A Determination of the Deflection of Light by the Sun's Gravitational Field, from Observations Made at the Total Eclipse of May 29, 1919

IX. A Determination of the Deflection of Light by the Sun's Gravitational Field, from Observations made at the Total Eclipse of May 29, 1919

By Sir F. W. Dyson, F.R.S., Astronomer Royal, Prof. A. S. Eddington, F.R.S., and Mr. C. Davidson. Communicated by the Joint Permanent Eclipse Committee. Received October 30, read November 6, 1919. Philosophical Transactions of the Royal Society of London, Series A, volume 220, pages 291 to 333, published April 27, 1920.

Contents of the original paper. I. Purpose of the Expeditions, page 291. II. Preparations for the Expeditions, page 293. III. The Expedition to Sobral, page 296. IV. The Expedition to Principe, page 312. V. General Conclusions, page 330.

I. Purpose of the Expeditions

1. The purpose of the expeditions was to determine what effect, if any, is produced by a gravitational field on the path of a ray of light traversing it. Apart from possible surprises, there appeared to be three alternatives, which it was especially desired to discriminate between —

(1) The path is uninfluenced by gravitation.

(2) The energy or mass of light is subject to gravitation in the same way as ordinary matter. If the law of gravitation is strictly the Newtonian law, this leads to an apparent displacement of a star close to the sun's limb amounting to 0.87 arcseconds outwards.

(3) The course of a ray of light is in accordance with Einstein's generalised relativity theory. This leads to an apparent displacement of a star at the limb amounting to 1.75 arcseconds outwards.

In either of the last two cases the displacement is inversely proportional to the distance of the star from the sun's centre, the displacement under (3) being just double the displacement under (2).

It may be noted that both (2) and (3) agree in supposing that light is subject to gravitation in precisely the same way as ordinary matter. The difference is that, whereas (2) assumes the Newtonian law, (3) assumes Einstein's new law of gravitation. The slight deviation from the Newtonian law, which on Einstein's theory causes an excess motion of perihelion of Mercury, becomes magnified as the speed increases, until for the limiting velocity of light it doubles the curvature of the path.

2. The displacement (2) was first suggested by Prof. Einstein in 1911, his argument being based on the Principle of Equivalence, namely, that a gravitational field is indistinguishable from a spurious field of force produced by an acceleration of the axes of reference. But apart from the validity of the general Principle of Equivalence there were reasons for expecting that the electromagnetic energy of a beam of light would be subject to gravitation, especially when it was proved that the energy of radioactivity contained in uranium was subject to gravitation. In 1915, however, Einstein found that the general Principle of Equivalence necessitates a modification of the Newtonian law of gravitation, and that the new law leads to the displacement (3).

3. The only opportunity of observing these possible deflections is afforded by a ray of light from a star passing near the sun. (The maximum deflection by Jupiter is only 0.017 arcseconds.) Evidently, the observation must be made during a total eclipse of the sun.

Immediately after Einstein's first suggestion, the matter was taken up by Dr. E. Freundlich, who attempted to collect information from eclipse plates already taken; but he did not secure sufficient material. At ensuing eclipses plans were made by various observers for testing the effect, but they failed through cloud or other causes. After Einstein's second suggestion had appeared, the Lick Observatory expedition attempted to observe the effect at the eclipse of 1918. The final results are not yet published. Some account of a preliminary discussion has been given, but the eclipse was an unfavourable one, and from the information published the probable accidental error is large, so that the accuracy is insufficient to discriminate between the three alternatives.

4. The results of the observations here described appear to point quite definitely to the third alternative, and confirm Einstein's generalised relativity theory. As is well-known the theory is also confirmed by the motion of the perihelion of Mercury, which exceeds the Newtonian value by 43 arcseconds per century — an amount practically identical with that deduced from Einstein's theory. On the other hand, his theory predicts a displacement to the red of the Fraunhofer lines on the sun amounting to about 0.008 angstroms in the violet. According to Dr. St. John this displacement is not confirmed. If this disagreement is to be taken as final it necessitates considerable modifications of Einstein's theory, which it is outside our province to discuss. But, whether or not changes are needed in other parts of the theory, it appears now to be established that Einstein's law of gravitation gives the true deviations from the Newtonian law both for the relatively slow-moving planet Mercury and for the fast-moving waves of light.

