Noether's theorems/History/The long neglect

It is generally said that Noether's paper went largely unused in physics for some decades after 1918. This page states what is actually established about that, which is less than the claim.

What is not established

No citation trace of the 1918 paper across the interval was performed for this volume. The question of how often, by whom, and in what connection the paper was cited between 1918 and the middle of the century is open, and nothing below should be read as answering it.

One nearby figure exists and is easy to misuse. Bessel-Hagen's 1921 paper, which applies Noether's theorems to electrodynamics, drew its first proper citation in 1934 and few afterwards for twenty years. That is a fact about his paper. It is not a fact about hers, and transferring it would be an error of exactly the kind this volume marks elsewhere.

What the secondary literature proposes

Several explanations circulate. They are recorded here as claims, with no verdict, because none has been checked against a citation record.

The paper appeared in a mathematics journal, in the idiom of the formal calculus of variations and Lie group theory. A physicist looking for a result about conservation laws would not have found it easily and might not have read it through if he had.

Its most famous consequences were not news. Energy, momentum and angular momentum were already known to be conserved. A theorem whose visible output is results already in hand looks, from a distance, like a re-derivation.

The physics that needed the second theorem did not yet exist. Gauge theories with non-abelian structure were built in the 1950s. Before them, the only theory whose energy relations were degenerate in the way the second theorem describes was general relativity, and interest in that particular question subsided in the early 1920s once it became clear no local answer was coming.

Noether herself did not return to the subject. She turned to abstract algebra and the work she is chiefly known for, and left no later exposition of the 1918 paper to point readers toward it.

The paper had no accessible translation. The first English version appeared in 1971.

Two cautions about the claim itself

Neglect is a comparative word and the comparison is usually left out. Neglected by physicists, or by mathematicians? The variational-calculus literature is not obviously the same story as the physics literature, and the usual account collapses them.

"Unused" is not "unknown". Hilbert cited her by name in his 1924 consolidated reprint and credited her with the general proof. Klein's collected works, published in 1921, carry a footnote stating both her theorems. Pauli's relativity article of the same period is in the same milieu. Whatever the citation count says, the people who had asked the question knew who had answered it. A claim of neglect has to be reconciled with that.

What would close this

A citation trace of Invariante Variationsprobleme across 1918 to 1960, separated by discipline, and read against the reprint history — the 1921 Klein collected works, the 1924 Hilbert reprint, the 1983 Noether collected papers. Until that exists, the verdict here is UNCOMPUTED, and the reason is that the work has not been done, not that it cannot be.

Provenance: this page contains no verbatim quotation and asserts no citation count for Noether's paper. The proposed explanations are recorded from the secondary literature as claims. See Sources.