COMPARISON
BETWEEN EXPERIMENT AND THEORY
FOR THE THERMAL CASIMIR FORCE
G. L. KLIMCHITSKAYA
Department of Physics, North-West Technical University,
St.Petersburg, Russia
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CONTENT
1. Introduction
2. Is the PFA exact enough for theory-experiment
comparison?
3. Experiments between metal test bodies using
a micromachined oscillator
4. Experiments with semiconductor and dielectric
test bodies
5. Torsion balance experiments
6. Conclusions
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1. Introduction
The magnitude of the thermal correction
to the Casimir force between test bodies
made of real materials, as predicted by the
Lifshitz theory and its generalizations,
strongly depends on models of dielectric
permittivities used for the description of
these materials.
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Models of the frequency-dependent dielectric permittivity
Permittivity of dielectric plates,
as determined by core electrons
Permittivity of dielectric plates
with dc conductivity included
The Drude model permittivity
for metallic plates
The plasma model permittivity
for metallic plates
The Lifshitz theory with
or
for perfect crystal lattices
violates the Nernst theorem
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2. Is the PFA exact enough
for theory-experiment comparison?
The region of experimental parameters:
For ideal metals in the zeroth order in d/R the PFA gives the same
contributions to the Casimir force at T=0 and to its thermal correction
as the exact theory
(Bordag, Pirozhenko, PRD, 2010; Teo, PRD, 2011)
Only the correction of order d/R to the PFA results is possible
in the exact theory.
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For plasma and Drude metals the exact computations of the
Casimir force were done for d/R>0.1 .
Deviations in ratios q of the Casimir forces calculated using the
plasma and Drude models in the framework of the exact theory
and PFA decreases from 9.2% to 2.5% when d/R decreases from
5 to 0.1.
Claim: at large separations the Drude model leads to a force that
Is smaller by a factor q=3/2 than the force with the plasma model
(instead of a factor q=2 as follows from the PFA).
(Canaguier-Durand, Maia Neto, Lambrecht, Reynaud, PRL, 2010)
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This is not always so!
The correct factor is:
outside the application region
of the PFA;
in the application region
of the PFA;
(Geyer, GLK, Mostepanenko, PRA, 2010)
For instance, according to the exact theory at separation of
5 micrometers q increases from approximately 1.48 to 1.63
when d/R decreases from 2.5 to 0.5.
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outside the
application region
of the PFA;
(Zandi, Emig, Mohideen, PRB, 2010)
Conclusion: inside its application region the PFA
works perfectly well.
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3. Experiments between metal test bodies using
a micromachined oscillator
Decca et al, PRD (2003), Ann. Phys. (2005), PRD (2007), EJPC (2007)
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The errors are shown at a 95% confidence level.
The red band shows the prediction of the plasma model.
The green band corresponds to the Drude model.
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The errors are shown at a 67% confidence level.
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The number of degrees of freedom
The penetration depth of electromagnetic oscillations into
a metal:
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Plasma model approach:
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Plasma model approach:
Fit of the mean values of the pressure measured:
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Plasma model approach:
Fit of the mean values of pressure measured:
Fit of different sets of individual measurements:
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Drude model approach:
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Drude model approach:
Fit of the mean values of the pressure measured:
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Drude model approach:
Fit of the mean values of pressure measured:
Fit of different sets of individual measurements:
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Could patch effect compensate the difference between
experimental data and the Drude model prediction?
(I) Patch effect due to polycrystallite structure in Speake-Trenkel model
(PRL, 2003) is negligibly small (Chen et al., PRA, 2004;
Decca et al., Ann. Phys., 2005)
(II) Recently an alternative “quasi-local” model of patches was suggested
(Behunin, Intravaia, Dalvit, Maia Neto, Reynaud, arXiv:1108.1761)
In this model:
--- patch effect due to polycrystallite structure is by orders of
magnitude larger than in the Speake-Trenkel model and much
exceeds the difference between experimental data and the Drude
model prediction;
--- it is claimed that the patch effect due to hypothetical large
contaminants can be equal to this difference.
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The parameters of these contaminants (the maximum size and
the root-mean-square voltage) are determined from the fit to
the difference between the experimental data and the Drude
model prediction.
This fit has the two defects:
--- the Drude model prediction was computed using too
simplified model of the dielectric permittivity and the
surface roughness was not taken into account;
--- in the fit, instead of the variance of the mean,
the experimental error determined at a 95% confidence
level was used.
