So the transverse coupling builds a massive lattice in \(\Xi\) which represents a massive particle \(\Xi_i^0\). The particles walking across the universe are structured like coupling of chains \(\Xi_i\) of intrisic quantum oscillators, belonging to the basic field \(\Xi\) (see structure hypothesys). Thus we think that the particle is coincident with a particular structure of IQuO chains coupling of base fields \(\Xi_i^0\), \(\Xi_i\).
The birth of massive particles in the scalar field \(\Xi^0\) of the object-universe or the birth of \(\Xi_i\)-lattice means that the universe can be expressed by \(\Xi^0\) or by \(\Xi\).
The field that represents the universe as a spacetime object, that we call universe’s spacetime field, is generically denoted by \(\Xi_U \equiv (\Xi^0, \Xi)\).
But we must not believe that \(\Xi\) is a sort of elastic ether pervading an absolute space: we remember that this has been refuted by the theory of relativity, because it is itself the spacetime.
Remembering that coupling massive introduces a local reference system \(\Sigma_0\) with a motion in the proper time \(\omega_0\) and the birth of a spatial dimension \(\lambda_0\), then we can consider the universe as set \(\Sigma_U\) of the local reference systems \(\Sigma_i\), associated with massive particles.
The symmetry group of the universe based on the IQuOs’ lattices is the Poincare group.
For every set of particles, we are able to build a whole RS with a its proper time \(\tau_c\) and a its proper space \(\lambda_c\), that are properties of the RS itself. Now, we can build a whole RS for every galaxy and extend it to the whole universe. The RS of the universe coincides with the comovent RS \cite{zeldovic1983}, with a proper cosmic time, that is the age of the universe. The comovent RS coincides with the spacetime lattice of the universe asoociated to the field \(\Xi_U\).
At the other hand to every set of identical particles with mass \(m_i\) we can connect a lattice of IQuO’s chains (with a further coupling to the structure of \(\Xi\)), that we call \(U_i\), with spatial rate \(\lambda_i\) and time rate \(\tau_i\) given by: \[\label{eq_iquolattice}
\left\{\begin{matrix}
\tau_i & = & \frac{\hbar}{m_i c^2}\\
\tau_i & = & \frac{\lambda_i}{c}
\end{matrix}\right.\] Similarly we can build a layer \(U\) for the whole universe, that is constituted by the set of the layers \(U_i\).