The Eddington limit, i.e. the maximum luminosity that can be obtained by accretion, is named after him.

**Eddington and general relativity**

Eddington was once asked by a journalist whether it was true that only three people understood general relativity. Of course, Eddington realized that such a statement was just another manifestation of journalistic stupidity but he answered with his famous question: "And who is the third?" :-)

Eddington, one of the most important early promoters of general relativity, made Einstein famous in 1919. His expedition confirmed Einstein's prediction that the light bending has to be twice as strong as Newton would have expected if he had assumed that light was a stream of massive particles moving at the light speed and influenced by Newton's gravitational force.

It seems rather likely today that Eddington's confirmation was a case of scientific misconduct. His accuracy couldn't have been good enough to make a decision. Nevertheless, the media were already powerful back in 1919. The London Times announced a "revolution in physics" on their title page. Masses started to adopt general relativity. Fortunately, general relativity was correct. But Einstein's remarkable intuition about classical physics was a more solid sociological explanation why it was correct than the journalists' belief in Eddington's statements.

**Eddington's observation was overhyped**

I find this phase transition irrational. Every good

*theoretical*physicist who was interested in gravity and special relativity had to know back in 1915-1916 that general relativity was almost certainly the right theory of gravity because it was the only plausible theory of gravity at its level of complexity that agreed with special relativity as well as the equivalence principle. Moreover, it correctly postdicted the precession of Mercury's perihelion.

On the other hand, even if Eddington's measurement were correct, it wouldn't have been a terribly accurate and complete new proof of Einstein's theory of gravity. Those who didn't want to rely on theoretical arguments couldn't have been satisfied either. Eddington's experiment was just an

*inaccurate*measurement of

*one ratio*whose value should be two. Precision tests of general relativity only started with the Pound-Rebka experiment in 1959, four years after Einstein's death.

Today, the effects of general relativity are important for GPS and a few other satellites but the experimental impact of this beautiful and essential theory remains limited.

**Eddington as a crackpot**

For pedagogical purposes, I want to end up with a discussion of Eddington's research in the 1930s. David Gross describes his numerological talk from 1938 on page 7 of his paper dedicated to Oskar Klein. If you read the text below, you might agree that Eddington could instantly shake his hand with Quantoken, Nigel Cook, and their intellectual peers.

Eddington started with the key assumption that the fine structure constant was exactly 1/136. Today, we know it is 1/137.036... so he only had a 1 percent error. In fact, Eddington himself knew that it was close to 1/137. See this paper published on the New Year 1929. He explains that even though the measured value was 1/137.1, the right number - by quantum mechanics and relativity - should be equal to 1/136 because 136 is the number of elements of a symmetric 16 x 16 matrix. ;-) In his 1930 paper, he briefly corrected his prediction from 1/136 to 1/137. ;-)

But that was just the beginning. In 1931, he applied the "cosmical constant" on protons. And in 1934 a 136-based quadratic equation for all elementary particles (rederived in 1940) followed. Later he used that number to deduce everything else about the Universe. The number of particles in the Universe was

*inevitably*"2 x 136 x 2^{256}" while the radius of the Universe

*was*1.23410 x 10^{25} meters.

Because Eddington was very popular with the media (see e.g. page 46 i.e. 6/22 here), something like Carl Sagan, he just assumed that the audience believed this crap. Just to be sure: it is very clear that there exists absolutely no rational or scientific reason why the fine structure constant or the number of particles or the radius of the Universe should be "simple numbers" and the latter two concepts can't even be properly defined, especially because they are time-dependent and depend on the definition of "now".

To make the things worse, the 1938 talk wasn't called "Intriguing numerological speculations" or anything like that. Instead, it was called "The cosmological applications of the theory of quanta." Wow! He was just like a person paid as a physicist who draws 30 different and random octopi and calls his painting "Quantum gravity and the standard model." ;-)

After Eddington's talk, his approach to all parts of physics including quantum mechanics and relativity was criticized by Bohr, Fowler, Gamow, Kramers, von Neumann, Rosenfeld, and Wigner. Kramers' criticism was the longest one and he was awarded a medal by Gamow, on behalf of all the young participants, for his service to the community. The medal reads "For the masterpiece of polite scolding."

Meanwhile, if you want to be really entertained, Eddington's science was revived by a scientist in Saudi Arabia. M.S. El Naschie wrote "On D. Gross’ criticism of S. Eddington and an exact calculation of alpha=1/137" in 2007. It is so much fun that I copy the full abstract here:

While Sir Arthur Stanley Eddington attempts to derive alpha=1/137 mathematically may be considered to be a stretch, as correctly noted by Nobel laureate David Gross, in the meantime such a theoretical derivation is possible and feasible. In the present work, we show that the inverse electromagnetic fine structure constant may be derived in various ways using a combination of the Green, Shwarz, Witten and Gross string theory and the ‘t Hooft-Susskind and Maldacena holographic principles.Besides the 136 science, you must also learn about "Shwarz" [sic], "Gross string theory", whatever it exactly is, and double the number of holographic principles. But once you do it, you may derive Eddington's numerology from string theory. Some people are simply loons and Elsevier Ltd happily prints them in peer-reviewed journals.

If you summarize Eddington's contributions, it might be fair to say that he gave physics exactly as many good gifts as bad gifts. After all, this is the average score for the people who are popular with the media.

And that's the memo.

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