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The data for the patch pressure (red line) were kindly
provided by R. O. Behunin and D. A. R. Dalvit.
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The characterization of the fit:
The theoretical force-distance dependence of the patches due to
hypothetical large contaminants is irrelevant to the difference
between the experimental data and the Drude model prediction.
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The difference between the
experimental data and the
Drude model prediction:
-- as calculated by Behunin et al.
(upper crosses);
-- calculated using the tabulated
optical data (Palik)
extrapolated by the Drude
model with account of
surface roughness
(lower crosses).
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4. Experiments with semiconductor and dielectric
test bodies
4.1 Optical modulation of the Casimir force between Au sphere and
Si plate
Chen, GLK, Mostepanenko, Mohideen, Opt. Express, 2007; PRB, 2007.
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Difference of the Casimir force in the presence and absence
of laser light
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4.2 Frequency shift of center-of-mass oscillations due to
the Casimir-Polder force
Obrecht, Wild, Antezza, Pitaevskii, Stringari, Cornell, PRL (2007);
Klimchitskaya, Mostepanenko, JPA (2008)
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4.3 The Casimir force between Au sphere and ITO plate
Chang, Banishev, GLK, Mostepanenko, Mohideen,
Phys. Rev. Lett., 2011.
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5. Torsion balance experiments
5.1 Confirmation of the thermal correction predicted for ideal metals
Masuda, Sasaki,
PRL 2009
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5.2 Purported observation of the thermal Casimir force
predicted by the Drude model
Sushkov, Kim, Dalvit,
Lamoreaux, Nature Phys. 2011
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5.2 Purported observation of the thermal Casimir force
predicted by the Drude model
Sushkov, Kim, Dalvit,
Lamoreaux, Nature Phys. 2011
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5.2 Purported observation of the thermal Casimir force
predicted by the Drude model
Sushkov, Kim, Dalvit,
Lamoreaux, Nature Phys. 2011
Fit using the Drude model:
f=19
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GLK, Bordag.Fischbach,
Krause, Mostepanenko,
Int. J. Mod. Phys. A, 2011
f=4
Fit using the Drude model:
Fit using the plasma model:
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Different types of surface imperfections demand use of more
sophisticated forms of the PFA
Unavoidable imperfections on lens surfaces make indefinite
values of the Casimir force below 3 micrometers.
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The Casimir force between
a perfectly spherical lens
and a plate, both described
by the Drude mode is shown
by the dashed line.
The red line shows the same
force between a sphere with
some surface imperfection
and a plate, both described
by the plasma model.
Bezerra, GLK, Mohideen, Mostepanenko, Romero, PRB, 2011
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6. Conclusions
1. The PFA is well applicable to all performed experiments with
smooth surfaces.
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6. Conclusions
1. The PFA is well applicable to all performed experiments with
smooth surfaces.
2. The thermal Casimir force, as predicted by the Drude model,
is in contradiction with a number of experiments.
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6. Conclusions
1. The PFA is well applicable to all performed experiments with
smooth surfaces.
2. The thermal Casimir force, as predicted by the Drude model,
is in contradiction with a number of experiments.
3. The suggested quasi-local patches are incapable to explain
the difference between data and the Drude model prediction.
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6. Conclusions
1. The PFA is well applicable to all performed experiments with
smooth surfaces.
2. The thermal Casimir force, as predicted by the Drude model,
is in contradiction with a number of experiments.
3. The suggested quasi-local patches are incapable to explain
the difference between data and the Drude model prediction.
4. The purported observation of the thermal Casimir force, as
predicted by the Drude model, is not an independent
measurement, but a fit using fitting parameters.
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6. Conclusions
1. The PFA is well applicable to all performed experiments with
smooth surfaces.
2. The thermal Casimir force, as predicted by the Drude model,
is in contradiction with a number of experiments.
3. The suggested quasi-local patches are incapable to explain
the difference between data and the Drude model prediction.
4. The purported observation of the thermal Casimir force, as
predicted by the Drude model, is not an independent
measurement, but a fit using fitting parameters.
5. At separations above 3 micrometers the experimental data
are in agreement not with the Drude model, but with the
plasma model. Below 3 micrometers a seeming agreement of
the data with the Drude model can be explained by a disregard
of surface imperfections.
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