the Classical Casimir effect

I'm getting ahead of myself in starting things, but...

Suppose, being a contrarian, we set out to show that the Casimir
effect can be understood as a feature of the classical EM field, with
quantization a correction. We reason as follows.

The (classical) Rayleigh-Jeans formula for the energy density of
thermal EM radiation is

u_lambda = 8 pi kT / lambda^4

Of course this suffers a little problem as lambda -> 0, but we are
going to use the long wavelength tail. Parallel conducting plates are
separated by a gap of width d, containing cavity/thermal radiation.
The separation imposes a cutoff: lambda < d. The energy density
excluded is

(8/3) pi kT / d^3 (integral of tail)

Enclosing the plates in a large surrounding cavity of fixed volume,
this means that the total energy of the cavity radiation decreases as
the plates approach. If the approach is quasi-static, this can only
happen if the system is doing work on the surroundings -- say, through
a rod attached to one plate. So (we glibly press on), there is an
attractive force/area between the plates, and the last expression is
its value.

Now, let's check our estimate against the accepted expression:

(F/A)_casimir = (h-bar c pi^2) / (240 d^4)

<http://en.wikipedia.org/wiki/Casimir_effect#The_Casimir_effect>

Nice! Different constants, different power of distance, and no
mention of the temperature. Other than that, perfect agreement. :-)
A triumph.

Ok... you question, if you choose to accept it is: what is there
glaringly conceptually wrong with the classical argument? Why
_shouldn't_ we expect some effect from the exclusion of long
wavelength thermal radiation? And for that matter, why shouldn't the
temperature play a role in an effect relating to vacuum excitation?
No role suggests we have calculated a 0K limit.

[I myself hear fallacy yapping all around, but just out of the field
of vision]

.