Eddington's Eclipse Experiment: 1919 and 2017

29 May 2019

2017 Eclipse Day Britton photo.JPG

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Today is the 100-year anniversary of Sir Arthur Eddington’s famous eclipse experiment that proved Einstein was right...

The Modern Eddington Experiment was performed during the 2017 eclipse in the United States. The last total solar eclipse in the continental United States was on February 26, 1979. I was five years old. We lived in Portland, Oregon, where the sun often hides above a blanket of clouds and rain for days at a time during the winter. My family drove to Goldendale, Washington, east of the Cascade Mountains, where the sky is usually bluer. According to my parents, it was sprinkling in Portland and cloudy in Goldendale. We joined a crowd on a hill and looked up anxiously. Minutes before the eclipse, the clouds parted to reveal the sun. People cheered. Then the moon's shadow swept over the land. I remember an eerie quiet accompanying the darkness. Birds stopped flying and chirping. I watched the sun disappear and reappear through paper eclipse glasses.

We drove 185 kilometres to see that eclipse in 1979. Some people travel thousands of kilometres to view the spectacle for fun. Others do it for science. One hundred years ago, in 1919, Sir Arthur Eddington and his associates led expeditions from England to Principe Island in the Gulf of Guinea and to Sobral, Brazil to test Albert Einstein's 1915 theory of gravity. They were trying to measure how much the paths of light from stars bend as they pass close by the Sun. When the moon blocks the bright sunlight, the dimmer light from distant stars becomes visible for such measurements. During the eclipse, photographs were taken through telescopes of a field of stars in the Hyades cluster surrounding the blocked sun. The apparent position of each star was then compared to the actual position of the same star photographed months before or after.

Sir Isaac Newton's theory of gravity predicts that the path of starlight should bend 0.87 arcseconds as it passes the sun's edge. An arcsecond is 1/60 of an arcminute, or 1/3600 of a degree, a very small angle. In Newton's theory, gravity is a force between two objects, proportional to the product of the masses and inversely proportional to the square of the distance between. Light, which Newton thought to be a particle with mass, would therefore be pulled toward the mass of the Sun as it flew by.

Albert Einstein's theory of gravity is radically different. Gravity isn't a force. Instead, Einstein conjectured, it is a feature of spacetime geometry. Einstein's theory predicts a deflection angle of 1.75 arcseconds for starlight grazing the Sun.

The eclipse during which Eddington tested Einstein's prediction occurred on May 29, 1919. I imagine Eddington and his fellow experimenters wringing their hands in the morning. It was cloudy in Sobral. In Principe, where Eddington was stationed, "there was a very heavy thunderstorm from about 10 a.m. to 11.30 a.m.—a remarkable occurrence at that time of year" (Dyson et al. 1920). The men must have been worried. This was no family excursion like I experienced in 1979. These were costly expeditions with a grand purpose. Fortunately, at both locations, the clouds were thin and intermittent during totality, and satisfactory photographs were obtained.

Eddington and company analysed their data and declared victory in a report read to the Joint Permanent Eclipse Committee of the Royal Society and the Royal Astronomical Society on November 6, 1919, in London. The measured deflections at the Sun's edge were 1.98 ± 0.12 arcseconds from Sobral and 1.61 ± 0.30 arcseconds from Principe. Of the two most likely outcomes—0.87 arcseconds from Newton's theory and 1.75 arcseconds from Einstein's theory—the results were closer to 1.75 arcseconds. "Einstein Theory Triumphs" was a headline in the November 10 issue of The New York Times.

Modern Eddington Experiment

The next total eclipse in the United States is August 21, 2017. I start fantasising about performing Eddington's 1919 experiment. My bubble is burst when I read on NASA's Testing General Relativity website that this is a very hard project for the unskilled amateur. A link is provided to an article by a skilled astronomer, Donald Bruns, who will perform the experiment near the top of Casper Mountain in Wyoming. Donald introduces me to a group collaborating to perform the Modern Eddington Experiment at locations from Oregon to Georgia. The group organizer, Toby Dittrich, is a physics professor at the Sylvania campus of Portland Community College, which is less than a mile from my home! I attend his lecture on the subject and join the group's email exchange. I may not be able to perform the experiment myself, but I'd love to see it done. I arrange to observe Richard Berry, former Editor of Astronomy Magazine, and his team perform the Modern Eddington Experiment in Lyons, Oregon, near Salem.

