In this paragraph we want to add some thoughts on gravity, inspired by the above results, which are more speculative in nature. Whatever the right gravitational interaction is, we have seen that the metric structure of space-time (37) can emerge from gauging the duration of multiple events in empirical space-time with light clocks. The special form of the gravitational acceleration, namely its independence of any probe-mass (weak equivalence principle) and the inverse-square dependence on spatial distance in the Newtonian limit, is fundamental to the result. Note that, if there were only one type of charged particle, the electron for instance with mass

${m}_{e}$, then the identical derivation as above would work with the Coulomb-acceleration:

In the last few decades there has been a series of approaches to explain gravity as an emergent phenomenon [

28,

29,

34,

35,

36]. We cannot give individual credit to these works here, and for a recent overview see e.g., [

37]. Our approach differs in two main points. Firstly, already empirical space-time at the level of Minkowski space

${\mathbb{M}}^{4}$ is emergent. More precisely, it is the metric structure, which emerges as a result of events and the choice of light clocks to measure duration (13). From there it only needs the gravitational acceleration in the Newtonian limit, to derive the dynamics of the metric structure and hence general relativity. Secondly, the irreversibility of events and their interpretation as “becoming” leads to the existence of two realms. On the one hand the realm of Hilbert space, where time is necessarily symmetric, and on the other hand the growing block-world of empirical space-time [

5]. The concept of a dynamical space-time, which emerges through events from an abstract realm, points to the possibility that the metric-field is not the counterpart in a quantum-interaction of gravity but really an emerging relational structure on empirical space-time. (This idea follows the tradition of Leibniz and Mach). The gravitational interaction would then happen between material systems outside of empirical space-time, totally in line with the other interactions [

38], or it could be the result of already known, but not yet calculated quantum effects, as R. Feynman suggests in his lectures on Gravitation (2003) Section 1.5 [

39]. The difficulty to define energy and its conservation in empirical space-time, whether gravitational or non-gravitational, might then reflect that it is not the metric field, which carries energy, but some other fields in Hilbert space. It is, on the other hand, to be expected that the emerging metric structure does somehow reflect energy of the fundamental fields, as the example of gravitational waves proves. A satisfactory mathematical definition within empirical space-time seems, however, only possible in special cases and in a linearized approximation [

30]. Nevertheless the recent LIGO experiments have been very accurately predicted by the mathematics of general relativity. The metric structure must consequently reflect energy for all forms of acceleration, as the physical length contraction, which is considered to be an effect in special relativity, shows [

40]. By the same token, the fact that there is the Planck length

${l}_{P}$, below which a massive particle would be hidden by its own horizon, might just be a fact of the emergent geometry of empirical space-time and need not be the result of a quantization of space-time itself. The corresponding Planck-time is then given by

${t}_{P}=\raisebox{1ex}{${l}_{P}$}\!\left/ \!\raisebox{-1ex}{$c$}\right.$, in line with our model (13). We get the Planck mass

${m}_{P}$, if the Compton wavelength equals the Planck length,

${\lambda}_{{m}_{P}}={l}_{P}$, and hence

${\alpha}_{C}={\alpha}_{G}$. This in turn allows the definition of the gravitational constant by:

So there is a connection between electrodynamics and gravity at the Planck scale. Maybe it is just the other way round, and there is a fundamental quantum of mass ${m}_{P}$, acting like charge in a field theory, from which the other quantities like ${l}_{P}$, or $G$ follow. In this context it also seems natural, that in the mathematical formulation of quantum-interactions in ${\mathbb{M}}^{4}$, without empirical backing at the smallest scale, integration is cut at ${l}_{P}$ and some infinities are avoided.