The recent death of Tom Stoppard, who cowrote the screenplay for “Shakespeare in Love,” reminded me of Dennis Overby’s Einstein in Love (2000). It’s a biography of Einstein during the two decades of his most groundbreaking work. In it, I found out that Eddington fudged the results of the famous experiment that was reported to have confirmed general relativity.
Three devices at two locations measured the deflection of stars near the sun during a solar eclipse. Einstein’s theory predicted a deflection roughly twice as large as predicted by Newtonian theory. Here were the results:
| Device | Estimate of deflection | Data quality | Comment |
|---|---|---|---|
| Sobral telescope | 1.98 ± 0.12 | Best | Too high for both theories |
| Sobral astograph | 0.86 ± ? | Next best | Close to Newton |
| Principe astrograph | 1.61 ± ? | Worst | In the Einstein neighborhood |
Eddington tossed the results closest to Newton, averaged the remaining two together, and got a results of “1.75, right on the relativistic mark.”
Well, gee, that seems bad. But Eddington turns out to have been right, as our phones demonstrate. “As predicted by Einstein’s theory, clocks under the force of gravity run at a slower rate than clocks viewed from a distant region experiencing weaker gravity. This means that clocks on Earth observed from orbiting satellites run at a slower rate. To have the high precision needed for GPS, this effect needs to be taken into account or there will be small differences in time that would add up quickly, calculating inaccurate positions.”
Here’s a longish quote from the book, with key sentences highlighted. At some point, I’ll use it as an example that comments on Imre Lakatos’s “methodology of scientific research programmes.”
In the end, Eddington and his crew had three sets of data from the three telescopes they had taken to the eclipse. By far the best plates were the ones exposed in the four-inch Irish telescope at Sobral. Measuring the seven stars on those seven plates gave a deflection of 1.98 seconds of arc, with an uncertainty of about 0.12 second. That was higher than Einstein had predicted, and taken alone would actually have cast severe doubt on general relativity. The next-best plates were from the Sobral astrograph. They showed many more stars, but heat from the sun had affected the mirror and blurred the images, and may even have affected the focus. The same analysis on these plates yielded a value for the deflection of 0.86, almost exactly the Newtonian prediction, but with a bigger uncertainty. Finally, there were the two plates from the Principe astrograph, shot through the clouds, with five blurry dumbbell-shaped stars on each. They were the worst quality of the lot. With only five stars, Eddington could not simply measure the images and solve an equation for the deflection. He had to engage in roundabout series of calculations: assume some amount of gravitational deflection, compute the other components contributing to the stars' displacements, and use those to recalculate the gravitational deflection, repeating the process until all the numbers were consistent. In such a manner he converged on a value of 1.61 seconds of arc for the gravitational deflection-very close to the Einsteinian prediction, especially when the rather large uncertainties were accounted for.
What, then, was the correct answer: 1.98, which was too high; 0.86, which was too low; or 1.61, which was just right, but unreliable? Was it an average of all three? Traditions and empires of the mind hung in the balance. The spread in the results should have been a big yellow caution sign that the experiment was flawed. Presumably there was only one right answer. Averaging the data from all three instruments, the philosophers and historians John Earmann and Clark Glymour have pointed out in a historical essay, would have led to an estimate of the deflection that was somewhere between the Newtonian value and the Einstein value, which was precisely what Eddington had reported to Lorentz in September. If Eddington wanted to exercise some judgment and keep only the best data—namely, that derived from the Sobral four-inch-then the answer would rule out general relativity.
As the American cosmologist Allan Sandage likes to say, quoting the British astronomer Sir Hermann Bondi, no experiment should be believed until it has been confirmed by theory. Bondi could have gotten that from Eddington. Eddington in 1919 already knew the truth: The truth was general relativity.
Eddington looked into the fuzzy forest of results and saw the trees leaning and he knew—or thought he knew—that there were only three choices for the amount of that lean. He threw out the Sobral astrograph, which had given the lowest number, and kept the other two. Their average was 1.75, right on the relativistic mark. General relativity was confirmed.
I can’t give page numbers because Google Books has plastered “Copyrighted material” over where the page numbers should be. This URL might get you to the text, though the search results when I just tried it don’t include the right page.