Phenomenology of the dispersion law in a three-dimensional quantum space

The concept of a quantum structure underlying space has been proposed for quite some time, yet it has largely eluded direct observation. There is a prevailing notion that the minuscule effects stemming from quantum space could, under certain astronomical conditions, accumulate to an observable magnitude. Typically, these effects are perturbative, limited to the first one or two orders. This study presents a full dispersion law derived from a three-dimensional quantum space model. Our primary focus is to investigate the in-vacuo dispersion phenomenon and the threshold anomaly. Furthermore, we briefly explore the implications of additional spatial dimensions within this framework and suggest a way of distinguishing between various theories that agree in the leading-order approximation.