Making Fun of Arthur Eddington

This is a great story, from John Barrow's book The Constants of Nature (recommended, if you like numbers).

Arthur Eddington was, of course, a great physicist. He had a command of both experimental and theoretical physics. He went to the middle of nowhere to measure the bending of starlight during a solar eclipse, thus verifying Einstein's prediction that masses bends spacetime. And he wrote a highly regarded book on general relativity, Mathematical Theory of Relativity.

But he also took a long detour into numerology that did not serve his reputation well. He claimed to have calculated the number of particles in the universe on a boat trip across the Atlantic. (He took it to be the mass of the universe divided by the mass of the proton, and then spent the long trip doing the long division.) In a 1939 lecture he stated this as follows:

"I believe there are 15 747 724 136 275 002 577 605 653 961 181 555 468 044 717 914 527 116 709 366 231 425 076 185 631 031 296 protons in the universe and the same number of electrons."

He also was obsessed with the number 137. He wasn't alone; the fine structure constant α = e²/ℏc is a dimensionless number, where e is the charge on the electron, h is Planck's constant, and c is the speed of light, and ℏ = h/2π. Being independent of any chosen measuring system, some think it holds some deep secret about the Universe -- and who knows, it just might. Today it's measured to be 1/137.036..., but for decades, before the experiments got precise, many speculated it was exactly equal to the inverse of the integer 137. If today the number 137 appears anywhere in the vicinity of n ≥ 2 physicists, glances will be exchanged and jokes will be made.

Eddington went pretty far afield with 137, and the related pure number given by the ratio of the masses of the proton to the electron (approximately 1840 in Eddington's time; 1836.153... today). Eddington tried to relate such numbers with some simple calculations based on reasoning that many saw as very ad hoc and downright comical. Some people decided to spoof him. G. Beck, Hans Bethe, and W. Riezler managed to get this paper published in the quite serious science journal Naturwissenschaften in 1931:

Remark on the Quantum Theory of Zero Temperature

We consider a hexagonal crystal lattice. The absolute zero of this is characterised by the condition that all degrees of freedom of the system freeze, that is all internal movements of the lattice cease. An exception to this is, of course, the motion of the electron in its Bohr orbit. According to Eddington each electron possesses 1/α degrees of freedom, where α is the Sommerfeld fine structure constant. Besides electrons, our crystal contains only protons, and the number of degrees of freedom for them is the same since, according to Dirac, a proton can be regarded as a hole in the electron gas. Thus, since one degree of freedom remains because of the orbital motion, in order to attain absolute zero we must remove from a substance 2/α - 1 degrees of freedom per neutron ( = 1 electron + 1 proton; since our crystal has to be electrically neutral overall). We obtain therefore for the zero temperature T_o

T_o = - (2/α - 1) Degrees.
Setting To = -273° we obtain for 1/α the value 137, which, within limits of error, agrees completely with the value obtained in an independent way. One can easily convince oneself that our result is independent of the special choice of crystal structure.

Cambridge. 10 December 1930

G Beck, H Bethe, W Riezler

If you know just a little physics, this is hilarious.

Better yet, Riezler was asked to give a seminar on the paper in Munich at Sommerfeld's weekly physics seminar! Eddinigton was not amused, nor was the journal's editor Herr Berliner. He published this erratum on March 6, 1932:

'The Note by G. Beck, H. Bethe and W. Riezler, published in the 9 January issue of this journal, was not meant to be taken seriously. It was intended to characterise a certain class of papers in theoretical physics of recent years which are purely speculative and based on spurious numerical arguments. In a letter received by the editors from these gentlemen they express regret that the formulation they gave this idea was suited to produce misunderstandings.'

Those guys sure did seem to know how to have fun.