\label{spacetimefield} The Einstein’s Theory of Relativity \cite{Einstein_1922} establishes a deep physical connection between space, time and material objects (particles-fields): we cannot describe particles and their interactions without space and time, and at the other hand space and time haven’t a physical sense without particles. In conformity with that, one could assert that if particles are to be considered as an objective reality, then also time and space shall objectively be considered as a unique real thing.
So we’ll call about Space-Time Object, and also we will intend the universe, like a set of particle-fields, as a field which nature is based on Space-Time (ST).
In order to explain the nature of physical object assigned to ST (and to the whole universe) we recall some fundamental characteristics:
The ST object is described like a 4-dimensional manifold \(S^* (x,y,z,t)\), a space-time lattice, where
the geometrical properties of bodies are not independent, but depend upon the distribution of masses \cite{Einstein_1922}.
In this way, in general relativity the metric results perturbed, as if it is a deformable object.
In cosmology, the expanding space could be considered as a field-object that dilates (deforms) in any directions.
There is a deep connection between the object electromagnetic field and the construction of the ST using the empirical definitions of time (remote synchronization of clocks) and space (spatial distances between distant objects) realized using light signals.
In this way we can say that light and space-time are inseparable. So, while the relativity principle describe a symmetry possessed by the spacetime (invariance of physics laws under rotations), the constance of the speed of light \(c\) may express a fundamental characteristic connected to the nature of spacetime.
Indeed, starting from the relativity principles, we can observe that any observer use only one Space-Time lattice whose structure constant could assume the same value in any reference system in relative motion (let you remember Lorentz transformations connect different orientations of 4-dimensional space in two different reference systems).
If the speed of light became a structure constant, then the ST could acquire the status of physical object, and we indicate it like spacetime lattice.
We observe that the speed of any physical object is absolute when it expresses a relationship between physical variables that are different from space and time.
This happens only in one case: in the propagation of a wave within an elastic medium, where the wave speed depends on the inertial, \(\rho\), and elastic characteristics of the medium, \(T\). \[\label{eq_wavespeed}
v^2 = \frac{T}{\rho}\] Certainly, the elastic medium is not the ether; therefore we must admit that the elctromagnetic field has some elastic and inertial properties, and works in itself as its own medium.
Indeed, if the dielectric constant \(\varepsilon_0\) is put in a correspondence with the elastic constant, and the magnetic constant \(\mu_0\) in correspondence with inertial constant, we can write: \[c^2 = \frac{1}{\varepsilon_0 \mu_0}\] This formula allows us of treating the velocity \(c\) as a structure constant of the physical system constituted by the electromagnetic field and spacetime.
In this way the close connection between particles and ST lead us to affirm that particles express the object ST and vice versa.
At this point, we must note that the relations (interactions) between particles determine the fundamental characteristics that we denote, in epistemological terms, like time and space, and, in experimental terms, the measure of time (with a clock) and space (with a ruler) in a given reference system consisting of objects. In this way the ST is deeply rooted in what we refer as particle-fields.
Let us now to recall that in electrodynamics the interactions between two electrons is meadiated by a mediator (the electromagnetic field), and it is expressed by reciprocal influences (coupling) between the particle and the mediator. So while considering that the electron is a fermion (a spinor \(\psi_i\)) and the photon is a boson (a 4-vector \(A_\mu\)), we could admit a common basic structure of the respective oscillators field that allows the coupling between fermions and bosons: in this way we intend that there must be a connatural structure between fermion (agent) and boson (inetrmediary agent).
Estending this common and innate basic structure to any kind of interaction, we may assume that all the particles can be considered as different empirical expressions (or physical states) of a single, basic object-field (see the processes of pair creation and annihilation). We call it Structure hypothesys.
So we say that the universe is an object whose physical nature is to be a field from which emerge the different particles like articulated structures of basic oscillators, while the spacetime, that is their latter, is the fundamental structure of the universe-field.