Bringing Noether’s theorem into introductory physics classes

The first theorem of Emmy Noether, published in 1918, is one of the most important discoveries of the early 20th century. The theorem, which relates symmetries found in the laws of physics to laws of conservation, serves as the foundation of the Standard Model of particle physics developed decades later.

In most introductory physics classes, however, Noether and her theorem are almost never mentioned. Eugene Hecht explored teaching the basics of Noether’s theorem in introductory physics classes by relating them to Newton’s laws.

“Noether’s work is on an advanced mathematical level, well beyond that of intro physics — this is likely why such a wonderful discovery has remained beyond the intro level until now,” said Hecht. “Traditionally we teach that energy, linear momentum, and angular momentum are each conserved, but we almost never go any deeper — why are these quantities conserved? Noether’s theorem provides a lovely answer, albeit a subtle one.”

While a full discussion of Noether’s theorem is beyond the scope of a typical introductory physics class, some elements of her work can be shown to students. Hecht focused on three conservation laws — energy, momentum, and angular momentum — and used conceptual language to discuss how they relate to symmetries of time, space, and orientation, respectively.

Hecht then examined Newton’s laws of motion within this context. While Newton would have had no knowledge of Noether’s theorem, Hecht demonstrated that the laws make implicit assumptions regarding symmetries and conservation laws that comport with Noether’s principles.

He hopes this approach will help students understand and appreciate the significance of Noether’s theorem much earlier in their physics education.

Source: “Noether’s theorem and newton’s laws,” by Eugene Hecht, The Physics Teacher (2026). The article can be accessed at https://doi.org/10.1119/5.0206210 .