1 / 18

The Casimir Effect

The Casimir Effect. River Snively. What I’m going to talk about (in reverse). The Casimir force Quantizing the electromagnetic field A non-Field Theoretic Casimir force Review of zero-point energy in quantum mechanics. Zero-point Energy (Quick Review). Quantum harmonic oscillator:

Download Presentation

The Casimir Effect

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. The Casimir Effect River Snively

  2. What I’m going to talk about (in reverse) • The Casimir force • Quantizing the electromagnetic field • A non-Field Theoretic Casimir force • Review of zero-point energy in quantum mechanics

  3. Zero-point Energy (Quick Review) • Quantum harmonic oscillator: = ћω(n + ½)\ • Ground state energy: • Don’t like this? Remove it by shifting H.

  4. Tunable QHO (A thought experiment) • Changing frequency changes energy minimum • Therefore, turning the knob takes work • This would’ve been unnatural if we’d shifted H

  5. Tunable QHO: reality check How hard is it to turn the knob? • Say ∆ω with one degree turn is 1017 s-1 • Then ∆E with one degree turn is 33 eV • So torque is 5·10-18 Nm/degree • Conclusion: tough to measure ZPE with a single oscillator.

  6. If only…

  7. A New Harmonic Oscillator: The EM Field • In the Coulomb gauge, vector potential satisfies wave equation • Expanding A in plane waves, Coulomb gauge says Ak is perpendicular to k • The other two components: wave equation requires they be SHOs with ω = kc • Main hypothesis of QED: Those harmonic oscillators are “quantum” For much clearer explanation of all this see Feynman and Hibbs, Quantum Mechanics and Path Integrals, ch. 9

  8. Max Planck

  9. Field Quantization: Consequences • For each momentum mode k there are two oscillators, each with ω = kc • Excitations = photons! • Take another look at E = ћω(n + ½) • Zero point energy: Twice ½ћω, summed over all k’s: (infinite!)

  10. INFINITE VACUUM ENERGY • Electromagnetic zero-point energy of vacuum: E = 2Σk ½ ћc|k| • Crisis avoided if we just consider changes in energy • Similar thing: the self-energy of the classical electron

  11. How could we change the vacuum energy? • One thing we could do: (put it in a box) • Then, allowed k modes are nπ/L • Moving walls changes summed-over frequencies • More realistically, could confine between parallel plates…

  12. The Prototypical Casimir Set-up • Ideal conductors, area L2 • Separation a (a << L) • An attractive Force (Casimir, 1948): • First measurement: Sparnaay 1958, with 100% uncertainty.

  13. What’s so attractive about this force? • No α in sight (*) • F/A = (.013 dyne/cm2)a-4 (with a in microns) small but not unobservable (Compare: atmospheric pressure ≈ 106 dyne/cm2.) • Sometimes not attractive

  14. (excerpt)

  15. An alternative set-up • Sphere-plate Casimir Effect: Mohideen and Roy, 1998 • Verified Casimir at .1 to .9 micron separations to 1%

  16. Conclusion: we’ve seen that… • The Casimir effect can be explained by zero-point energy • The effect is large enough to observe experimentally (nowadays) • The Casimir effect is not inherently “quantum field theoretical,” just inherently “quantum.”

  17. Thank you…

  18. References • Hendrik Casimir, On the attraction between two perfectly conducting plates. Proc. Akad. Wet. Amsterdam (1948). • R. L. Jaffe, The Casimir Effect and the Quantum Vacuum, Phys. Rev. D 72, 021301 (2005). • M. J. Sparnaay, Measurements of attractive forces between flat plates, Physica 24, (1958). • S.K. Lamoreaux, Demonstration of the Casimir Force in the .6 to 6 µm Range, Phys. Rev. Lett. 78, 5 (1997).  • U. Mohideen & A. Roy, precision Measurement of the Casimir Force from.1 to .9 µm, Phys. Rev. Lett. 81, 21 (1998). • R.P. Feynman & A.R. Hibbs, Quantum Mechanics and Path Integrals • A. Zee, Quantum Field Theory in a Nutshell • F. S. Levin & D. A. Micha (editors), Long-Range Casimir Forces • V.M. Mostepanenko & N.N. Trunov, The Casimir Effect and its Applications

More Related