Fact and folklore about the deflection of light by the Sun

Most people are familiar with the dramatic story of how Albert Einstein’s theory of general relativity made a surprising prediction that was spectacularly confirmed and thus enabled his counter-intuitive idea to become the accepted view. The story goes that he predicted that the path of light would be bent by the presence of a strong gravitational field. Arthur Eddington then measured that bending during a solar eclipse and got a result that agreed with Einstein’s prediction, thus providing strong support for the revolutionary idea that space was curved by matter and that light followed that curved path. Part of the dramatic appeal of this story, as recounted in the folklore, is that Einstein’s prediction that light would be bent by the Sun seemed to be utterly novel and thus its confirmation carried much greater impact than it would have otherwise.

But as is usually the case with scientific history, the actual story is more complicated and less dramatic but also, in my opinion, far more interesting because of the light it sheds on how science actually proceeds, a topic that is (warning: shameless plug coming up!) at the heart of my forthcoming book The Great Paradox of Science: Its surprising success against all odds.

The reality is that Isaac Newton (1643-1727) had already raised the possibility that light could be bent by gravitational fields. Newton had proposed a particle model of light and that remained largely the dominant view until the early 1800s. If light is a particle, then it was believed to have mass and, if it did not move with infinite speed, then it made sense that it would feel the gravitational field of the Sun and its path get deflected.

Ole Romer had already inferred in 1676 from the motion of Jupiter’s moons that the speed of light was finite and Newton was aware of this. Using Newtonian mechanics and gravity, it is possible to calculate the amount of bending but at that time, the precise speed of light was still unknown and it may be that Newton did not feel that he had sufficient data (for example, the mass of light particles was unknown) to actually do the calculation himself. In his book on optics published in 1704 at the age of 62, he may have also felt that he was running out of time to follow up all his ideas and so he listed a series of what can be called ‘homework problems’ to be addressed by others later, one of which was “Do not Bodies act upon Light at a distance, and by their action bend its Rays, and is not this action strongest at the least distance?”

This homework problem was eventually taken up by Johann G. von Soldner, who published his result in 1804. It turns out that if one assumes a mass m for the light particles, that mass cancels out and disappears from the final result for the deflection, so knowledge of its precise value is unnecessary. Domingos S.L. Soares has reproduced that calculation. For light that just grazes the surface of the Sun, the value for the deflection angle is 2GMS/c2RS, where MS is the mass of the Sun and RS is its radius. This is exactly half the value obtained using the theory of General Relativity.

In chapter 6.3 of Kevin Brown’s book Reflections on Relativity that is available electronically, he tells us the interesting story of Einstein’s entry into this problem .

The idea of bending light was revived in Einstein’s 1911 paper “On the Influence of Gravitation on the Propagation of Light”. Oddly enough, the quantitative prediction given in this paper for the amount of deflection of light passing near a large mass was identical to the old Newtonian prediction, d = 2m/r0. There were several attempts to measure the deflection of starlight passing close by the Sun during solar eclipses to test Einstein’s prediction in the years between 1911 and 1915, but all these attempts were thwarted by cloudy skies, logistical problems, the First World War, etc. Einstein became very exasperated over the repeated failures of the experimentalists to gather any useful data, because he was eager to see his prediction corroborated, which he was certain it would be. Ironically, if any of those early experimental efforts had succeeded in collecting useful data, they would have proven Einstein wrong! It wasn’t until late in 1915, as he completed the general theory, that Einstein realized his earlier prediction was incorrect, and the angular deflection should actually be twice the size he predicted in 1911. Had the World War not intervened, it’s likely that Einstein would never have been able to claim the bending of light (at twice the Newtonian value) as a prediction of general relativity. At best he would have been forced to explain, after the fact, why the observed deflection was actually consistent with the completed general theory. Luckily for Einstein, he corrected the light-bending prediction before any expeditions succeeded in making useful observations. In 1919, after the war had ended, scientific expeditions were sent to Sobral in South America and Principe in West Africa to make observations of the solar eclipse. (Was the specific location of Principe chosen for its name, as a subliminal tribute to Newton’s Principia?) The reported results were angular deflections of 1.98 ± 0.16 and 1.61 ± 0.40 seconds of arc, respectively, which was taken as clear confirmation of general relativity’s prediction of 1.75 seconds of arc. This success, combined with the esoteric appeal of bending light and the romantic adventure of the eclipse expeditions themselves contributed enormously to making Einstein a world celebrity.

