deletions | additions       diff --git a/Space Time field.tex b/Space Time field.tex  new file mode 100644  index 0000000..ec3dcf3  --- /dev/null  +++ b/Space Time field.tex 
...
\section{The Space-Time field}   \subsection{The Space-Time field}\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 \emph{objective reality}, then also time and space shall objectively be considered as a unique \emph{real thing}.\\   So we'll call about \emph{Space-Time Object}, and also we will intend the universe, like a set of particle-fields, as a \emph{field} which nature is based on \emph{Space-Time} (ST).\\   In order to explain the nature of \emph{physical object} assigned to ST (and to the whole universe) we recall some fundamental characteristics:   \begin{enumerate}   \item The ST object is described like a 4-dimensional manifold $S^* (x,y,z,t)$, a space-time lattice, where   \begin{quote}   le proprietà geometriche (metrica) sono collegate agli oggetti e ai relativi fenomeni\footnote{trovare la citazione (e la fonte) originale} \cite{Einstein_1922}   \end{quote}   In this way, in general relativity the metric results \emph{perturbed}, as if it is a \emph{deformable object}.   \item In cosmology, the expanding space could be considered as a \emph{field-object} that dilates (\emph{deforms}) in any directions.   \item There is a deep connection between the \emph{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.   \end{enumerate}   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 one ST \emph{lattice} whose \emph{structure constant} must assume the same value in any Referenca System in relative motion (Lorentz transformations connect different orientations of 4-dimensional space in two different reference system).\\   If the speed of light became a structure constant, then the ST could acquire the \emph{status} of \emph{physical object}, and we indicate it like \emph{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 ($T$) of the medium.   \begin{equation}   v = \frac{T}{\rho}   \end{equation}   Certainly, the elastic medium is not \emph{the ether}; therefore we must admit that the elctromagnetic field has some \emph{elastic} and \emph{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, to write:   \begin{equation}   c^2 = \frac{1}{\varepsilon_0 \mu_0}   \end{equation}   The velocity $c$ is not described by spatial or temporal characteristics, that are relative, and so it could assume the \emph{absolute} role of \emph{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 \emph{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 \emph{influences} (coupling) between the particle and the mediator. So while considering that the electron is a fermion and the photon is a boson, we must admit a common basic structure of the respective oscillators field that allows the \emph{coupling} between fermions and bosons. Estending this common and \emph{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 \emph{object-field} (see the processes of pair creation and annihilation).\\   So we say that the universe is an \emph{object} whose physical nature is to be a \emph{field} from which emerge the different particles like articulated structures of \emph{basic oscillators}, while the spacetime, that is their latter, is the fundamental structure of the \emph{universe-field}.   %   \subsubsection{The intrinsic quantum oscillators}\label{iquo}   %   As you know, the most elementary field structure (whatever may be its nature) is the scalar field: any observer will represent the object "universe-field", in its most basic form, using a scalar, which we denote by $\Xi$. It's obvious that $\Xi$ will be represented in any reference system by the scalar field $\Xi (x, y, z, t)$, where $(x, y, z, t)$ are the coordinates defined in that reference system. Therefore to treat the Universe-(ST) as an "object-field" we start to define an elementary scalar field $\Xi$, whose basic oscillators will be called Intrinsic Quantum Oscillator (IQuO) \cite{iquo2012}. The scalar field $\Xi$ is contituted by a set of 1-dimensional chains af IQuO elastically coupled, where the \emph{quanta} associated to this \emph{Fundamental Field} can propagate.\\   An analogy could be more useful to understand better this definition: