 an earlier proposal by the author \cite{bimonte},
we have shown in this paper that it is possible to resolve this
difficulty by using modified dispersion relations to evaluate
$\epsilon(i \xi)$. The new form of dispersion relations involves
certain weight functions, that we called window functions, that
are aimed at suppressing the contribution of low frequencies, for
which no optical data are available. The key feature of the new
dispersion relations, as contrasted with the standard KK formula,
is that they involve both the real and the imaginary parts of the
permittivity. This does not constitute a problem, because refined
optical techniques like ellipsometry permit to measure both
quantities accurately \cite{sveto}. The window functions
introduced in our first work produced unsatisfactory results, when
applied to the handbook data for gold \cite{geyer}. In this paper,
we demonstrated by means of a Monte Carlo simulation that the bad
performance of these window functions originated from the fact
that they lead to a large amplification of possible small
experimental errors in the optical data. In this paper we have
addressed this instability by introducing a new class of weight
functions, which differently from the old ones lead to a positive
definite kernel in the dispersion formula, in such a way that no
instability occurs anymore. We have shown that the improved choice
of window functions efficiently suppresses the contribution of low
frequencies,  in such a way that it is now possible to compute
with high precision the Casimir pressure between two
  gold plates in vacuum,  using currently available
optical data, like  the handbook data \cite{palik} and the new
data of Ref. \cite{sveto}.

When we used the handbook data,  we found it necessary to exclude
from our computations all data for frequencies less than 0.6
eV/$\hbar$, whose original source was Ref. \cite{dold}. The reason
for not using these IR data is  that the film used by these
authors appears to posses a plasma frequency of 7.7 eV/$\hbar$,
which is exceedingly smaller than the value of 9.2 eV/$\hbar$ that
we obtained from Theye's data \cite{theye}, which are part of the
handbook data from the near IR to the UV. The latter value of the
plasma frequency is very close to the commonly accepted  value of
9 eV/$\hbar$ \cite{lambrecht}. After excluding the data of
\cite{dold} the window method produces less accurate results,
because the residual handbook data that ar left over start from a
rather large frequency of 0.6 eV/$\hbar$. Nevertheless,  the
Casimir pressure can still be estimated by the window method with
an uncertainty that we estimated smaller than 0.3 $\%$. When the
Drude prescription is used, the values of the Casimir pressure
obtained by the window method agree with those obtained by the
standard approach, based on KK relations and the Drude
extrapolation, within 0.2 $\%$ for separations larger than 50 nm,
and therefore they remain inconsistent with the experimental data
of \cite{decca}.

A much higher precision can be obtained when the data of
\cite{sveto} are used. Thanks to the fact that these data extend
to longer wavelengths than the tabulated data, the uncertainty in
the windowed prediction for the Casimir pressure decreases to 0.1
$\%$, for separations larger than 50 nm. This is an order of
magnitude better than the 1 $\%$ uncertainty that was estimated in
\cite{sveto} to result from uncertainty in the Drude parameters,
within the standard KK approach.  The magnitudes of the Casimir
pressure predicted by the window method were found to be in very
good agreement with predictions based on the standard KK formula
for the mica sample of \cite{sveto}. However for the two samples
deposited on Si substrates that we considered significant
discrepancies  were found, the windowed Casimir pressures
exceeding the KK  values by more than 1  $\%$ for sample 1 and by
more than 2  $\%$ for sample 4, for separations less than 200 nm.
The discrepancy for samples 1 and 4 is too large to be explained
by uncertainty in the Drude parameters, and we attribute it to the
fact that the Drude model was shown in \cite{sveto} not to
describe well the dielectric function of these films in the IR, as
evidenced by the presence in their optical data of an unexplained
IR absorption band. It is quite possible that for this reason
predictions for the Casimir force based on the Drude model are
less accurate for these films.

In conclusion our results demonstrate that the window approach can
be used to predict the Casimir pressure between two metallic
plates very accurately, on the basis of  standard optical data
extending from the IR to the UV, without the need of further
extending optical measurements  to longer wavelengths than those
reached by current laboratory optical apparatus.  We hope that the
results of this work will help clarifying present difficulties
raised by the interpretation of experiments probing the thermal
Casimir effect.







{\it Acknowledgements} The author thanks the ESF Research Network
CASIMIR for financial support. Warm thanks are also due to G. L.
Klimchitskaya and V. M. Mostepanenko for their constructive
criticism, which greatly helped the author improving the
manuscript, and to the authors of Ref. \cite{sveto} for sharing
their data. The author acknowledges also interesting
correspondence with G. Palasantzas on the consequences of
incomplete Kramers-Kronig consistency of optical data.




Now that you’ve made your card, get an envelope and a stamp and send it to someone who could use a reminder of God’s love and care.
These Angel Friends printable paper dolls from Making Friends are so much fun!
Angels are messengers, but sometimes we misunderstand their language.
Assemble the items with the kit and add the printed list of the meaning of each item to brighten someone’s day.
A number of years ago at the beginning of the Christmas shopping season a terrible tragedy occurred in the city where we lived. An armed young man in a crowded shopping mall killed and injured others before taking his own life. Local news coverage seemed to be non-stop. The entire city was in mourning at a time which would normally be joyful. Holiday events were cancelled, but some went on in an attempt to keep going on with life.
I have a soft heart and knew from experience if I allowed it I could follow the deep emotions right into a deep dark pit of depression. Some time ago I determined that would not happen again.
To distract me from the non-stop news coverage and help me focus on God’s love and provision I began making one angel art or craft project a day. I continued this for several years beginning at Thanksgiving and continuing until Christmas. In recent years I stopped doing this, but in light of current events I think it’s time to bring back the daily angel. I already had my blog posts scheduled for November and December, but Spirit started nudging me to do this instead. I have learned when Spirit nudges, I move.
This year I am starting on the first Sunday of Advent with this introduction. Beginning tomorrow and continuing through Christmas Eve I will post The Daily Angel with a daily quote, scripture, video or reflection. I will also include a link to an angel craft project or a video demonstration of an angel project. There are no real rules for this, but I would like to encourage you not to use this as a time to make your holiday gifts or items to sell at craft fairs because the urgency of completing these projects brings a different energy to the process. Some of these projects are more involved than others. Feel free to extend a project over several days if needed. Our purpose is to focus on God’s love and provision which we are reminded of through His angel messengers. We don’t want anyone to feel rushed or stressed over this.
So during this time of darkness for so many, breathe. Relax into God’s love. Focus on His angels as messengers sent to teach, guide, protect, remind us of God’s, love and grace and warn us when necessary. Then join me on December 25th for an uplifting musical video presentation with an important message for our times. Blessings during this holiday season.
Each year I celebrate A Season of Angels beginning at Thanksgiving and continuing through Christmas, making one angel craft project each day. I started doing this after a local tragedy during the holiday season several years ago but I still do this each year.
This is different than making crafts to sell or give as gifts. I do this as a form or meditation or prayer to help keep me focused on Spirit and the values that really matter.
This year I invite you to join me each day from now till Christmas. Slow down and take a little time each day to make (or at least work on) a small angel project each day