Is There a Fundamental Limit to Space and Time? The Planck Scale Explained

Video Description

This video explores the fundamental lower limits of space and time by considering what would happen if two electrons are squeezed closer and closer together. After discussing the ratio of electric and gravitational forces, Heisenberg's uncertainty principle is combined with Einstein's theory of special relativity to show that at very small distance scales the strength of gravity becomes comparable to the electrostatic force. It is shown that when the two electrons are squeezed to a distance equal to the Planck length, a black hole form, placing a fundamental lower limit on the distances that can be meaningfully probed. It is shown that the Planck length, mass and time can all be derived using dimensional analysis and by combining the fundamental constants of quantum mechanics, relativity and gravity. References: [1] Nima Arkani-Hamed. Space-time is doomed. Messenger lectures, Cornell, 2010. url: https://www.cornell.edu/video/nima-arkani-hamed- spacetime-is-doomed. [2] Arkani-Hamed, “The future of fundamental physics”, Daedalus, Vol. 141, No. 3, Science in the 21st Century (Summer 2012), pp. 53-66 (14 pages) [3] Hossenfelder, S. Minimal Length Scale Scenarios for Quantum Gravity. Living Rev. Relativ. 16, 2 (2013). https://doi.org/10.12942/lrr-2013-2 [4] Mead, C.A., “Possible Connection Between Gravitation and Fundamental Length”, Phys. Rev., 135, B849–B862 (1964). [5] R. J.Adler, “Six easy roads to the Planck scale” Am. J. Phys.78, 925–932 (2010). https://doi.org/10.1119/1.3439650 [6] Edward Witten. “Reflections on the Fate of Spacetime”. In: Physics Today 49.4 (1996), pp. 24–30. [7] David Gross. “Einstein and the Quest for a Unified Theory”. In: Einstein for the 21st Century: His Legacy in Science, Art, and Modern Culture. Ed. by Galison P. L., Holton G., and Schweber S. S. Princeton University Press, 2008, 287–297. V [8] Frank Wilczek; Scaling Mount Planck I: A View from the Bottom. Physics Today 1 June 2001; 54 (6): 12–13. https://doi.org/10.1063/1.1387576 [8] L. J. Garay, “Quantum gravity and minimum length,” Int. J. Mod. Phys. A 10 (Mar, 1994) 145–166, arXiv:9403008Wdqqwd. [9] Salecker, H. and Wigner, E.P., “Quantum limitations of the measurement of space-time distances”, Phys. Rev., 109, 571–577 (1958). [10] Ng, Y.J. and van Dam, H., “Limitation to quantum measurements of space-time distances”, Ann. N.Y. Acad. Sci., 755, 579–584 (1995). [arXiv:hep-th/9406110]. [11] Low, A.M., “The Chandrasekhar Limit: A simplified approach, Phys. Educ. 58 045008 [12] M Srednicky, Quantum Field Theory, Cambridge University Press, 2007. [13] Hobson, M., Efstathiou, G., & Lasenby, A. (2006). Frontmatter. In General Relativity: An Introduction for Physicists (pp. I-Vi). Cambridge: Cambridge University Press. [14] R. J. Adler, M. Bazin, and M. Schiffer, “Introduction to General Relativity,” (McGraw Hill, N. Y. 1965, second edition 1975) [15] Gorelik, G.E., “Matvei Bronstein and quantum gravity: 70th anniversary of the unsolved problem”, Phys. Usp., 48, 1039–1053 (2005). [16] Adler, R.J. and Santiago, D.I., “On gravity and the uncertainty principle”, Mod. Phys. Lett. A, 14, 1371 (1999). [DOI], [arXiv:gr-qc/9904026]. [17] Planck,M.,“Ueber irreversible Strahlungsvorgänge”,Ann.Phys.(Berlin),1,69(1900). [18] Scardigli, F., “Generalised uncertainty principle in quantum gravity from micro-black hole gedanken experiment”, Physics Letters B, Volume 452, Issues 1–2, 1999 [19] Oriti.D, “Approaches to Quantum Gravity”, 2009, Cambridge University Press, ISBN: 978-0-521-86045-1. A summary article of the video: https://iopscience.iop.org/article/10.1088/1361-6552/acfe54 You can help support this channel via the Physics Explained Patreon account: https://www.patreon.com/physicsexplained You can follow me on instagram: https://www.instagram.com/physics_explained_ig You can follow me on Twitter: https://twitter.com/PhysicsExplain1