General Relativity

Before I witness the experiment, I study relativity. I start with special relativity, which Einstein gave us in 1905. Increments of time and space, it turns out, are not absolutes. You and I will measure different increments of time and calculate different increments of distance between two events if we’re moving at different speeds (this effect isn’t noticeable for the common speed differences we experience). Increments of spacetime, the mathematical fusion of space and time, are absolute. You and I will calculate the same spacetime increment between two events regardless of our different speeds.

Special relativity is the special case where mass doesn’t change spacetime. I need a basic understanding of the general case where mass does change spacetime, because it is the mass of the Sun - through its influence on spacetime - that causes starlight to bend in the eclipse experiment. In spacetime, objects that are free from other forces move in straight lines. The main idea of general relativity is that mass causes spacetime to curve. If an object moves in a straight line in spacetime, and the spacetime through which it moves is curved, then the path of the object from a distant perspective will appear curved. The classic analogy, considering the curvature of space only, is travel on the surface of the Earth. Someone walking south to north along a meridian is walking in a straight line from their point of view. From the perspective of someone out in space, the walker is following a curved path.

While it is proper to recognise spacetime as a unified quantity, it is helpful to contemplate time and space separately when following the progression of predictions for the eclipse experiment outcome. First, consider time and its curvature, then space and its curvature.

In 1911, Einstein had the time part understood. The time part arises from the equivalence principle, one of Einstein's aha moments, which equates the experience and physical laws within a uniform acceleration to those within a uniform gravitational field of equal magnitude. Richard Feynman, Nobel Laureate in 1965, used a thought experiment involving a rocket to demonstrate an implication of the equivalence principle on time (Gottlieb and Pfeiffer, 2013).

Imagine you and I are in a rocket in deep space accelerating "upward." I'm at the top and you're at the bottom of the rocket. We both have clocks and lasers. Every time a second passes on my clock, I send a laser pulse down towards you. Because the rocket is accelerating upward, you receive my pulses faster than the seconds pass on your clock. If you forget that the rocket is accelerating, you'd think that time up where I am must be moving faster than it is down where you are. Now you send a laser pulse up toward me every time a second passes on your clock. Because the rocket is accelerating upward, I receive your pulses slower than the seconds pass on my clock. If I forget that the rocket is accelerating, I'd think that time down where you are must be moving slower than it is up where I am.

The equivalence principle says that the experience I just described must be the same if, instead of accelerating in space, the rocket is parked on a planet where the acceleration due to gravity is equivalent. You would think that time moves faster up where I am, and I would think that time moves slower down where you are. The mass of the planet makes this so.

What does this mean for light waves passing by the sun? Take the perspective from outer space: since time slows down close to the massive sun, the speed of light appears to slow down. Arthur Eddington described the resulting effect like this (Eddington 1920):

“The wave-motion in a ray of light can be compared to a succession of long straight waves rolling onward in the sea. If the motion of the waves is slower at one end than the other, the whole wave-front must gradually slew round, and the direction in which it is rolling must change. In the sea this happens when one end of the wave reaches shallow water before the other, because the speed in shallow water is slower. It is well known that this causes waves proceeding diagonally across a bay to slew round and come in parallel to the shore; the advanced end is delayed in the shallow water and waits for the other. In the same way when the light waves pass near the sun, the end nearest the sun has the smaller velocity and the wave-front slews round; thus the course of the waves is bent.”

In 1911, considering the curvature of time alone, Einstein predicted that the amount by which “the course of the waves is bent” in the eclipse experiment, for light waves grazing the sun, would be 0.87 arcseconds, the same value calculated using Newton’s theory. This is not the correct answer. General relativity was not yet complete.

Mass causes space to curve too. We need to include the curvature of space piece in order to accurately predict the deflection angle in the eclipse experiment. The mass of the sun causes space nearby to stretch.

