What effect does the quantum world have on radio waves? For example, if I could shrink myself down and stand on the nucleus (or even smaller sub atomic particles making up the nucleus) with a device which could measure radio waves of the surrounding world (ie with all the signals modern day humanity produces), what readings would I pick up? Would they be the same as normal or would the quantum aspects somehow effect the signals and if so, in what way would they be effected?
If you are an electron in an atom and you have some energetic spectrum, a radio-wave may cause your transitions from one level to another. Your quantum character is manifested in your discrete energy levels.
If you are an electron in a solid state, in a metal, for example, then your spectrum may be continuous and any energies are allowed. In this case you behave as a classical charge.
I'm NOT physicist but I think there are a few concepts here that are being confused.
Firstly an antenna is "tuned" to a particular Radio Frequency ie. its better at resonating an AC signal (free electrons) at lengths that are around a wavelength.
Secondly an electron absorbs a quanta of EMF around an atom by transitioning from one level to another. Your quantum character is being manifested in finding electrons that can gain discrete energy levels when absorbing the quanta of emf (remember the dual nature of EMF that even though its wavelength may be 160 metres it must be absorbed by a single electron.
I expect the probability of an electron absorbing an EMF quanta is no greater in an smaller antenna than a larger antenna, more a factor of cross sectional area I expect.
Whether a free electron will resonate in an antenna will be determined by the factors like SWR and antenna geometry/length NON quantum effects
All interactions of matter with radio waves - including those we perceive as classical - are at heart quantum mechanical. In particular, the free electrons in a metallic antenna react to the electric fields in radio waves much as classical particles would because at conduction-band energies there is a continuum of allowed energies and the electrons are effectively (in the technical sense) free.
The real way in which manifestly quantum mechanical effects show up is when the photon energies of the EM radiation (which equal $h\nu$ or some multiple of it) are comparable to the energy difference between two discrete-energy states. Since radio waves are at the bottom of the EM spectrum, this energy difference must be very small (of the order of meV or smaller).
The best example of these small energy differences in action is probably the hyperfine structure of hydrogen, which reflects the slight energy difference caused by magnetic interactions between the electron and proton magnetic moments (the latter of which is very small), depending on whether their spins are parallel or antiparallel. These are two states with discrete energies and transitions between them cause absorption and emission of microwaves at about 21 cm wavelengths.
Because of their long wavelength, it is hard to detect individual radio photons. (In fact, it is possible but still quite a feat to reliably produce and detect single photons. This can be done in the visible and IR ranges but this kind of optics at longer wavelengths get progressively harder.) On the other hand, it's easy to make quite intense radio waves (like the MW powers routinely used by radio stations) by simply sending huge numbers of photons.
This does not mean, however, that the mismatch between the radio wavelength (of the order of 1 m) and atomic wavelengths (of the order of 0.1 nm) make it hard for the two to interact. This is already a problem for optical wavelengths, on the order of 400 nm, and simply means that radiation of this type should be treated in the dipole approximation which treats the electric field as locally constant. This only breaks for EM radiation of X-ray frequency and above, which does interact quite differently with matter.
As far as I know, the lowest frequency radio wave emitted by an atom is the Hydrogen 21 cm line (~ at 1.4 GHz).
Therefore if you were an electron in the Hydrogen atom, you would see the photon with a wavelength of 21 cm as a change in energy (as a hyperfine transistion, actually). If it were of a longer wavelength, what you will see is a locally constant electric field, which varies with time.
In that case the electric field interacts with the electron much like a classical picture (i.e., it accelerates it in a particular direction), but quantum mechanically speaking you won't "change". Your energy level will still be the same, and if you are bound to an atom/molecule, then absolutely nothing will happen.
On the other hand, if you are a free electron then you would be accelerated in the direction of the electric field and at the same frequency as the incident electric field is oscillating.
A radio wave is nothing more than a photon. A photon can be envisioned as a fuzzy particle with dimensions about the same as the wavelength. It is thus many tens of meters in size. The probability of interaction between an antenna of nuclear dimensions and such a large photon is extremely small.