Peter,
I hope you won't mind if I share the Grand Design with you; a simple version. Aether waves are the ontological building blocks of our universe. All the properties of light (permitivity, permeability, etc.) are built into them. They were inspired by wave-functions of the form,
[math]\psi = e^{i \omega t}[/math]
and the two postulates of special relativity.
#1. The laws of physics are the same in all inertial frames of reference.
#2. The speed of light in free space has the same value C in all inertial frames of reference.
These postulates are hard to explain ontologically, but there is a way. One has to assume that the laws of physics are implemented by the set of (aether) waves that obey,
[math]c = \lambda f[/math]
Inertial frames are a mathematical tool that allows you to set up a coordinate system; but I will refer to them in the ontological sense when I say: inertial reference frames are made of those same aether waves. Particles with mass are the smallest physical objects that can be described with inertial frames. Whatever equations and descriptions are used to describe particles of the Standard Model, those equations describe one or more aether waves. Quarks, gluons, protons, neutrons, hadrons, electrons, leptons all have a unique spectral signature, a range of aether medium frequencies. When those particles are annihilated by their antiparticle, the spectral signature is released as gamma rays. It is this spectral signature that establishes that particle's relationship to its inertial frame's clock (progression of time). This is the simplest way that Standard Model particles can obey the postulates of relativity; they are made out of aether waves which satisfy c = wavelength*frequency.
We experience inertia because the composition of frequencies that make up our particles, they have to frequency shift from one set of aether wave frequencies to another set of aether wave frequencies. We experience this as a force that disturbs inertia.