Uploads from Richard Behiel

Currently Playing: Electromagnetism as a Fifth Dimension (Kaluza-Klein)

This video explores how electromagnetism, when viewed from a gauge-theoretic perspective, looks eerily like the fingerprint of a fifth dimension. This is called the 5D Kaluza-Klein model. The video is based on the first part of the 1987 paper “Kaluza-Klein theories” by David Bailin and Alex Love. The link below had a free PDF when I started working on the video, but as I’m uploading now, it looks like it has gone behind a paywall… so that’s not great. *However*, the video still stands on its own, and does not require you to read the paper, the paper is just there for reference. You also might be able to access it for free with a university email if you’re a student or professor, and hopefully the free PDF will be available again someday (if so, print it!). https://iopscience.iop.org/article/10.1088/0034-4885/50/9/001 This video also cites the books “Introduction to Elementary Particles” by David Griffiths, “Gauge Theories of the Strong, Weak, and Electromagnetic Interactions by Chris Quigg, and “A Relativist’s Toolkit” by Eric Poisson. Those references provide context and credibility, but as with the paper, the video can stand on its own even if you don’t have those. I do always recommend Griffiths though, fantastic book. Shoutout also to Conner for composing the piano piece “Fifth Dimension”! :) Check him out on SoundCloud, his username is OKCP. https://m.soundcloud.com/okcp If you enjoyed the video, please consider supporting this channel, for access to Python animation codes, video note PDFs, and your name in the credits: https://www.patreon.com/RichardBehiel/ Thank you to everyone who has been supporting my channel on Patreon, and enabling me to make these videos. Timestamps: 00:00 Video Intro 12:45 Video Outline & Books Cited 25:05 Distance Formula to Metric Tensor 44:34 Comparing g_munu and g_AB 50:27 The Mostly Wild 5D Metric Tensor 1:00:41 Dissecting g_AB into g_munu, B_mu, and Phi 1:18:18 Interpreting g_munu and B_mu, Reassembling g_AB 1:26:18 Defining A_mu, a U(1) Gauge Field in the Metric Tensor 1:30:50 Example of Calculating a Weird Metric (Oblique Coords.) 1:41:13 "The Tube" Demonstration that A_mu is a U(1) Gauge Field 1:54:04 "Part 1.5", Optional Rigorous Transformation Calculations 2:20:31 Part 1 Conclusion 2:24:12 Introduction to "The Miracle" 2:33:10 A Miraculous Proof 2:49:03 A Miraculous Curvature Formula 3:11:47 Quantization from Periodicity 3:17:01 Klein-Gordon Eq., Quick Overview 3:35:56 Mass Quantization 4:00:08 Charge Quantization 4:16:22 What is General Covariance? 4:23:31 The Meditation 4:39:16 Summary of the Flaws 4:52:30 The Two Main Flaws 5:05:26 Concluding Thoughts 5:11:18 Patreon Credits