Why neutrino oscillations proved neutrinos have mass — contradicting the original Standard Model

How the Higgs mechanism works — spontaneous breaking of electroweak symmetry gives W and Z bosons their mass

Higgs field's non-zero vacuum expectation value breaks symmetry, endowing W and Z bosons with mass

What the Goldstone theorem says — every spontaneously broken continuous symmetry produces a massless boson

Goldstone theorem: Spontaneously broken continuous symmetries yield massless Goldstone bosons

What the Standard Model's particle content is — 6 quarks, 6 leptons, 4 gauge bosons, 1 Higgs

Standard Model: 24 fundamental particles (6 quarks, 6 leptons, 4 gauge bosons, 1 Higgs)

What the renormalization group does — explains how physics changes with the scale of observation

Renormalization group describes scale-dependent behavior in physical systems

Why nothing with mass can reach the speed of light — the Lorentz factor γ diverges as v approaches c

As velocity v approaches c, Lorentz factor γ increases, preventing massive objects from reaching light speed

What the Higgs field does — permeates all space, gives mass to fundamental particles through coupling

The Higgs field permeates space, endowing particles with mass via interaction