Fundamental elements of physical theories of systems of objects are examined. Consider the Newtonian mechanics, Maxwellian electrodynamics, relativistic mechanics, general relativity, and the Dirac theory of the electron. Each of these theories has specific differential equations whose solutions accurately describe the state and the time evolution of systems of particles that belong to the theory’s domain of validity. Well-known textbooks prove that these theories can be derived from the least action principle that applies to an appropriate Lagrangian or Lagrangian density. The Noether theorem proves that the Euler-Lagrange differential equations of these theories conserve energymomentum, angular momentum, and charge. The electroweak theory, which is a part of the Standard Model of particle physics, is a contradictory example. Although this theory is about 50 years old, textbooks still do not show the explicit form of its differential equations that describe the electromagnetic interactions of the W± particles. Hence, the electroweak theory fails to show that solutions of its missing differential equations fit experimental data. For this reason, the electroweak theory belongs to the set of physical ideas that are not even wrong.
Cottingham, W.N. and Greenwood, D.A. (2007) An Introduction to the Standard Model of Particle Physics. 2nd Edition, Cambridge University Press, Cambridge.
https://doi.org/10.1017/CBO9780511791406
