The Number on the Door

In December 1958 Wolfgang Pauli was admitted to the Red Cross hospital in Zurich with a sudden, violent pain. He was given room 137. Pauli, who had spent much of his working life circling that number, asked a visitor whether he had noticed it. He died there on 15 December.

To most people 137 is a room, a bus route, a page. To physicists it is the denominator of the fine structure constant, the quantity that sets how strongly light and electrons pull on one another. Arnold Sommerfeld introduced it in 1916, trying to explain why lines in the hydrogen spectrum split. It has since been measured with extraordinary precision, and its inverse sits at roughly 137.036. Nobody knows why. Richard Feynman remarked that all good theorists put the number on their wall and worry about it.

What unsettles is not the size of the number but its consequence. Alpha is small, which makes electromagnetism weak enough to calculate and strong enough to hold atoms together. Push it far enough in either direction and, on most accounts, the chemistry that lets stars burn and molecules bind begins to fail. A modest number decides whether structure forms at all.

Israel is about to rediscover this. On 27 October voters will elect all 120 members of the 26th Knesset, and a government needs 61. The polls have refused to break the deadlock since the Knesset dissolved in July. A recent KAN survey had the two blocs tied at 52 seats each, while Channel 12 put the change bloc on 54, the coalition on 50 and the Arab parties on 12. Neither camp reaches 61 alone. The outcome turns on a small number both would rather not name.

That number is the Arab parties. For most of Israel’s history they have sat in the chamber but outside the sum. The one independent exception proved the rule. In June 2021 Mansour Abbas took Ra’am into the Bennett and Lapid government, the first time an independent Arab party had joined a governing coalition. Netanyahu had hoped for Ra’am’s support that spring too, until Ra’am and a partner on his right ruled each other out. The government that did form held the narrowest possible majority of 61 seats. It lasted a year. Its critics called that proof the bond could not hold. Its admirers called it proof the bond could form at all.

Physics has its own history of people who refused the number the universe handed them. In 1929 Arthur Eddington argued that the inverse of alpha could be obtained by pure deduction, and that it was exactly 136. When measurements came in closer to 137, he found a reason to add one. It earned him the nickname Sir Arthur Adding-One. Later measurements settled near 137.036, leaving both integers behind.

Israeli politics has its Eddingtons too. After the April 2019 election, Benjamin Netanyahu’s right wing bloc was counted at 65 seats, a comfortable majority on paper. The sum included the five seats of Avigdor Lieberman’s Yisrael Beiteinu. Lieberman refused to join over the Haredi draft, no government formed, and within weeks of being sworn in the Knesset voted to dissolve itself, the first time it had done so before a government was even formed. The theory had counted a seat that was never there. Four more elections followed in little over three years, each fought on the assumption that the arithmetic would eventually submit. It did not. It produced stalemates, a rotation agreement and finally a government resting on a party that few of its partners had counted in the sum when the campaign began.

The deeper problem with Eddington’s search only became clear after his death. He assumed there was a single number to find. There is not. Alpha changes with the energy at which it is measured. The vacuum around an electron seethes with fleeting pairs of particles that partly screen its charge, so from a distance the electron looks weaker than it is. Probe closer, at higher energy, and more of the screening falls away. At the scale of atoms the inverse is about 137. At the energy of the Z boson, one of the particles that carries the weak force, it is about 128. The famous number is not so much a law of nature as a reading taken from where we happen to stand.

Coalition arithmetic behaves the same way. Seen from the distance of a campaign, the Arab parties look faint, their weight screened by slogans about who is and is not a legitimate partner. Seen from inside a negotiating room, the screening falls away. In 2021 Ra’am had won just four seats. Without those four there was no Bennett government at all. The closer anyone gets to actually forming a coalition, the stronger the pull of the seats they spent the campaign discounting.

Where, then, does 137 come from? Most physicists now think the question has to be pushed back a level. Electromagnetism is not fundamental. It emerges from a deeper electroweak theory, and alpha is set by couplings beneath it. Run those couplings up to energies around a trillion times beyond anything our largest accelerator reaches, and the strengths of the forces come close to meeting at a single value. On this picture the forces began as one, and 137 is simply what one strand of that unity became after a very long descent into the cold world where atoms form.

Israel has its own high energy value. The Declaration of Independence in 1948 appealed directly to the state’s Arab inhabitants to help build it on the basis of full and equal citizenship, with “due representation in all its provisional and permanent institutions”. The Knesset is one of those institutions. That was the coupling at the founding scale, the moment of greatest political heat. More than seven decades later, the reading voters will take on 27 October is a dozen seats that both blocs treat as outside the sum. It is telling that Naftali Bennett now campaigns on a constitution in the spirit of that same declaration. Whether anyone means to follow the number back up is another question.

There is a Hebrew coda to the number. In gematria, which gives each letter a value, the word kabbalah, meaning that which is received, adds up to 137: qof 100, bet 2, lamed 30, heh 5. The Nobel laureate Leon Lederman observed that 137 “shows up naked all over the place”. The Hebrew word is apt. A constant is not chosen. It is received, and the only honest response is to build with it rather than against it.

That is the lesson the October count is likely to teach, whoever leads the larger bloc. The Arab parties’ dozen or so seats are not an anomaly to be explained away by adding one. They are part of the constant.

The strongest objection is not arithmetic but principle. Ra’am is the political arm of the southern branch of the Islamic Movement, and since 7 October many Jewish Israelis have found statements by other Arab politicians disqualifying. That objection deserves a hearing, not a sneer. But Israeli coalitions have long counted partners whose principles large parts of the electorate reject, from Haredi parties that resist the draft to a far right that others consider beyond the pale. The question has never been whether a partner is liked. It is whether its terms can be met without breaking the structure.

A government formed without them will be narrow, hostage to whichever faction can extract most for a single seat. A government formed with them will face the accusations that met Abbas, and must decide whether it can survive them.

None of this is sentiment. Coupling in physics is not affection but a measured strength of attraction, and as the running of alpha shows, that strength depends on how close the parties stand. Ra’am did not join in 2021 out of love for Bennett. It joined for budgets, for fighting crime in Arab towns, for housing, and said so openly. That is what a workable bond looks like: specific, transactional, strong enough to hold a structure and loose enough that neither side dissolves into the other.

Pauli never solved 137. Nor did Eddington, Feynman or anyone since. What they established is that the number is real, that it governs whether atoms hold together, that its value depends on where you stand, and that wishing it rounder changes nothing.

Room 137 was cleared after Pauli died. Whatever he had with him went elsewhere. The number stayed on the door. When the new Knesset sits this autumn, whoever gathers 61 will find the same thing waiting: not a room full of the people they wanted, but a number they did not choose.