If electromagnetic waves travel through the electromagnetic field, what is the electromagnetic field? I know sound waves travel through a medium like air or water.

This is a really good question to ask and it was asked about light waves in the early 20s. This lead to the logical need for "ether" so that lightwaves could have a medium to serve as "water" in your example. However, the presence of ether could not be demonstrated and turned out to be unneeded with the discovery that light behaves as both a wave and and particle. Along with way came a realization that what was called "free space" which would a true vacuum with "nothing" in it doesn't exist anywhere in the empirical universe so everywhere has atomic particles that slow down EM waves as collisions happen - some locations have tightly packed atoms that do that really well.

This is a much more authoritative answer to your question. Hope it helps:

Propagation of an Electromagnetic Waves

The elctromagnetic waves never require any medium for their propagation. In fact it is the elctromagnetic waves which create the field. Since elctromagnetic waves are corpuscular in nature therefore never require medium as they are electric and magnetic fields oscillating perpendicular to each other. On the other hand sound and water waves which are mechanical in nature are distortion in the medium itself . For example distortion in any material(classical mechanics) sets up waves in i i.e., water, sound. We determine medium with respect to the nature of waves. There are two types:

  1. Mechanical (Require Medium)
  2. Electromagnetic (Do not require medium as are themselves medium)

It is well known that all of free space and materials have electrical permittivity and magnetic permeability. As a result any induced em fields may propagate in and through free space as it has both an absolute permittivity ([math]\epsilon_0[/math])and absolute permeability ([math]\mu_0[/math]) which effectively provide it with "material like properties" much like air through which sound waves travel.

Due to free space having such properties it means any inducing em field may create both electric and magnetic flux densities which allow for the propagation of such em fields.

There are many and various views and theories but the empirical existence of [math]\epsilon_0[/math] and [math]\mu_0 [/math]suggest that free space has material like properties.

According to the conventional interpretation, EM waves propagate through spacetime, not "through the EM field". See Maxwell's Equations. Back at the end of the 19th Century, people like Fitzgerald & Lorentz (and even Maxwell himself, I gather) thought there must be some medium that EM waves propagated through, called the "luminiferous aether". This view has been abandoned by most scientists, but it still has advocates. Talk to Shiva Meucci.

The question makes the unwarranted assumption that electromagnetic waves travel through the electromagnetic field. This is not correct. The EM waves and the EM field are the same thing.

IT like this: imagine a big swimming pool sith ping-pong balls floating in it... the balls are painted with luminous aint, so they glow in the dark: now switch off the lights.

See the balls move, but you cannot see the water.

The balls are electric charges.

The EM field is just like the water except there is no water.

It is just way that we can use to describe how the balls move.

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