Here's an analogy to help visualise this. Imagine a bowling ball resting in the centre of a trampoline. The bowling ball stretches the trampoline. This is an imperfect comparison. The real way in which the space around a massive body like the sun is deformed is beyond my capacity of visualisation. Space doesn't actually stretch "down" as in the trampoline analogy, but space does indeed deform.

Now we can ask the same question we did before, when considering the curvature of time, but now for the curvature of space: What does this mean for light waves passing by the sun? Again, take the perspective from outer space, and pretend we don’t see the stretched space near the sun. The light is traveling over an elongated distance that we don’t see, and so to us it appears that the speed of the light slows down. More slowing means more slewing.

In 1915, Einstein's completed theory of general relativity had both parts: the curvature of time and of space due to mass. Using the completed theory, the total deflection angle of starlight in the eclipse experiment is calculated to be 1.75 arcseconds.

Eclipse Day

The morning of August 21, 2017, I'm at Richard Berry's Alpaca Meadows Observatory in Oregon, in a pasture of alpaca-mowed yellow grass. Cars are whizzing by on Highway 22 behind a row of Douglas firs. Last night eleven scientists and artists gathered in the ranch house on the other side of a dry creek, where Richard and Eleanor Berry hosted a cosy dinner. This morning I'm hovering around Jacob Sharkansky, Abraham Salazar, and the Tele Vue Genesis telescope and STT-8300M computer-controlled camera they will use to photograph the deflected positions of stars during totality.

Jacob and Abraham are students at Portland Community College. They are remarkable young men. Jacob is a shy 17-year-old earning his high school diploma from the community college while taking college-level classes. Abraham is a 33-year-old civil engineering major who worked ten years in construction and has a family with two kids, one a newborn. They both were inspired to perform the Modern Eddington Experiment in Toby Dittrich's physics class.

There isn't a cloud in the sky today. The team's major concern is the focus of the telescope, which depends on temperature. They have plenty of experience focusing on stars during the cool night, but none during the mid-morning of a warm August day. It will cool down some during totality; still, the best focus setting is a bit of a guessing game.

The partial eclipse starts 72 minutes before totality. Ten minutes before totality, all the observers start finding their spots and conversing in muted voices. Shadows on the ground sharpen. Two minutes before totality, Richard gives the order: "Get to your stations." Jacob starts pacing around the small wood shed sheltering the computer connected to the camera. There are no cars driving on the highway now. Ten seconds before totality, Abraham removes the filter protecting the camera from the sunlight. I gasp at totality and utter something I can't - and probably don't want to - remember. I see, with my naked eye, two short red hairs on the rim of the sun. These must be solar prominences from the sun spots Richard pointed out prior to totality.

The telescope camera, automated by the computer, takes 2-degree by 1.5-degree photos at various exposure durations: 0.1, 0.6, 1.0, and 1.6 seconds. The goal is to see stars within a donut around the sun. Outside the donut, the starlight deflection due to the sun's gravity is too small to measure. Inside the donut, stars can't be seen through the brightness of the corona. Like the telescope focus, the ideal camera exposure duration is uncertain. The camera needs time to capture enough starlight to locate the center of each star, but not so much time that the corona washes out the starlight. Before totality ends, the telescope turns away and photographs a group of star positions uninfluenced by the sun's gravity (this is the eclipse reference image).

I see a diamond ring, and totality is over. It could not have lasted long enough! The Modern Eddington Experiment team is elated. Jacob is striding laps around all the equipment in the pasture, grinning. The team captured 23 images of stars around the blocked sun. The data collection phase of the experiment is complete. We all stand in a row and shoot photos of the exhilarated trio and their telescope. The men are relieved at having executed the procedure they had rehearsed over the last three months. Now comes the challenging work of analysing the data.

