Contents Appendix3

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Einstein's Theory of Relativity


Classical Mechanics 

by   Paul Marmet Bohr Radius ao = 5.29◊10-11 m
Coulomb constant k =1/4pe0=8.988◊109 N∑m2/C2
Eccentricity of Mercuryís 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 = 1.6727406◊10-27 kg
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 = 6.626◊10-34 J∑s
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

Appendix 1        Contents   Appendix2

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