Summary

I.       Casimir force in QED:       

 High precision experimental precision achieved with scanning probes                        

       Applications require control of this force, and its shape dependence

II.    Repulsion/Levitation?

 Metamaterials, las invisibility cloaks:     

 Geometry: 

III.   Scattering approach relates Casimir forces for multiple objects to scatterings from each 

 Exactly solvable shapes: (sphere, cylinder, knife-edge, wedge, cone, ...)

(Analytical results for sharp shapes; strong temperature dependence; ...)         

IV.   Earnshaw's theorem:             

  No levitation is possible with electrostatic interactions:  

 No levitation is possible with Casimir forces with dielectric composites: 

V.   Out of equilibrium levitation is possible:

 Classical radiation pressure:                                

                  Non-classical (near field) counterpart

VI.   Dynamic phenomena: Friction of vacuum!

 A rotating dielectric will slow down in vacuum:                

Acknowledgments

Thosten Emig, Noah Graham, Robert Jaffe

Jamal Rahi, Matthias Krueger

Mohammad Maghrebi, Vlad Golyk

M. Hertzberg, A. Scardicchio, A. Rodriguez, S. Johnson, U. Mohideen, R. Zandi

Outline Casimir force Repulsion? Scattering approach Earnshaw's theorem Out of equilibrium Dynamic phenomena Summary