visible light - How do electromagnetic waves travel in a vacuum?

This is perhaps a total newbie question, and I will try to formulate it the best I can, so here it goes. How does an electromagnetic wave travel through for example, the vacuum of space?

I usually see that waves are explained using analogies with water, pieces of rope, the strings of a guitar, etc, but it seems to me that all those waves need a medium to propagate. In fact, from my point of view, in those examples the wave as a "thing" does not exist, it's just the medium that moves (involuntary reference to The Matrix, sorry).

But in space there is no medium, so how does a wave travel? Are there free particles of some sort in this "vacuum" or something? I believe the existence of "ether" was discarded by Michelson and Morley, so supposedly there isn't a medium for the wave to travel through.

Moreover, I've seen other answers that describe light as a perturbation of the electromagnetic field, but isn't the existence of the field, potential until disturbed? How can it travel through something it does not exist until it's disturbed by the traveling light in the first place? (this last sentence is probably a big misconception by me).

Answer

The particles associated with the electromagnetic waves, described by Maxwell's equations, are the photons. Photons are massless gauge bosons, the so called "force-particles" of QED (quantum electrodynamics).

While sound or the waves in water are just fluctuations (or differences) in the densities of the medium (air, solid material, water, ...), the photons are actual particles, i.e. excitations of a quantum field. So the "medium" where photons propagate is just space-time which is still there, even in most abandoned places in the universe.

The analogies you mentioned are still not that bad. Since we cannot visualize the propagation of electromagnetic waves, we have to come up with something we can, which is unsurprisingly another form of a wave, e.g. water or strings.

As PotonicBoom already mentioned, the photon field exists everywhere in space-time. However, only the excitation of the ground state (the vacuum state) is what we mean by the particle called photon.