What, fundamentally, is an electromagnetic wave? As far as I know, all wave phenomena are derivations of an oscillating processes, e.g. particles vibrating in a medium. I can't imagine a wave process which couldn't be explained as moving particles: sound wave - movement of gas molecules, waves on the water - movement of water molecules, earthquake - movement of ground particles (and finally molecules), even phonons - vibrational movement of crystal lattice. Phonons are virtual but the atoms arranged in lattice are real.
I tend to think that the reason has to do with the restless nature of the photons along with the uncertainty principle - the impossibility to localize a primary chunk of matter (with momentum) - when we catch the wave (stop the process) the frequency is gone. But again, it looks like it is a particle and we just can't observe it with our methods.
So, what is the electromagnetic wave? How can it move vibrating across the vacuum? How can we physically interpret phenomenon of electromagnetic waves?
The concept of field is itself very complex phenomenon to understand its physical meaning by our "everyday" mind. The field looks like a math tool to describe and predict nature events. But its physical representation is unclear. I can't think of light as some 3-D helix shaped pulsing of continuous substance :) The world is quantized and it's obvious that the
sine-shape like objects cannot be elementary in reality.