It seems clear that the effect here found must be attributed to the sun's gravitational field and not, for example, to refraction by coronal matter. In order to produce the observed effect by refraction, the sun must be surrounded by material of refractive index 1 plus 0.00000414 divided by the distance from the centre in terms of the sun's radius. At a height of one radius above the surface the necessary refractive index 1.00000212 corresponds to that of air at about one seven-hundredth of an atmosphere, hydrogen at about one two-thousandth of an atmosphere, or helium at about one four-thousandth of atmospheric pressure. Clearly a density of this order is out of the question.

V. General Conclusions

39. In summarising the results of the two expeditions, the greatest weight must be attached to those obtained with the 4-inch lens at Sobral. From the superiority of the images and the larger scale of the photographs it was recognised that these would prove to be much the most trustworthy. Further, the agreement of the results derived independently from the right ascensions and declinations, and the accordance of the residuals of the individual stars, provides a more satisfactory check on the results than was possible for the other instruments.

These plates gave, from declinations, 1.94 arcseconds; from right ascensions, 2.06 arcseconds.

The result from declinations is about twice the weight of that from right ascensions, so that the mean result is 1.98 arcseconds, with a probable error of about plus or minus 0.12 arcseconds.

The Principe observations were generally interfered with by cloud. The unfavourable circumstances were perhaps partly compensated by the advantage of the extremely uniform temperature of the island. (The deflection obtained at Principe is stated here in the original; the figure is not legible in the scan read for this sheet, and is therefore not reproduced. The sentence continues:) The probable error is about plus or minus 0.305 arcseconds so that the result has much less weight than the preceding.

Both of these point to the full deflection 1.75 arcseconds of Einstein's generalised relativity theory, the Sobral results definitely, and the Principe results perhaps with some uncertainty. There remain the Sobral astrographic plates which gave the deflection 0.93 arcseconds, discordant by an amount much beyond the limits of its accidental error. For the reasons already described at length not much weight is attached to this determination.

It has been assumed that the displacement is inversely proportional to the distance from the sun's centre, since all theories agree on this, and indeed it seems clear from considerations of dimensions that a displacement, if due to gravitation, must follow this law. From the results with the 4-inch lens, some kind of test of the law is possible though it is necessarily only rough. The evidence is summarised in the following table and diagram, which show the radial displacement of the individual stars (mean from all the plates) plotted against the reciprocal of the distance from the centre. The displacement according to Einstein's theory is indicated by the heavy line, according to the Newtonian law by the dotted line, and from these observations by the thin line.

Radial displacement of individual stars, in arcseconds. Star 11: calculation 0.32, observation 0.20. Star 10: calculation 0.33, observation 0.32. Star 6: calculation 0.40, observation 0.56. Star 5: calculation 0.53, observation 0.54. Star 4: calculation 0.75, observation 0.84. Star 2: calculation 0.85, observation 0.97. Star 3: calculation 0.88, observation 1.02.

Thus the results of the expeditions to Sobral and Principe can leave little doubt that a deflection of light takes place in the neighbourhood of the sun and that it is of the amount demanded by Einstein's generalised theory of relativity, as attributable to the sun's gravitational field. But the observation is of such interest that it will probably be considered desirable to repeat it at future eclipses. The unusually favourable conditions of the 1919 eclipse will not recur, and it will be necessary to photograph fainter stars, and these will probably be at a greater distance from the sun.

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Text above from F. W. Dyson, 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", Philosophical Transactions of the Royal Society of London, Series A, volume 220, pages 291 to 333 (1920). Public domain; read from the Internet Archive scan at archive.org/details/philtrans06337895.