Light Deflection at the Sun

 
 
 
 
 
 
 

Albert Einstein shot to fame in November 1919 when an announcement was made by British astronomers at a scientific meeting in London: Measurements of starlight during a solar eclipse earlier that year had vindicated the gravitational deflection of light at the Sun, as predicted by General Relativity. Moreover, it was argued, the data were not compatible with Newton's time-honoured theory of gravitation.


In Einstein's theory of General Relativity, just four years old in November 1919, space-time in the vicinity of a large mass such as the Sun is curved, and light rays passing nearby the Sun get bent. As a consequence, the actual location of a star observed in the vicinity of the Sun ("wahre Position") is not at the position where it appears to be ("scheinbare Position"), but a bit closer to the Sun. The deflection angle δ for the light passing just at the rim of the Sun can be calculated from the speed of light, c, the gravitational constant, G, and the mass and radius of the Sun. It is


- we will come back to the extra factor (1+γ)/2 in a second. If wee keep in mind that the Sun has an apparent diameter of half a degree, or 1800 arc seconds, the deflection of light from a star close to the rim of the Sun is just 1/1000 of the Sun's diameter. Moreover, for light passing at larger distances d from the Sun, the angle drops as 1/d - so this is a tiny effect!

Actually, a similar deflection of light had already been calculated before Einstein. The British physicist Henry Cavendish, and, most notably, the German astronomer Johann Georg von Soldner had used Newton's mechanics and calculated the hyperbolic trajectory of a particle which passes at the speed of light nearby a large mass. This calculation yields a deflection angle that is just half as big as the value obtained from General Relativity.

This difference between the two calculations is nowadays encoded in a parameter called γ, where γ = 1, or (1+γ)/2 = 1, corresponds to the bending of light as predicted by General Relativity, while γ = 0, or (1+γ)/2 = 1/2, is the value for the Newtonian calculation. Actually, γ is just one out of a set of several parameters which are used in a framework called parametrised post-Newtonian formalism. This formalism had been developed to describe, in a unified framework, the observable consequences of different possible theories of gravitation. For example, γ describes how much space curvature is produced by a unit rest mass. Newtonian gravity comes with γ = 0 (no curvature), and General Relativity has &gamma = 1. Other conceivable theories of gravitation might come with still other values of γ, and the measurement of γ is a way to distinguish between them.

Negative of the solar eclipse of May 29, 1919, photographed by Andrew Crommelin in Sobral, Brazil. Stars are marked by horizontal lines. (via Wikipedia, from F. W. Dyson, A. S. Eddington, and C. Davidson, Phil. Trans. Royal Soc. London. Series A 220 (1920) 291-333, page 332)

While Soldner had apologised to the readers of his 1801 paper for calculating an effect that he judged unobservable, astronomers a hundred years later had more confidence in their capabilities. Since it is not possible to observe stars in the vicinity of the Sun under normal circumstances, they had to seize the rare opportunity of a total eclipse of the Sun, when stars nearby are visible. By comparing the apparent positions of these stars to the true positions (measured at night, at a different time of the year, when the effect of gravitational bending by the Sun can be neglected), the deflection of light by the gravitational field of the Sun could be established.

Motivated by these considerations, the British astronomer and relativity aficionado Arthur Stanley Eddington organised two expeditions to observe a solar eclipse on May 29, 1919, with a zone of totality roughly along the equator. He travelled to Principe, an island in the Atlantic ocean, while a second team observed the event from Sobral in Brazil.

The results of these observations were made public at the meeting in London in November 1919 that made Einstein a scientific star: The measured deflection of light did fit to the Einstein value, while it was much less compatible with the Newtonian bending.

Of course, not only Einstein denialists point out the huge error bars of the eclipse measurements. Eddington had only a few stars on his photographic plates, due to bad weather, and the main telescope of the Sobral team had suffered misalignment caused by heating in the plain daylight before the eclipse. As a result, data taken with this instrument had been discarded - which is a tricky point, since they seem to have favoured a Newtonian value for the light deflection.

However, the 1919 eclipse data have just been the beginning of a long series of ever-improving measurements of the gravitational deflection of light. This finally brings us to our plottl.

