The Dirac Equation: The Most Important Equation You’ve Never Heard Of

Thanks to Brilliant for sponsoring this video! Try Brilliant free for 30 days and get 20% off an annual premium subscription by following the link 👉 https://brilliant.org/PhysicsExplained/ You can help support this channel via the Physics Explained Patreon account: https://www.patreon.com/physicsexplained What is the Dirac Equation, and why is it carved into the stone floor of Westminster Abbey, alongside the tomb of Isaac Newton? In this video, we explore the deep mathematical reasoning and physical insight that led Paul Dirac to one of the most revolutionary equations in modern physics. We begin by examining the foundations of quantum mechanics and the structure of Schrödinger’s equation, before turning to the challenge of incorporating special relativity into quantum theory. This leads us to the Klein-Gordon equation — an early attempt that, despite its elegance, fails to preserve a consistent probabilistic interpretation. From here, we follow Dirac’s search for an equation that is both fully relativistic and first-order in time, motivated by the belief that mathematics itself could reveal nature’s underlying structure. Along the way, we introduce spinors, matrix-valued operators, and the constraints they must satisfy, culminating in the Dirac Equation and its elegant covariant form. This is Part One of a two-part series. In Part Two, we’ll explore how this equation reshaped our understanding of matter — and led to one of the most astonishing predictions in all of physics: antimatter. You can follow me on instagram: https://www.instagram.com/physics_explained_ig You can follow me on X: https://twitter.com/PhysicsExplain1