I have been reading back over the paper by James Clerk Maxwell titled A dynamical Theory of the Electromagnetic Field. Early on in the paper he is rejecting the action at a distance hypothesis in favour of the existence of a medium for transmission. "that we are obliged to admit that the undulations are those of an aethereal substance, and not of the gross matter, the presence of which merely modifies in some way the motion of the aether."
So the idea of waves in the aether was the prevailing view at the time and the idea of fields were what we now call classical fields i.e. a three dimensional map of the force vectors.
Maxwells often quoted statement:
"This velocity is so nearly that of light, that it seems we have strong reason to conclude that light itself (including radiant heat, and other radiations if any) is an electro magnetic disturbance in the form of waves propagated through the electromagnetic field according to electromagnetic laws."
suggests the modern view that it is the electromagnetic field that is the medium for the transmission of light.
But he goes on to say:
If so, the agreement between the elasticity of the medium as calculated from the rapid alternations of luminous vibrations, and as found by the slow processes of electrical experiments, shows how perfect and regular the elastic properties of the medium must be when not encumbered with any matter denser than air.
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Maxwell shows that the velocity of electromagnetic waves and the velocity of light are the same and so provides evidence that they are waves in the same medium.
Then later on the measurements in Michelson and Morley experiment indicate that the speed of light is unaffected by the movement of the experimental apparatus. For this reason the idea of the existence of a medium for the transmission of light is rejected.
So we get light as a particle through empty space as one possibility but light is clearly a wave so what is it that is waving? During the latter part of the 20th century up to now the idea prevailed that the electromagnetic field was the transmission medium for light waves.
Then we get results from LIGO that show that the speed of gravitational waves and the speed of electromagnetic waves from a distant neutron star merger are the same even though the waves have travelled 130 million light years across expanding space so that the recession velocity of the event is around 1% of the speed of light.
This must mean that the medium for the transmission of gravitational waves and the medium for the transmission of electromagnetic waves (including light) are the same. Here we are following Maxwells logic: same speed implies same means of transmission. So the medium for the transmission of light must be spacetime itself.
So how do we get back to Maxwells equations from a theory of waves in spacetime? Once we understand the nature of electric charge we can see that the electrostatic force is as a result of the tendency of objects in spacetime to accelerate towards a lower energy state. Once we have explained the property "force" we can then derive the classical "field" and we are back to Maxwell's equations but with a new understanding of the nature of mass, charge, force and field.