In the QED framework, the vacuum is not actually treated as empty space, but is rather the province of the zero point field (ZPF), which has a non-zero level of energy. This can be derived from the uncertainty principle: if a system had zero energy sitting in a confined space (i.e., the bottom of an EM potential well), it would have a definite momentum and position at the same time, which is forbidden by the uncertainty principle.
Empirical evidence for this ZPF comes potentially from the Casimir effect, which is a tiny force measured between two parallel neutral metal plates brought very close together — the region between these plates should exclude longer wavelengths of the ZPF, and thus have lower energy than the outside region, producing a net force. However, it is also possible that this force reflects a radiation reaction effect, as it can be derived from QED on that basis alone (Jaffe, 2005).
The stochastic electrodynamics (SED) and stochastic optics models (Marshall & Santos, 1988; Marshall & Santos, 1997; deLaPenaCetto96) incorporate the ZPF as actual random oscillations in the classical EM field (described by Maxwell’s equations), and show how such a field could produce various phenomena such as photon antibunching statistics, which have been taken as one of the last elements of definitive support of the quantum photon model over the semiclassical approach (a classical EM field interacting with a quantized atomic system).
A major problem associated with all of these ZPF models is that the amount of energy in the ZPF would be astronomically huge. Also, it would seem to predict a higher level of spurious photon detection events than is actually observed, although there may be a reasonable solution to this latter problem (Marshall & Santos, 1997).
The semiclassical theorist Jaynes suggested that instead of imagining that this ZPF fills all of space, it may just reflect noise emitted by atomic and molecular systems, which will be most intense in the immediate vicinity of these sources, and fall off dramatically outside of them. This could potentially eliminate the problem of the huge energy level, as it would just be a small additional contribution to the observed mass values of atomic systems.
In any case, we will be on the lookout for these issues in developing the WELD models. The interaction between a discrete electron point particle and the Maxwell EM field will undoubtedly produce a lot of “ripples” of EM signals as it moves about, hopefully consistent with the spectrum of blackbody thermal radiation. However, there may be additional sources of noise, and additional elements of stochasticity that may need to be added.
For example, there is a long history of work on the connection between stochastic (brownian) motion and QM wave equations, which was developed by Nelson (1966) building on original ideas from Feynmann (see Sciarretta, 2018 for a historical overview and recent developments). It may be that we need to make particle movement stochastic, to avoid strong aliasing effects of the cubic lattice.