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Gianluigi Filippelli edited Massive coupling.tex
over 10 years ago
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Following this account, we conjecture that the mass is the expression of the proper frequency related to a particular elastic coupling, additional to the one existing between the oscillators of the field $\Xi$.\\
If the frequency $\omega_0$ generates the proper time $\tau$ of the massive particle, for symmetry it must be exist a \emph{wavelength} $\not{\lambda}$ that generates the \emph{proper space} of the particle.\\
Following De Broglie, we have:
\begin{equation}\label{eq-lambda} \begin{equation} \label{eq:lambda}
\left\{\begin{matrix}
p_0 & = & \frac{2\pi\hbar}{\lambda_0}\\
p_0 & = & m c
...
\end{equation}
We state that \not{\lambda}_0, the Compton wavelength, defines the \emph{spatial rate} of the proper spacetime lattice of the particle. So, only when the \emph{massive} coupling is built between the \emph{oscillators} of the field $\Xi$, we can speak about proper time and proper space.\\
In this way we can assert that a massive object generates a spacetime lattice equivalent to a frame reference.\\
It is simple to deduce that lattices of particles of relative motion differ for a Lorentz transformation. Now, combining (\ref{eq-mass}) and
(\ref{eq-lambda}), (\eqref{eq:lambda}), we have:
\begin{equation}
E^2 = m^2 c^4 + p^ c^2 \; \leftrightarrow \; \omega^2 = \omega_0^2 + k^2 c^2
\end{equation}