Historical research guide · 0365 · 2005
The Casimir Effect and the Quantum Vacuum
Robert L. Jaffe
In one minute
Robert Jaffe, of MIT’s Center for Theoretical Physics, wrote this short 2005 paper to correct one sentence that had spread through the cosmology literature: that the Casimir effect proves zero-point energy is real. The force itself is not in question — two conducting plates in vacuum do attract, and by 2005 the measurement was good to about one per cent. What Jaffe shows is that the same number comes out a second way, from ordinary quantum electrodynamics, by summing Feynman diagrams for the charges and currents in the plates themselves. Read that way the Casimir force is the relativistic, retarded van der Waals force between the plates, and it fades away as the fine-structure constant is turned down; the famous formula, which looks as though it depends on nothing but Planck’s constant, the speed of light and the gap, is the limit of infinite coupling. Jaffe is equally careful about what he has not shown, and says plainly that he expects zero-point energies to stay in the theory.
Connection
This is chapter 2’s precision rule, and the site holds it because the strong version of a claim is the one nobody can take away: the Casimir effect proves that the vacuum couples to matter and pushes on it, which is exactly what the chapter needs, and the separate question of a drawable reservoir belongs to chapter 6, where different experiments settle it. Jaffe also leaves the largest question wide open — whether zero-point energies gravitate and set the cosmological constant — and that open question is the research programme.
From the source
Casimir forces can be computed entirely from Feynman diagrams with external lines, that is from S-matrix elements, with no reference to the vacuum or its fluctuations; Schwinger gave such a derivation for a scalar field and Schwinger, DeRaad and Milton extended it to electromagnetism.Section: The Casimir effect without the vacuum; Equation 6
The Casimir force between plates is the relativistic, retarded van der Waals force between the charged particles in the metal, and like every other observable effect in quantum electrodynamics it vanishes as the fine structure constant goes to zero.Abstract; Introduction, bullet list, p. 3
The standard force law that appears to depend only on Planck’s constant, the speed of light and the separation is an asymptotic form, exact only in the limit where the fine structure constant is taken to infinity.Abstract; Section: The dependence of the Casimir effect on the fine structure constant
The perfect-conductor idealisation is adequate only when the fine structure constant is much larger than the electron mass times c divided by four pi times h-bar, the conduction-electron density and the square of the separation — about ten to the minus five for copper plates half a micron apart, which the physical value near one over 137 amply satisfies.Equations 4–5
In the exactly soluble one-dimensional scalar model the force vanishes quadratically as the coupling to the plates goes to zero, and only in the limit of infinite coupling does the material dependence disappear and the familiar boundary-condition answer emerge.Equations 7–9
Whether the zero-point energies of quantum fields contribute to the energy density of the vacuum, and so to the cosmological constant, is left open; Jaffe records that he doubts a consistent formulation of relativistic quantum mechanics without zero-point energies exists, and that condensates carrying energy appear at many scales in the Standard Model regardless.Conclusion
The way in
https://arxiv.org/abs/hep-th/0503158How to cite it
Robert L. Jaffe (2005) The Casimir Effect and the Quantum Vacuum doi:10.1103/PhysRevD.72.021301