Data Analysis

Richard presents his team’s success, and the status of the data analysis, at a workshop for local astronomers on July 21, 2018, eleven months after the eclipse. The workshop is in the garage of a business in the Swan Island Industrial Park by the Willamette River, in Portland. It’s hot outside and the garage door is open. I wander in at 4:30 pm and find a plastic chair. A man is giving a presentation to about 22 people seated casually around three tables. There is a drill press behind the large flat-screen monitor showing his slides. Behind me is a barbecue for dinner later in the evening. The applause after the talk wakes up an old dog, who struggles to its feet and hobbles away. Many of the questions posed to the speaker are in the spirit of brainstorming. What if you did this? What if you did that?

The next speaker shares his experiences with high-speed computing, then it’s Richard’s turn. I learn that Richard was first contacted by Toby Dittrich on March 18, 2017, only five months before the eclipse. Not much time to prepare. For comparison, Donald Bruns (who isn’t at the meeting; he lives in San Diego) spent 20 months preparing for the experiment. While Richard and the students pulled off the eclipse day procedure brilliantly, the data analysis phase has suffered from the lack of preparation time. It also hasn’t helped that the students moved on—as students do—to the next chapters in their lives. No new students came onboard to assist with the data analysis.

As mentioned earlier, an arcsecond is a very small angle. A successful eclipse experiment needs to measure starlight deflections in the 0.3 to 1 arcsecond range (1.75 arcseconds is for starlight grazing the sun). Richard shows a slide with the various factors affecting the measured positions of stars. The biggest two influences are atmospheric refraction and optical distortion. The effect of atmospheric refraction, about 2.5 arcseconds, can be accounted for by knowing the weather conditions. The effect of optical distortion is around 3 arcseconds.

A good bit of news is that we know the actual positions of the stars within about 0.002 arcseconds, courtesy of the European Space Agency’s Gaia satellite, which has been surveying the stars since 2014. This is convenient; Eddington’s team had to take photographs themselves before and after the 1919 eclipse to determine actual star positions.

Richard’s talk lasts about an hour. I can tell that some of the workshop attendees would love to have the data in order to try their hand at the analysis.

Results

A problem clouding the results is that the telescope’s plate scale is different between key images. Plate scale is the number of arcseconds per pixel. The plate scale is not the same for the eclipse image, the eclipse reference image, and an image taken six months after the eclipse. This impacts the ability to accurately account for optical distortion in the eclipse image. Good optical distortion parameters were determined from the image taken six months after the eclipse. But because of the different plate scale values, the optical distortion parameters from the six-months-after image cannot be uniquely rescaled for the eclipse image.

Richard ends up collaborating with Donald Bruns on the data analysis. The best approach is probably to use the plate scale from the eclipse image and the optical distortion parameters from the six-months-after image. It’s not perfect. The computed values of starlight deflection at the sun’s edge are 1.68, 2.15, and 1.68 arcseconds based on the software used to determine the actual star positions (Astrometrica, MaxIm DL, and Astro Photography Tool, respectively). The average of these values is 1.84 arcseconds. Analysing the data in other potentially reasonable ways yields results farther away from the accepted value of 1.75 arcseconds from general relativity. All things considered, confidence in the results is low.

Richard presents the results at an American Association of Variable Star Observers conference in Arizona on November 16, 2018. He suggests spending two years before an eclipse practicing the experiment by measuring the positions of stars around the full moon. Work out everything, including the data analysis. On eclipse day, the main difference would be gravitational deflection from the sun.

Donald Bruns did spend almost two years preparing for the 2017 eclipse. He measured a deflection of 1.75 arcseconds with an uncertainty of 3.4% (Bruns 2018). Wow.

The next total eclipse in the United States is in 2024. There won’t be a total eclipse in the United Kingdom until 2090. Take a vacation, however, and you can see one in Spain in 2026. If you want to replicate one of the great experiments in science, start practicing two years ahead.

References

Comments

In my view, the result is quite okay! The closer the stars are to the sun, the greater the deviation from relativistic value. The empirical formula is

d = 1.75"/r + 0.3"/r^2

https://ui.adsabs.harvard.edu/abs/1985AN....306...77S/abstract
http://articles.adsabs.harvard.edu/pdf/1985AN....306...77S

Conversely, the result from Mr. Bruns is very suspicious.

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