MODERN-EDDINGTON-EXPERIMENT PROSPECTUS by Bradley E. Schaefer (Louisiana State University)
The goal is to get many lay observers to travel to the path of the 21 August 2017 total solar eclipse, take CCD images of the star field around the eclipsed Sun, and use their own data to test whether Einstein’s prediction of gravitational bending of light is true. Part of the goal is to get a wonderful EPO and Citizen Science program. Part of the goal is to also provide the all-time best measure of the gravitational bending of light (getting 2-3X better than even the analysis of the entire history of VLBI measures of 541 radio sources).
In the past year, off-the-shelf amateur-astronomy equipment has suddenly made possible this layman version of Eddington’s great 1919 experiment. And this can be done straight forwardly by any layperson, and with greatly better accuracy than done by Eddington or any later workers. The whole Eddington total solar eclipse experiment has only been successfully run for seven eclipses, the last one being in 1973. In 2017, after 44 years, the Eddington experiment can be done again with many people spread across the whole width of America.
One of the all-time most famous science experiments was the epic measure of the gravitational bending of light as seen by a small shift of starlight passing near the Sun during a total solar eclipse in the year 1919. This experiment was designed to prove the arcane theory of General Relativity advanced by Albert Einstein, a German physicist. The lead scientist, Sir Arthur Eddington, was a British astronomer, who did all the planning at the height of the fighting in World War I. The epic expeditions to Sobral in Brazil and to Principe Island off the coast of Africa on 29 May 1919 conducted what we can call the ‘Eddington Experiment’ to measure the bending of light as seen around an eclipsed Sun. On 6 November 1919, Eddington announced to the world, at a packed and quivering meeting of the Royal Astronomical Society, that Einstein’s General Relativity prediction was confirmed. All the big newspapers put the discovery at the top center of their front page, realizing that man’s view of the world had just taken a big change. This announcement made Einstein instantly famous, with big parades in New York City, and his fame has never diminished, even to being named as the “Person of the Century”. Eddington’s eclipse also served to break the blockade on ‘German science’, helping to prove that science is above politics and is international in scope and meaning.
The Eddington experiment was sucessfully run for six eclipses from 1919 to 1952, plus a last one in 1973. These results together gave a good answer that the GR shift was indeed real, even though the 1-sigma measurement error on the shift was between 6% and 50%, while the exhaustive and modern 1973 eclipse only resulted in 11% errors. Some of these results have engendered long controversies.
The question of the gravitational bending of light has now been measured to awesome accuracy with modern techniques (Will, 2015, Class. Quantum Grav. 124001). In 1995, VLBI observations were made of the very bright point sources 3C273, 3C279, and 3C48 (with one passing so close as to be occulted by the Sun) with incredibly high positional accuracy, so as to prove the GR shift to 0.34%, while in 2009 this wasimproved to 0.03%. A 1997 set of observations of very-high-precision optical astrometry with the Hipparcos satellite demonstrated the GR shift to an accuracy of 0.2%. A 2010 global survey of VLBI positions of 541 radio sources over all history got the GR shift down to 0.012%.
GREAT EPO AND GREAT CITIZEN-SCIENCE
A large scale project to have non-professional-scientists perform a modern- Eddington-experiment can provide a wonderful opportunity for EPO and for Citizen- Scientist involvement. The idea is that many people can get involved in one of the greatest experiments, repeating it themselves personally, and this will foster a close knowledge of the science and of how science works. The people will have a personal investment in testing GR. Conceptually, it will show how science works by testing predictions. And it will bring the counter-intuitive predictions of GR close to people, where they can see the bending for themselves. The 2017 total solar eclipse provides a wonderful opportunity.
Conceptually, much of physics has the trouble that people cannot test the evidence or even see the effects. All that laymen and press people and politicians can do is read about the Higgs Boson, and there is nothing to see and nothing to do. And for GR, the claims are very esoteric, completely invisible, and can only be performed by big- money teams. With a variety of public-science results being attacked, the credibility of science is at stake, and much of the higher results are just mysteries to the public. A modern-Eddington-experiment can completely break this dilemma for science. The reason is that any laymen can perform the test of the validity of an esoteric claim, and they can do it with their own off-the-shelf equipment. Suddenly we have some of the most esoteric claims in all physics becoming intimately testable by anyone.
WORLD-BEATING TEST OF GR TO 50 PARTS-PER-MILLION
I have made a very detailed and realistic calculation of the accuracy at which the Modern Eddington Experiment can test Einstein’s prediction. I find, with a star catalog that only goes to V=10.5 magnitude, that 100 observers with good equipment will be able to measure the GR shift to an accuracy of 0.019%. But the expected equipment can get down to more like V=12.1 mag, so I estimate that the Modern Eddington Experiment can actually get down to ~0.005% accuracy. (All known and imagined systematic effects can be accurately corrected to smaller levels.) Suddenly, we are dealing with improving on the previous world’s best measure of gravitational light bending by a factor of two-to- three.
The merit for science of this Modern Eddington Experiment is that GR has been under attack from many directions, and many subtle modifications have been proposed. Some of these attacks are attempts to explain either Dark Energy or Dark Matter by modifications to the law of gravity. Further, we know that GR must be modified so as to become consistent with quantum mechanics. We do not know the regime over which discrepancies with GR might appear, and we’ll never know unless we look closely, improving the accuracy of experimental tests. The Modern Eddington Experiment is a precision test to 50 parts-per-million, pushing the accuracy down by a substantial factor, and who knows whether any discrepancy will appear.
