Did you know that Einstein's most important equation isn't E=mc^2? Find out all about his equation that expresses how spacetime curves, with Sean Carroll. Buy Sean's book here: https://geni.us/AIAOUHn YouTube channel members can watch the Q&A for this lecture here: https://www.youtube.com/watch?v=sO5adbV_mu8 Become one of our YouTube members for early, ad-free access to our videos, and other perks: null This lecture was recorded at the Ri on Monday 14 August 2023. 00:00 Einstein’s most important equation 3:37 Why Newton’s equations are so important 9:30 The two kinds of relativity 12:53 Why is it the geometry of spacetime that matters? 16:37 The principle of equivalence 18:39 Types of non-Euclidean geometry 26:26 The Metric Tensor and equations 32:22 Interstellar and time and space twisting 33:32 The Riemann tensor 37:45 A physical theory of gravity 43:28 How to solve Einstein’s equation 47:50 Using the equation to make predictions 51:05 How its been used to find black holes The real Einstein's Equation is part of general relativity, which relates the curvature of spacetime to the mass and energy distributed within it. Sean explains why the geometry of spacetime has anything to do with gravity, and how this famous equation expresses the way that spacetime curves. Sean Carroll is Homewood Professor of natural philosophy at Johns Hopkins University. He won the Royal Society Winton Prize for his book about the search for the elusive Higgs boson, The Particle at the End of the Universe, and The Big Picture was an international bestseller. His most recent book is Something Deeply Hidden. He lives in Baltimore. Copies of Sean's latest book, 'The Biggest Ideas in the Universe 1: Space, Time and Motion', are available from Amazon and all good bookstores. The Ri is on Twitter: http://twitter.com/ri_science and Facebook: http://www.facebook.com/royalinstitution and TikTok: https://www.tiktok.com/@ri_science Listen to the Ri podcast: https://podcasters.spotify.com/pod/show/ri-science-podcast Our editorial policy: https://www.rigb.org/editing-ri-talks-and-moderating-comments Subscribe for the latest science videos: http://bit.ly/RiNewsletter Product links on this page may be affiliate links which means it won't cost you any extra but we may earn a small commission if you decide to purchase through the link.