The thermal Casimir force has nothing to do with Lifshitz theory

July 13, 2012 - PRLog -- Background
Recently, the thermal Casimir force [1] in the gap between neutral surfaces at ambient temperature was claimed measured for the first time at Yale. The thermal Casimir force differs from the ZPE force proposed in 1948 by Casimir who extended the ZPE of quantum mechanics to the field. ZPE stands for zero point energy.  See http://arxiv.org/abs/1011.5219

In 1955, Lifshitz [2] predicted the existence of the thermal Casimir force. Like Casimir, Lifshitz only considered the force between neutral plates. The thermal Casimir forces derived with Lifshitz theory are the Drude and Plasma models having different dielectric properties for the plate materials.
However, the Yale experiment showed significant electrostatic forces that had to be removed to obtain what was thought to be the real thermal Casimir force. To compensate for the unwanted electrostatic forces, a minimizing potential was applied by servo-control during the experiment. For large gaps d, the thermal Casimir force was found to decrease by 1/d². However, for small gaps the force decreased by 1/d⁴ suggesting the affirmation of ZPE Casimir force. for perfect mirrors. In large gaps, the ZPE Casimir force is far smaller than the thermal Casimir force, and therefore the researchers assumed the higher than expected measured force was the thermal and not the ZPE Casmir force.  However, the force produced by the servo in removing the unwanted electrostatic force was not considered.

Problem
Lifshitz theory for the thermal Casimir force does not predict the charging of neutral surfaces separated from each other by gaps. Similarly, charging of neutral plates is not predicted in Casimir’s theory of the ZPE Casimir force. Since 1948, however, Casimir experiments including MEMS and semiconductors in photolithography unequivocally show charge is created upon bringing otherwise neutral surfaces close to each other.

Given that Casimir and Lifshitz theories cannot explain the charge created in the Yale experiment, a theoretical basis is not available to assure the force being measured is the sought after thermal Casimir force, and not the force generated by the servo in minimizing the potential to compensate for the electrostatic charge created in the experiment.

Grenoble Experiment
Subsequent to the Yale experiment, the thermal Casimir force was measured [3] at 4.2 K in the Grenoble experiment. The AFM tests showed Lifshitz theory to predict 50% lower thermal Casimir force than measured. AFM stands for atomic force microscope.Like the Yale experiment at ambient temperature, significant charge was created that is not included in Lifshitz theory. Absent a theory that predicts charge creation in submicron gaps between neutral surfaces, the 50% discrepancy between Lifshitz theory and experiment cannot be explained. Like the Yale experiment, the servo-controlled force was not considered.

QED Induced Electrostatic Force
The QED induced electrostatic force is proposed to explain the thermal Casimir force in the Yale and Grenoble experiments. QED stands for quantum electrodynamics. The QED force like Lifshitz theory has a thermal origin, but differs in that it is based on the thermal kT energy of atoms in the gap surfaces. Here k stands for Boltzmann constant and T for absolute temperature.

The QED force is the consequence of inducing the thermal kT energy of atoms in the plate surfaces to create photons that charge the plates by the photoelectric effect. The QED photons have Planck energy E = hc/2d, where h is Planck’s constant and c the speed of light. For gold surfaces, the quantum yield requires QED photons having energy > 5 eV, and therefore charging may only occur for gaps d < 0.2 microns. For a detailed description of the QED electrostatic force, see “The QED Induced Electrostatic Force” at http://www.nanoqed.org/, 2012.  

Discussion
In correcting for the unwanted electrostatic forces, both Yale and Grenoble experiments used a servo to impose a voltage to minimize the potential across the gap during force measurements. In this way, it was thought the neutral thermal Casimir force alone would survive to be measured. However, the QED photons created at gaps d < 0.2 microns have high Planck energy leaving residual charges trapped beneath the surface that cannot be removed by minimizing potentials of a few 100 mV. Ibid    

Yale  The Yale experiment at 300 K is similar to the Grenoble experiment in that the unwanted electrostatic forces are compensated by servo-control of the minimizing potential. What was thought to be the thermal Casimir force is in fact the QED force. The controversy whether the Drude or Plasma force is the correct thermal Casimir force is resolved – neither is.  Lifshitz theory that cannot predict charge in otherwise neutral surfaces simply is not applicable to the derivation of the thermal Casimir force. Ibid  

Crenoble  In the Grenoble experiment, the QED force for Au-Au surfaces measured at 4.2 K is shown in the thumbnail. The data depicted as a dashed red line is coincident with the QED force but is displaced downward for clarity. The classical electrostatic 1/d² force is shown as a green solid curve. The QED force is coincident with the 1/d⁴ curve for d < 600 nm, but for clarity is only shown for d > 700 nm as a solid red line. At large gaps d > 700 nm, the QED force produced under servo-control is higher than the classical electrostatics force. Hence, what is thought to be the thermal Casimir force is actually the QED force Ibid      

Conclusions
1. The thermal Casimir force derived with Lifshitz theory does not create charge upon bringing neutral surfaces close to each other. The controversy whether the Drude and Plasma models is correct is dwarfed by the dominance of the QED electrostatic force.

2. Servo-control of removing unwanted electrostatic forces creates the QED force that follows the 1/d² law at large gaps changing to 1/d⁴ law at small gaps. However, the 1/d⁴ behavior is the consequence of the servo-control having nothing to do with Casimir's 1/d⁴ force law for perfect mirrors by the field ZPE.    

References
[1]  A. O. Sushkov, et al., “Observation of the thermal Casimir force,” Nature Physics, 7, 230, 2011.
[2]  E. N. Lifshitz,” The theory of molecular attractive forces between solids.” Sov. Phys. JETP 2, 73-83, 1956.
[3]  J. Laurent et al., “Casimir force measurements in Au-Au and Au-Si cavities at low temperature,” Phys. Rev.B, 85, 035426, 2012.