In this video, we'll unify special relativity and quantum mechanics, to derive the beautiful Klein-Gordon equation! Then we'll explore some of its properties, to see what it can (and can't) tell us about the nature of things. This is part of a video series that's building toward an exploration of the Dirac equation, and then a triumphant return to the hydrogen atom. Thanks for checking out this video, and if you are so inclined, please consider joining my Patreon, for full access to the slides from these videos, and additional notes and links to supplemental materials. I'll also be on there to answer any questions you might have about physics, math, and life, and your input will help guide the future direction of this channel. All support is greatly appreciated. https://www.patreon.com/RichardBehiel Chapters: 0:00 Intro 1:40 Deriving the KG Equation 7:24 Four-Momentum Eigenstates 12:38 Superposition 14:36 KG vs Schrödinger 16:48 Group Velocity & c Speed Limit 23:16 Fourier Transforms & Antimatter 31:01 The 2nd-Order-in-Time Problem 33:15 Probability Density & Current 39:55 The Mystery of Spin 42:27 Concluding Remarks by Paul Dirac #physics #math #quantum #relativity