Continuous electromagnetic radiation What I believe (I am not a physicist) would be called the "classical" description of electromagnetic radiation is that it is an oscillation of magnetic and electric waves, each producing the other through Maxwell's equations (in particular Faraday and Ampere). This would lead me to believe that, if I could hold a charge in my hand, and shake it back and forth at some particular frequency - say, that of blue light - that I could produce a continuous wave of electromagnetic radiation. If I could do it in one single direction - back and forth - then perhaps I could create polarized light.
Then I read some comments and answers on this site that appear to indicate wave properties of light are only realized by large populations of photon particles - that a single photon does not have a wavelength, per se, and the Standard Model indicates a photon is a particle, so not a wave.
In the experiment described above, would I indeed produce light? Would it be in the form of photon particles, or is the particulate nature of photons only a manifestation of the atomic or nuclear (bound systems) discrete transitions that produce photons by way of the fact that those transitions involve discrete energies (or perhaps the measurement devices that detect them)? If light is not produced, how can this be reconciled with Maxwell?
Is the production of a single, continuous wave of electromagetic radiation not possible? (i.e. non-particulate light)
 A: Your experiment would produce light because every accelerating charge releases radiation. Your hand shaking a charged particle is essential what a radio antenna does, just with a much greater number of charges so the signal is detectable from far away. When you go to the doctor and have an X-ray taken, those X-rays are generated by a beam of electrons impacting a dense metal like tungsten. The electrons slow down and stop inside the metal, and that acceleration creates the X-ray radiation (the technical term is bremsstrahlung, which is German for "braking radiation"). When a beam of electrons passes through a magnetic field, it changes direction, which is also an acceleration and also releases light called synchrotron radiation.
Here's a video of all the cool things we can do with this light.
Now, due to the quantum nature of reality, all of the above effects are actually producing streams of photons. The original equations describing effects like synchrotron radiation are classical calculations and give accurate results, but quantum effects are needed in some cases for more accuracy--especially with bremsstrahlung, which has electrons bouncing off atoms. A more detailed description can be had from Quantum Field Theory and a cartoon version looks something like this:
An electron at rest has the electromagnetic field because it has an electric charge (this is somewhat tautological since the definition of electric charge is an ability to interact with the electromagnetic field, but anyway). The electric charge couples the behavior of the electron with the electromagnetic field. If you grab that electron an pull on it, it starts to move. To put it another way, you gave it some kinetic energy. Now, because the electron is couple to the electromagnetic field, some of the energy you put into the electron by pulling it gets shunted into the electromagnetic field instead. This creates stable traveling waves in the electromagnetic field (a.k.a., light) much like throwing a rock in a pond creates ripples that travel away from the impact site. These electromagnetic waves will be detected somewhere else as photons due to quantum mechanics, but they are perfectly continuous waves before that detection. Because the waves carry off energy, the electron has less kinetic energy and moves more slowly.
A: The source of EM radiation is the emission of photons from excited electrons (mainly, because other subatomic particles also emit photons). Starting from this very fundamental point, it will be clear that EM waves and EM radiation are not the same.
A photon is an quanta of energy with a magnetic and an electric field component, both of which oscillate transversely to the direction of propagation. And in a vacuum, both components are perpendicular to each other. If we take a Cartesian coordinate system, x is the direction of propagation, y and z are the directions of the electric and magnetic fields.

...electromagnetic radiation is that it is an oscillation of magnetic and electric waves, each producing the other through Maxwell's equations...

The EM wave you describe occurs in two possible cases: The propagation of a single photon and the EM radiation of a number of synchronously accelerated electrons.
Photons from a thermal source have different energy contents and different directions of their field components (y and z are all 360° to x).
The synchronous acceleration of the electrons happens on the surface of an antenna rod. What we get is modulated EM radiation with polarised photons: The electric field component of the emitted photons is parallel to the electric field in the rod, the magnetic component is perpendicular to it.

... if I could hold a charge in my hand, and shake it back and forth at some particular frequency - say, that of blue light - that I could produce a continuous wave of electromagnetic radiation.

Yes, you will stimulate the emission of EM radiation. Shake a single charge at a certain frequency, you will stimulate a series of photon emissions. At the points of maximum acceleration with higher energy content and near the point of no acceleration with less energy. The number of photons emitted depends on the confinement of the electron in your hand.

If I could do it in one single direction - back and forth - then perhaps I could create polarized light.

I am not sure about that, because the acceleration is not due to an electrical potential. Take to AC electrodes instead of your hand, yes, you get polarised EM radiation.