I have performed very detailed calculations so as to make realistic estimates of the real accuracy in measuring the shift, I have used this to optimize the system parameters, and I have a detailed study of the systematic problems. Here are the concluding paragraphs from the separate reports on the measurement errors and the systematic errors:
Let me now summarize all these model results: (A) The modern Eddington experiment is easily feasible with current off-the-shelf amateur equipment, all leading to a greatly better value for the GR shift than Eddington got. (B) The optimal configuration is something like D=6″, F=800mm, E=3s, plus an SBIG STX-16803 camera, with Npixel=4096, Lpixel=9μ, and Emax=100,000e-. (C) For purposes of getting good measures of the GR-shift, the acceptable range for system parameters is 3″<D<11″, 600mm<F<900mm, 1s<E<10s, and Npixel>>3000. (D) For purposes of EPO, a very wide range of equipment is possible, including any scope that can get a field-of-view larger than two degrees or so, and even including telephoto lenses with F>200 mm and even including older-generation CCD cameras with Npixel>2500. (E) The two biggest uncertainties in the model are the seeing FWHM and the sky brightness, where even poor cases will still result in a measure of the GR shift only ~2X worse than for expected conditions. (F) To optimize on the sky conditions, observers should choose a site in an open field at high altitude in the US west close to the centerline, shade the telescope up until soon before totality, and carefully focus on Venus or Sirius during the partial phase. (G) Known bad equipment choices are to use video rates, to use a color CCD, to use a CMOS detector, to not have a ‘goto’ telescope mount, to have F<200mm, to have a field of view <1.5°, or to have Npixel<2500. (H) For the ‘standard’ equipment and expected sky conditions, a single image might should a shift with a 1.0% accuracy. With roughly 30 images taken during totality, these can be combined to produce an uncertainty of 0.19% from one telescope. If we had 100 observers, then we can expect to get to 0.019% accuracy. Actually because of the known incompleteness of my 1222 star catalog to below V=10.5, the inclusion of the stars down to V=12.1 will improve the overall accuracy by around 4X, so I think that we will really have an overall accuracy of ~0.005%. (I) As given in my companion report, all the systematic errors can easily be conquered. Thus, PlateScale/GRshift degeneracies can be solved to high accuracy with near simultaneous pictures of the Pleiades and with measuring the plate scale from over a wide range of angles from the Sun, while coma and any optical distortions will be completely mapped out with the near-simultaneous Pleiades images. At this time, I know of no uncorrected systematic effects at larger than the part-per-million level. (J) For comparison, a single observer can get accuracy better than all prior pro-expeditions from Eddington eclipses, better than Hipparcos, and better than VLBI up until 2004. That laypeople can readily do so awesomely well with off-the-shelf equipment and no huge time commitment makes this great EPO and Citizen Science. (K) For comparison the current best measure of gravitational light bending is 0.012%, for 541 VLBI sources as measured over all history, yet we are likely to do better by a factor of 2-3X. Thus, the Modern Eddington Experiment suddenly becomes front-line science with a world-beating high-precision 50-parts-per-million test of Einstein’s GR.
I have identified three substantial systematic effects; detecting too few stars, the PlateScale/GRshift degeneracy, and coma (plus any other optical distortions) making for possible apparent radial shifts. In addition, other significant systematic effects arise
from differential stellar aberration across the field, differential atmospheric refraction across the field, and shifts of the star centroids when riding on the sloping background of the solar corona. Fortunately, all of these can be completely conquered by a few simple solutions: First, take pictures of the Pleiades (or Praesepe) immediately before and after totality. Second, have a large field of view, so the outer stars set the plate scale. Third, also take picture of the night sky to define coma and focus effects (and any other distortions) on the nights before the eclipse. Fourth, use a CCD camera with adequately long exposures. Fifth, use an analysis procedure that makes exact calculations of the differential stellar aberration, differential refraction, and the chi-square fit of the stellar PSF riding on top of a sloping background. With this, all systematic effects are completely solved, with the exception of unavoidable dust storms or fairly thick clouds.
All this is to say that the modern Eddington experiment is feasible.
PROJECT REQUIREMENTS FOR THE OBSERVER
The modern-Eddington-experiment is simple and involves easy observations. Nevertheless, there are a variety of pretty strict requirements that the observers must follow. Here is a list of the requirements: ***For purposes of making the best measure of the GR shift, the telescope aperture must be between 3-inch and 11-inch, while the focal length must be between 600 mm and 900 mm. For EPO purposes, the constraints are weakened to allow telephoto lenses with F>200 mm. ***They must use a monochrome CCD camera that reads out in FITS format. ***For purposes of getting the best measure of the Einstein shift, the CCD camera must have more than 4000 pixels across. For EPO purposes, it is acceptable to have a CCD that has more than 3000 pixels across. ***The telescope must be well mounted, polar-aligned, accurate-tracking, and with ‘goto’ ability. ***On the nights before eclipse, run full scale practice ten times. Also take image series on star fields, including a series with small variations in focus. ***During the partial phases before totality, keep the scope shaded, focus on Sirius, and take a series of images on the Pleiades (or Praesepe) soon before the start of totality. ***During totality, take a series of exposures with an exposure of something around 2 seconds. ***Immediately after the end of totality, start taking images of the Pleiades.
All these requirements and recommendations are pretty easy. In all, this whole experiment is straight forward and well within the normal capabilities of laymen or amateur astronomers.