The Planck scale: Is there a fundamental limit to space and time?

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:

[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)
[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).
[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] 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.

[ryancampbell]

There are a lot of other great physics channels out there that go into the larger and theoretical concepts of physics, but few that go into the math in such a clear and digestible way!

[hkhj]

YouTube is an amazing gift of humanity

[EastingAndNorthing]

Deriving the Planck length from the fundamental units blew my mind!

[Aelov]

I'm not the smartest person in the world, but I do understand physics at least. This is the first video that described WHY the planck length is the planck length in a meaningful way that I could understand. It also helps me visualize why planck time is the same way.

[EngRMP]

OMG, not only is your grasp of physics impressive... but your ability to describe it and paint such a rich picture of the universe is incredible.

[milesakic]

One of the rare physics channels that gives us the whole mathematical background while most of them are just random spawnage of fancy words that even the owner fails to understand. Even though I almost knew all of this, it was fun seeing it again and having it sistemized. Also, it made me fully understand what's the task of quantum gravity and what kind of challenges are there for the new generations of scientists and engineers. Great work !

[jakeklier]

A year of college physics in just under 30 minutes. Understanding how these constants are related to each other gives me inner peace.

[rogerforsythe]

Fifty years of not understanding, 15 minutes into this video and it is crystal clear. Astonishing.

[jimcarpenter]

Hands down the clearest, most vivid description of the subject I’ve ever seen. Well done!

[Badmanxl]

It's refreshing to learn something that's not political religious or about entertainment this is one channel I would like to support.

[jayaramanganapathi]

Drawing out Plancks constants using 2 different routes was great. This lays them down in the minds more firmly.

[sadsam]

A lot of other physics channels, programs, and documentaries always show how beautiful and connect our world is, but without really explaining how we came to those conclusions, or even proving it, in a more formal manner. However, this video actually shows, very precisely how ACTUALLY all those variables are tied together to their most fundamental level.
Although I only managed to grasp the math on a more surface level, it really inspired me to learn more about math, and maybe understand this at its fullest!
Thanks!

[davidlisovtsev]

every time this man says "big G" I'm forced to imagine a giant gangsta G extorting the other letters.

[aussieozborn]

Mate, your method of description and explanation, tone, inflection and delivery style is second to none. Some of the more frenetic formulae gets a bit lost on undereducated me, but you make it way easier than all others. Bravo, good sir!
Oh, and buy my next album...a geezer would hafta be bloomin' radio to not shell out couple of Ayrtons....

[underpowerjet]

19:10 blew my mind. I knew theoretically anything could be squeezed down small enough to create a blackhole. But, showing it through calculations what the lower bound of the mass, equavalent to that a flee egg, squeezed down to 10^-35 meters could create it as well. That is just so facinating!
Please make more videos like this! This was awesome!

[hrperformance]

The whole video was awesome but I really appreciated the addition of the final quote.

[TheNameOfJesus]

I stopped the video at 23:45 and solved the same problem that Planck must have solved. And it was surprisingly easy. I feel some affinity with Planck now. It was simple arithmetic. We hold these guys as geniuses and all they did was solve a simple math problem that anyone in grade school should be able to solve. I guess what makes Planck a genius is that he found a question worth asking.

[maxsantana]

This video gave me the chills because it was well put together. Just like when you hear a good song. Math is beautiful.

[iwalk]

Honestly the best physics channel out there - I cannot be more grateful that you have returned!

[SerbanOprescu]

I never thought such concepts could be explained in such an easy to understand way. This video is astonishing.