So there we have it.

Much of what we think of as scientific history as written in textbooks and popular science articles and books is actually folklore and we should view it with skepticism. I’ve quoted Richard Feynman before on this:

[W]hat I have just outlined is what I call a “physicist’s history of physics,” which is never correct. What I am telling you is a sort of conventionalized myth-story that the physicists tell to their students, and those students tell to their students, and is not necessarily related to the actual historical development which I do not really know! (QED: The Strange Theory of Light and Matter, p. 6)

In the course of writing my book, I have been reading a lot of science history written by actual science historians who have gone back and looked at the contemporary records and it has been an enlightening experience.


  1. djlactin says

    interesting despite the typos: ‘Paradox od Science’ should be ‘Paradox of Science’ (I think!)
    you NEED parentheses around “c2RS” in the equation (think of the order of operations in arithmetic!) [I do not waste time with such trivialities as superscripting and subscripting, mostly because the HTML tags don’t seem to work!]

    (please delete this post after you make the corrections.)

  2. Pierce R. Butler says

    The reported results were angular deflections of 1.98 ± 0.16 and 1.61 ± 0.40 seconds of arc, respectively…

    I can’t recall where I read this, but allegedly the results were within the margin of error for the equipment used -- yet Eddington went ahead and announced the confirmation of Einstein’s theory anyhow.

    Would’ve been one helluva scandal if later findings hadn’t supported that leap o’ faith.

  3. says

    Sounds like it’s going to be a fun read!!

    Weren’t there also a fair number of scientists who cooked the books? The ones we remember are the ones who nudged their math a bit in the direction they knew was right -- sometimes you gamble and win, sometimes you lose. If I recall correctly, Hawking said Eddington cooked his numbers, but maybe he didn’t?

  4. Pierce R. Butler says

    Rob Grigjanis @ # 2 -- Thanks for setting me straight (again)!

    Hawking fell victim to the urge to scandal-monger?!? [No heroes, no heroes, no heroes…]

    Marcus Ranum @ # 3: Weren’t there also a fair number of scientists who cooked the books?

    Gregor Mendel did that (or so I’ve read); apparently nobody replicating his little garden experiment has ever gotten such clean tidy numbers.

    Less justified-by-further-research, of course, are the “cold fusion” data of Fleischmann & Pons, and certain animal-behavior figures of Marc Hauser, formerly of Harvard.

  5. Rob Grigjanis says

    My favourite quote from the article linked in #2, by a minor player (my bolding);

    The second theory of Einstein in 1914 [GR] is far more speculative and
    I fear only accord with observations will make me accept it. Besides the analysis is too beastly for words. I can well understand the compatriots of Riemann and Christoffel burning Louvain and sinking the Lusitania.

    A bit over the top, but anyone who’s worked with Christoffel symbols will sympathize.

  6. fentex says

    That account of missed opportunities to measure, and find a flaw, in Einsteins original Relativity calculations is fascinating.
    Might have to buy this book.

  7. Mano Singham says

    djlactin @#1,

    Thanks pointing out the ‘od’ error that I have corrected. As for the other, I am puzzled. Does you browser not show the 2 as a superscript for c? Is anyone else not seeing it either. I write superscripts as anglebracketsup/anglebracket2anglebracketsup/anglebracket where anglebracket refers to “< " and /anglebracket refers to ">“. I hope that’s clear!

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