Why does Faraday cage bar spacing need to be smaller than wavelength?

[cesiumfrog]

so how does the mainstream theory explain this? What dimensions does an EM wave have in the transverse?

According to mainstream physics, the transverse extent of a photon is exactly zero.

Why is it [the effective area of a small antenna] proportional to the square [of the incident wavelength]?

Dimensional analysis? (Read the link provided.)

Please expand on the overlap/cancellation part, this seems to suggest that the attena cause a phase-shift of half a wavelength between the transmitted and "re-readiated" wave.

The oscillating transverse electric field, in an EM wave, applies an oscillating transverse acceleration to any free charges. Look up "simple harmonic motion": the position of the charges will lag the acceleration by 180 degrees, hence the phase shift.

½mv^2 = E = hf, mv = p = h/l

Those non-relativistic approximations are invalid for the speeds you wish to consider.

but where do the eddy currents get the energy to produce these waves? they must absorb it from the incoming wave, yet the incoming wave never actually touches the metal wire.

Of course the incoming wave touches the wire, in fact it permeates all space. And above the 'skin depth' of the wire, it supplies energy driving simple harmonic motion of charge (which is in turn damped by the production of a re-radiation which cancels out most of the field beyond the skin depth, effectively converting the energy into a reflected beam).

 

[granpa]

if you consider how electrons oscillating in an antenna produce a radio wave I would think that the EM wave is not actually produced directly at the antenna itself but rather it is produced in the space immediately surrounding it (by the expanding and collapsing electric and magnetic fields which are out of phase with the moving electrons). so I suppose that the reverse process of absorbing the EM wave doesn't actually require the wave to strike the antenna directly. I suppose its absorbed by the field that immediately surrounds the antenna that is produced by the oscilating electrons inside the antenna itself.

so perhaps the photon doesn't extend 1/2 wavelength to each side after all. (of course, being a wave, it will tend to spread out)

 

[gareth]

According to mainstream physics, the transverse extent of a photon is exactly zero.

But how does this fit in with the wave theory of light, there is limit (look up "diffraction limit" and "Airy disc") to the extent an EM wave can be localised on a spot.

These state that an EM wave is effected by apertures in the transverse, if the photon has zero dimensions in the tranverse, why it is affected?