Slide 1

The Casimir Effect River Snively

Slide 2

What Im 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

Slide 3

Zero-point Energy (Quick Review) Quantum harmonic oscillator: = (n + )\ Ground state energy: Dont like this? Remove it by shifting H.

Slide 4

Tunable QHO (A thought experiment) Changing frequency changes energy minimum Therefore, turning the knob takes work This wouldve been unnatural if wed shifted H

Slide 5

Tunable QHO: reality check How hard is it to turn the knob? Say with one degree turn is 10 17 s -1 Then E with one degree turn is 33 eV So torque is 510 -18 Nm/degree Conclusion: tough to measure ZPE with a single oscillator.

Slide 6

If only

Slide 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 A k is perpendicular to k The other two components: wave equation requires they be SHOs with = 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

Slide 8

Max Planck

Slide 9

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

Slide 10

Electromagnetic zero-point energy of vacuum: E = 2 k c|k| Crisis avoided if we just consider changes in energy Similar thing: the self-energy of the classical electron

Slide 11

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

Slide 12

The Prototypical Casimir Set-up Ideal conductors, area L 2 Separation a (a