The Casimir Force – Neutral or Electrostatic?
Since Casimir, experiments performed at ambient temperature have generally confirmed the Casimir force at gaps less than about 0.2 mm, and since the tests were performed absent pressure in a vacuum, it can only be concluded that the Casimir force has a thermal origin. Conversely, a vacuum origin to the Casimir force would be indicated, if the Casimir force were confirmed  in tests near absolute zero. But tests near absolute zero have never been performed, and therefore the claim that the Casimir effect produces a force from the ‘nothing’ of the vacuum is speculative, and at the very least violates the conservation of energy. In contrast, the modified Casmir theory asserts the ZPE finds its origin in the thermal kT energy of the atoms on the surfaces of the gaps.
2.1 Thermal Origin of the Casimir Force
The Casimir force in the gap is produced by the ZPE that finds origin  in the Planck energy E representing the thermal kT energy of the atoms on gap surfaces by the harmonic oscillator. The Planck energy E of the harmonic oscillator  is given,
Fig. 2 Thermal Planck Energy E - Harmonic Oscillator at Ambient Temperature
2.2 Source of ZPE Energy
The ZPE is proposed to find its origin in the cavity QED induced spontaneous emission of momentarily suppressed IR radiation from groups of atoms that move into  the high frequency VUV cavity. Similarly, static electricity may be explained  by the cavity QED induced spontaneous emission of suppressed IR radiation from micron size particles trapped in the gap between contacting surfaces.
In the Casimir effect, the surfaces separated by gap d are comprised of atoms having thermal kT energy and emit IR radiation at wavelength l IR. If d / l IR < 0.1, spontaneous emission of atoms between conducting parallel plates separated by a gap d is fully suppressed (Fig. 1 of ). Since Fig. 2 shows most of the thermal kT energy at ambient temperature resides at l IR > 10 mm, and since the Casimir force is only significant  in the VUV at d < 0.10 mm, the IR radiation is fully suppressed by cavity QED as d / l IR << 0.01. The IR radiation from surface area A comprised of atoms having thermal kT energy is suppressed because the gap always undergoes fluctuations O(d) on the order of atomic dimensions, the fluctuations intermittently moving a number NA of atoms into the VUV resonant gap, i.e., NA = A O(d) / D3, where D is the spacing between atoms in the surface at solid density. Since the atomic emission occurs at half IR wavelengths ˝ l IR > d , the EM energy UEM suppressed by cavity QED,
Typically, D ~ 0.3 nm. To conserve EM energy, the sub-surface atoms spontaneously emit at least half of the VUV radiation into the gap. The number NP of VUV photons spontaneously emitted having Planck energy EVUV,
To illustrate the modified Casimir theory, assume a fluctuation of NA = 1010 atoms. For a single layer of atoms, O(d) = D, the NA atoms cover a circular surface area A = 3.1x10-10 m2 having a diameter of about 20 mm. Prior to the fluctuation, the atoms have thermal kT energy of 0.0258 eV while the boundary conditions on the gap d = 0.1 mm require a ZPE having an EM resonant wavelength lc = 0.2 and EVUV = 6.2 eV. Steady heat transfer from the surroundings provides a continuous supply of thermal kT energy to compensate for the cavity QED induced spontaneous emission of suppressed EM energy. From equations 4 and 5, UEM = 62 pJ and the number NP = 3.1x107 of VUV photons.
2.3 Field Ionization
The electric field induced in the gap surface by the spontaneous emission of far IR photons induces the ionization of surface atoms to produce electrons and charged atomic states. Dependent solely on the power P produced in the particle while avoiding arguments of coherency of multi-IR photons, field ionization is significant because the thermal kT energy is induced by cavity QED to undergo spontaneous emission over very short times.
Laser induced field relations  may be used to quantify field ionization induced by cavity QED. Consider the gap surface atoms as a laser spontaneously emitting a short pulse of coherent thermal kT energy at far IR frequencies. The power P,
where, t is the time of spontaneous emission. At the gap surface area A, the laser intensity I is,
where, m0 is the permeability of free space. The electric field Ef is,
Assuming a spontaneous emission time t < 100 ps, equations (6) and (7) give the laser power P > 620 mW and intensity I > 2 GW×m-2. In equation 8, taking O(d) = D gives the surface field Ef > 8.7 x105 V×m-1 suggesting electrons are liberated from the Au surface atoms by field ionization.
