Einstein's (small) mistake

Breakthrough Starshot plans to accelerate a gram-mass spacecraft up to one-fifth the speed of light to reach nearby stars in our lifetimes. In a recent video (https://youtu.be/Ksb6Vh0BT_E), I discussed some work I'd taken on calculating how the speed of the spacecraft (a light sail) changes as one shines an intense laser beam on it. It turns out my equations differ with the predictions of the Breakthrough team, and indeed just about everyone whose worked on this problem all the way to Einstein himself, who treated it as an example calculation for relativity. Remarkably, there does appear to be a small mistake in this example calculation (but not relativity itself) and in this video I explain how I came across it, why I'm convinced it's right and the nature of serendipitous discovery.::More about this Video::► The paper (now accepted for publication) is available here- David Kipping (2017), "Relativistic Light Sails": https://arxiv.org/abs/1704.04310► Asst Prof David Kipping homepage: www.davidkipping.com► Philip Lubin (2016), "A Roadmap to Interstellar Flight": https://arxiv.org/abs/1604.01356► Kulkarni, Lubin & Zhang (2016), "Relativistic solutions to directed energy": http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=2555764► Arthur Compton (1923), "A Quantum Theory of the Scattering of X-rays by Light Elements": https://journals.aps.org/pr/abstract/10.1103/PhysRev.21.483► Albert Einstein (1905), "Zur Elektrodynamik bewegter Körper": http://onlinelibrary.wiley.com/doi/10.1002/andp.19053221004/abstract► Breakthrough Initiatives website: https://breakthroughinitiatives.org► Cool Worlds Lab website: http://coolworlds.astro.columbia.edu► Columbia University Department of Astronomy: http://www.astro.columbia.edu► Background music by MelodySheep "Secrets of the Stars": https://www.youtube.com/watch?v=BuxFXHircaI::Playlists For Channel::Latest Cool Worlds Videos ► http://bit.ly/NewCoolWorldsCool Worlds Research ► http://bit.ly/CoolWorldsResearchGuest Videos ► http://bit.ly/CoolWorldsGuestsQ&A Videos ► http://bit.ly/CoolWorldsQAScience of TV/Film ► http://bit.ly/ScienceMovies::Follow us::SUBSCRIBE to the channel http://bit.ly/CoolWorldsSubscribeCool Worlds Lab http://coolworlds.astro.columbia.eduTwitter https://twitter.com/david_kippingInstagram https://www.instagram.com/cool.worldsTHANKS FOR WATCHING!! ヅ Learn more about your ad choices. Visit megaphone.fm/adchoices