Its upper part shows, as a function of time along the horizontal axis, the results for measurements of the light-bending parameter (1+γ)/2, as established by different methods.

Improvement of the measurement of the gravitational bending of light and radio waves by the Sun (upper part of the figure) over the last 80 years. The horizontal black line at (1+γ)/2 = 1 corresponds to the prediction of General Relativity. [Source: The Confrontation between General Relativity and Experiment by Clifford Will, Living Rev. Relativity 9 (2006), cited on <2008/01/13> (http://www.livingreviews.org/lrr-2006-3), Figure 5.]

Marked in red are data from measurements with visible light, all but one taken at solar eclipses. The 1919 eclipse is the left-most data point. As we know already, these eclipse data come with large uncertainties and huge error bars - some do not even fit on the plot (the red arrows at the upper edge) - and there has been been only a modest progress up to the 1970s. The last eclipse expedition with published data about light deflection was to Mauritania, resulting in the paper Gravitational deflection of light: Solar eclipse of 30 June 1973. I. Description of procedures and final result. by Brune et al., Astron. J. 81 (1976) 452-454.

However, since the advent of satellites, it is not necessary anymore to wait for an eclipse to observe stars in the vicinity of the Sun. Thus, an analysis of the star catalogue established by the astrometry satellite Hipparcos could confirm the Einstein value for the bending of light, (1+γ)/2 = 1, to within 0.1 percent (Froeschlé, M., Mignard, F., and Arenou, F.: Determination of the PPN parameter γ with the Hipparcos data, Proceedings from the Hipparcos Venice ’97 Symposium (ESA, Noordwijk, Netherlands, 1997) - PDF)

And, of course, light is only part of the electromagnetic spectrum. For example, one can use radio telescopes to measure the deflection of radio signals from quasars, completely analogous to the the measurement of starlight, but with the bonus that there is no need to wait for eclipses. Early attempts to do so from the 1960s and 1970s are marked by the blue dots - the results vindicate, and improve on, the optical observations (E. B. Fomalont, R. A. Sramek: Measurements of the Solar Gravitational Deflection of Radio Waves in Agreement with General Relativity, Phys. Rev. Lett. 36 (1976) 1475-1478.)

And finally, the interferometric combination of radio telescopes from all over the globe has further improved the quasar data. These so called VLBI (Very Long Baseline Interferometry) light deflection measurements have reached an accuracy of 0.02 percent, and they fit perfectly well to the predictions of General Relativity (Shapiro, S.S., Davis, J.L., Lebach, D.E., and Gregory, J.S.: Measurement of the solar gravitational deflection of radio waves using geodetic very-long-baseline interferometry data, 1979-1999, Phys. Rev. Lett. 92 (2004) 121101.)

Thus, Eddington had got it right, and as it looks from today's data, General Relativity rules!



PS: The lower part of the plot shows the so far best determination of γ. It uses a different but related effect, the so-called Shapiro time delay, which is based on the apparently reduced speed of light in the vicinity of large masses. This time delay can now be measured extremely precisely thanks to the telemetry data of spacecraft travelling around in the Solar System - Viking, Voyager, Cassini. The Shapiro time-delay measurements using the Cassini spacecraft yielded an agreement with General relativity to 0.001 percent (B. Bertotti, L. Iess and P. Tortora: A test of general relativity using radio links with the Cassini spacecraft, Nature 425 (2003) 374-376).

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Einstein Online has a great first introduction to the Gravitational deflection of light by Steven and Irwin Shapiro.

For the calculations of Cavendish and Soldner, see Clifford M. Will: Henry Cavendish, Johann von Soldner, and the deflection of light, American Journal of Physics 56 (1988) 413-415 (subscription required).

The 1919 eclipse expedition and its motivation and background by Einstein's prediction of the bending of light is described, e.g., by Peter Coles: Einstein, Eddington and the 1919 Eclipse, arXiv:astro-ph/0102462v1. For a recent discussion about the analysis of the photographic data, see Daniel Kennefick: Not Only Because of Theory: Dyson, Eddington and the Competing Myths of the 1919 Eclipse Expedition, arXiv:0709.0685v2 [physics.hist-ph]. The original paper of the 1919 eclipse expedition is 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 222 (1920) 291-333.

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This post is a latecomer to our A Plottl A Day series.