The origin of a bizarre quantum phenomenon

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In this journey towards Heisenberg's matrix formulation of quantum mechanics, here I present the origin of zero-point energy, one of the most bizarre predictions of quantum theory. Also known as vacuum energy, zero-point energy is a consequence of Heisenberg's uncertainty principle; however, its origin is a wrong theory and a wrong plot.

Erratum: at 8:48 instead of "ln(1-p)^n" it should say "ln [p(1-p)^n]." This is just a typo, the rest of the calculation is correct. Thanks to ‪@Miguel_Noether‬, ‪@charlottedarroch‬ and ‪@martindimov3494‬ for reporting this.


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[References]

∘ M. Planck, "Ueber eine Verbesserung der Wienschen Spectralgleichung," Verh. Dtsch. Phys. Ges. 2:202 (1900)
∘ M. Planck, "Eine neue Strahlungshypothese," Verh. Dtsch. Phys. Ges. 13:138 (1911)
∘ M. Planck, "Über die Begründung des Gesetzes der schwarzen Strahlung," Ann. Phys. 37 (4): 642 (1912)
∘ M. Planck, "Loi du Rayonnement Noir," Proceedings of the First Solvay Conference in Physics, p.93 (1912)
∘ H. S. Kragh and J. M. Overduin, "The Weight of the Vacuum," SpringerBriefs in Physics (2014)
∘ A. Einstein and O. Stern, "Einige Argumente für die Annahme einer molekularen Agitation beim absoluten Nullpunkt," Ann. Phys. 40 551 (1913)
∘ A. Eucken, "Die Molekularwärme des Wasserstoffs bei tiefen Temperaturen," Verh. Dtsch. Phys. Ges., Nr. 4:141 (1912)
∘ P. Ehrenfest, "Bemerkung betreffs der spezifischen Wärme zweiatoniger Gase," Verh. Dtsch. Phys. Ges. 15, 451 (1913)
∘ D. M. Dennison, "The Rotation of Molecules," Phys. Rev. 28, 318 (1925)
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[Credits]

Max Planck by G.G. Bain, public domain
Thermally agitated molecule, no author under CC BY-SA 3.0
OAM vs angle states animation by JozumBjada under CC BY-SA 4.0
Deutsche Physikalische Gesellschaft (DPG)
Second Solvay Conference (1913) by Institut International de Physique Solvay, public domain
Molecule motion by Mbrzeczek under CC BY-SA 4.0
Walther Nernst, public domain
Arnold Eucken, public domain
Werner Heisenberg by AIP
Bohr's letter requesting funding for Heisenberg, RE:source, Rockefeller Archive Center https://resource.rockarch.org/story/t...
Hummerbuden Helgoland by Dionysos1970 under CC BY-SA 4.0
Helgoland in 1945, San Diego Air and Space Museum


AIP: American Institute of Physics, Emilio Segrè Visual Archives
CC BY-SA 4.0 https://creativecommons.org/licenses/...