The secrets of Einstein's unknown equation – with Sean Carroll

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Published 2023-11-02
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.

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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.

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All Comments (21)
  • The Q&A for Sean's talk is available exclusively for our YouTube members here: https://www.youtube.com/watch?v=sO5adbV_mu8&t=0s Despite our fancy name, we're actually a charity that relies on donations to keep going. If you sign up to become a Science Supporter on our YouTube channel, you'll be helping us connect more scientists with the public, so we can bring you more incredible lectures like this one. You can sign up here: youtube.com/channel/UCYeF244yNGuFefuFKqxIAXw/join
  • This man made advanced physics accessible to the masses. If there is something similar to the Nobel Prize for science communication then he truly deserves one.
  • @stephenhicks826
    I'm 70 year old retired Physics teacher and was mesmerised by Carroll's wonderful presentation. The best teachers have a way of bringing clarity and simplicity to very difficult concepts. Brilliant, thank-you.
  • @thomasdaniel100
    I suffered a brain injury a few years ago and it is sometimes difficult to understand simple concepts, nevermind complex concepts. Thank you Sean Carroll for simplifying subject matter for those of us who want to understand the science we love so much. Thank you RI for the same. I may not be able to do the math and I may never be an engineer again but this video makes me feel like im included again.
  • @peterspiker9960
    As I get older I find the admiration I used to have for my favourite musicians is fading (only a little) and I’m becoming more fascinated by what people like Sean M. Carroll have to teach me. I may be too old for out-and-out hero worship, but I am definitely a big fan of these big thinkers. Hooray for RI, Mindscape and Sean Carroll!
  • @daxramdac7194
    This was the best presentation I've seen on this subject. And I'm not at all surprised that it was given by Sean Carrol with his brilliant ways of explaining things, his clear voice, and keeping your attention. The historical context shown behind the equation, and the motivation behind its construction over time was not only fascinating, but so excellently and expertly presented, without having to go off on any tangents or use too many analogies. And without insulting the intelligence of the audience with things like "imagine the swing you played on as a kid" or "imagine the strings on a guitar", just straight build up of the logic behind going from the Newtonian formulation up to the final Einstein equation, and all the players involved along the way. Perfect.
  • Always fantastic to see a Sean Carroll lecture, especially at the RI. Day one of the membership has started well!
  • @gcewing
    Plot twist: After this lecture was over, the audience tried to leave the hall and found they were in a rocket ship far out in space accelerating at 1g.
  • @BikeArea
    You are fully blown away by this guy's rhetorical talent and the uninterrupted talk. He never stutters, hangs or uses filler words. :face-blue-smiling: By the way: Great to hear a german word he uses (Ansatz). 😀
  • @migfed
    This is clearly the next step: start explaining the math in a friendly way. Sean Carroll at his best. Thank you so much.
  • @myopenmind527
    One of the best communicators in science. I’ve never failed to be equally entertained and educated by listening to his talks.
  • @Chaobai
    I really like the way Sean Carroll presents all the scientific concepts. He always explains how they evolve over time and that really helps me understand how we get where we are in science for a certain topic. Most worthy membership I have ever had.
  • @miinyoo
    Sean is a great communicator and a sweetheart. I think equations are fun but they often look misleading largely for short hand reasons. Unpacking equations and looking at all the knobs hidden by symbols really is the only way to understand them. Having Sean break them open and show their inner working bits is an enormous help.
  • @erikfinnegan
    Prof. Carroll is the only science communicator who can pull off this feat of educating the general public about Maths. So vivid. So approachable.
  • @willemvdk4886
    Yes! A new Sean Carroll lecture! This man is such a good presenter and spokesperson for science.
  • @phillupson8561
    Always love a Sean Carroll lecture, just think without the Internet we'd have to smart enough to get into his class and I suspect many of us wouldn't make it, what a time to be alive.
  • Absolutely stunning. To be a master both of the subject AND of how to convey it is remarkable.
  • Fantastic talk as usual from Sean Carroll and his books are worth reading. Great content thanks RI
  • @IvanMorenoPlus
    Sean Carroll is a joy to read, but he is way funnier and more to the point in a lecture! Perhaps the best explanation of Einstein's field equations I have seen. Thank you!
  • @amritsharma5373
    What a great lecture. Thanks to Sean and the Royal Institute for making it accessible.