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\subsection{The massive coupling}\label{massive}   %   Also the mass of the particles must be expressed by a property of the "ST". We recall the general relativity where the space-time lattice (used by an observer at a given reference system) is curved by the mass of the objects. The mass thus becomes a physical characteristic (gravitational charge $\Gamma$) acting on the ST, through the gravitational field. This fact can be easily shown by using the Newtonian dynamics of gravitational forces expressed by the gravitational charge $\Gamma$. Observing a massive object in free fall on earth we have:   \begin{equation}   \left\{\begin{matrix}   F_{EO} & = & G \left ( \frac{\Gamma_E \Gamma_O}{R_{EO}^2} \right )\\   E_{EO} & = & m_g g   \end{matrix}\right.   \Rightarrow g = \left ( G \frac{\Gamma_E}{R_{EO}^2} \right ) \left ( \frac{\Gamma_O}{m_g} \right )   \end{equation}   The equivalence principle \cite{einstein1907} leaded to the equivalence between the gravitational charge $\Gamma$ and the gravitational mass $m_g$ (in this case intended as \emph{resinstance} to the gravitational force)\footnote{inserire citazione del principio formulato da Einstein?}. We must recall that a lot of experiments \cite{equivalence2008,equivalence2009,equivalence2012} shown the equivalence between the inertial mass, $m_i$, and the gravitational mass, $m_g$, so $m_i = m_g = \Gamma$ and we can conclude that the mass (inertia) $m$ of an object became a characteristics acting to the ST. So, taking into account of general relativity and and of the connatural structure of the massive particles and gravitational field, we can derive that the mass of a particle must be expressed from a fundamental property of the field $\Xi$. Now we conjecture that the mass is given by a particular \emph{elastic coupling} (a \emph{massive coupling}) between the oscillators of $\Xi$.\\   In order to understand better this conjecture we use the relativistic invariant given by the proper time $\tau$. In the Minkowsky spacetime we read the forth component of the speed, $u_4 = ic$, with $c$ speed of light, like an index for the \emph{movement in time}.\\   So we could interpret the series of events in every any system like \emph{the index of the passage of time} in it. This characteristic is associated to the massive object, because when it takes existence, \emph{time is starting to move}. It must then exist a characteristic of the object that is connected with this type of motion, rather it is its generator.\\   The \emph{uniform motion in time} recalls the clock, so it must exist \emph{into} every particle-object a periodical motion that produces the \emph{motion in time}. So we call about an \emph{internal clock} with $\omega_0$ the proper frequency, and the characteristic connected with the proper time will coincide with the proper mass $m_0$. In support of this, we recall that the hamiltonian $H$ is the generator of the motion transformations.\\   The new conception of \emph{motion in time}, with proper time, is useful to understand the notion of rest energy $E_0$: we refer to it like the \emph{energy of motion in time}.  diff --git a/layout.md b/layout.md  index c341f8b..acba7ad 100644  --- a/layout.md  +++ b/layout.md 
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introduction.tex  Space time field.tex  The intrinsic quantum oscillators.tex  The massive coupling.tex  results.tex  Tables.tex  figures/figure_1/figure_1.jpg