2.4 Photoelectric Yield
Photoelectric yields gP are generally thought to be a function of the surface material, but may also depend on geometry. Indeed, microscopic particles are known  to have significantly higher yields than for the bulk surface. In Casimir force [4,5] experiments, microspheres and plates are common, and although both are usually Au coated, may not have the same yield.
Generally, the Casimir force only begins to be come significant below gaps d < 0.1 mm, or at EM resonant wavelengths lc < 0.2 mm. This is consistent with the work function W of most metals that gives the Planck energy EVUV below which electrons are not produced, i.e., electrons are not produced if EVUV < W. For example, the work functions W of Au and Al are about 4 eV that is equivalent to an EM resonant wavelength lc ~ 0.3 mm, or a gap d ~ 0.15 mm. For Al and Au coated gap surfaces, the photoelectron yield gP data ( Fig. 2 of  ) for EVUV from 4-12 eV is approximated by,
where, EVUV is in eV. For EVUV = 6.2 eV, the photoelectric yield gP = 4.5x10-6.
2.5 Number of Electrons and Electrical Charge
The number Ne of electrons produced depends on the number NP of VUV photons and the photoelectric yield gP of the gap surfaces in electrons per photon,
In the Casimir force experiments, both the sphere and flat plate are usually Au coated, and therefore there may not be any difference in the photoelectric yield gP. If so, the net charge Q produced is zero and there is no Casimir force in the modified theory. But the coatings are not likely identical, and geometrical effects may be significant. Hence, a parameter h < 1 is used to characterize the mismatch of otherwise identical materials, the charge Q produced,
Here the charge Q is upper bound by taking h = 1, or a perfect mismatch of photoelectric yields. For the photoelectric yield gP = 4.5x10-6 and number NP = 3.1x107 of VUV photons, the number of electrons Ne = 140 and charge Q = 2.2x10-17 C.
2.6 Casimir Force
The VUV radiation in the gap in combination with the photoelectric yields of gap surfaces means electrical charge Q is produced, and therefore the modified Casimir force Fc is attractive finding its origin in electrostatics,
where, eo is the permittivity of free space. For the Ne = 140 electrons and gap d = 0.1 mm, the modified Casimir force Fc = 4.5x10-10 N. For comparison, a 0.1 mm gap gives an experimental  Casimir force Fexp = 1.4x10-10 N.
The Casimir force Fc for the standard and modified theory normalized to the force Fc,0.1 at gap d = 0.1 mm are compared by maintaining the same heat flow,
Similarly, the number Ne of electrons is,
In contrast, the Casimir force in the Standard Theory,
where, the gap d is in microns. The range on d is from 0.1 to 0.05 mm corresponding to wavelength lc range form 0.2 to 0.1 mm, or Planck energy EVUV from 6.2 to about 12 eV.
Casimir forces in the modified theory are significantly higher than by the standard theory. Fig. 3 shows the Casimir force in the modified theory is about 6 orders of magnitude greater than that by the standard theory at a gap of 0.05 mm. Similarly, the number of electrons increases rapidly below as contact is approached.
Fig. 3 Standard and Modified Casimir
Force and Electrons
A modified Casimir theory is presented to explain the interaction between bodies separated by gaps less than about 0.1 mm, the conclusions of which are summarized as follows:
The modified Casimir force between bodies separated by an evacuated gap is attractive and finds its origin in electrostatics because of electrical charge produced by the bodies. The electrical charge is produced by the photoelectric effect from the field ionization of surface atoms induced by the spontaneous emission of thermal kT energy by cavity QED.
In the MEMS device, the permanent adhesion observed upon contact cannot be caused by neutral surfaces. Electrostatic discharge is a more likely explanation, but the standard Casimir theory is based on an attractive force between neutral bodies.
The modified Casimir force based on electrical charge build-up may occur even as a current flowing in the ground between the bodies dissipates the charge. But the rapid increase in charge for gaps less than 0.1 mm suggests that measurements of current rather than force may be a meaningful measure of the Casimir force.
In the modified Casimir theory, the ZPE finds its origin in the thermal kT energy of the atoms, and therefore the ZPE and the Casimir force cannot exist at absolute zero.
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