The good thing about Poisson is its sum property which states that,
"Suppose that \(N\) and \(M\) are independent random variables, and that \(N\) has the Poisson distribution with parameter \(c\gt0\) and \(M\) has the Poisson distribution with parameter \(d\gt0\). Then \(N+M\) has the Poisson distribution with parameter c+d."
and
"Suppose that N has the Poisson distribution with parameter \(c\gt0\). Thenfor \(n\in N^+\), \(N\) has the same distribution as \(\sum_{i=1}^n N_i \) where (\(N_1,N_2,…,N_n\)) are independent, and each has the Poisson distribution with parameter \(\cfrac{c}{n}\)."
which lead us to conclude that, as \((c+d)\rightarrow 1\), \((N+M)\rightarrow A\), where \(A\) is the total number of particles in the population presenting the Poisson statistics. ie,
\(\sum_i^{A}n_{\lambda\,e\,i}=1\)
That simply,
\(A.n_{\lambda\,e}=A.p\cfrac{mc^2}{\Delta Q}=A.\cfrac{1}{2c}\cfrac{mc^2}{\Delta Q}=A.\cfrac{mc}{2\Delta Q}=1\)
\(A=2\cfrac{\Delta Q}{mc}\)
As \(p\) is derived from \(c\) along one direction, for all direction in 3D space inside a sphere,
\(A_v=\cfrac{4}{3}\pi A^3=\cfrac{32}{3}\pi \left(\cfrac{\Delta Q}{mc}\right)^3\)
\(A_v\) is the Avogadro Constant (an assumption), referring to mass measured in \(kg\).
If we replace,
\(\Delta Q=m_{\small{Q}}c^2\)
that the entanglement quantum packet has an equivalent mass (inertia), \(\small{m_{\small{Q}}}\) in the time dimension.
\(A_v=\cfrac{32}{3}\pi c^3\left(\cfrac{m_{\small{Q}}}{m}\right)^3\)
If \(A_v\) is a constant then, the ratio \(\cfrac{m_{\small{Q}}}{m}\) is also a constant.
\(6.022140e26=\cfrac{32}{3}*\pi*(299792458)^3\left(\cfrac{m_{\small{Q}}}{m}\right)^3\)
\(\left(\cfrac{m_{\small{Q}}}{m}\right)^3=\cfrac{6.022140}{9.029022}\)
\(\left(\cfrac{m_{\small{Q}}}{m}\right)^3=0.66698\)
\(\cfrac{m_{\small{Q}}}{m}=0.8737\)
which is large. This lead to the postulation that \(A_v\) is wrong, that in fact,
\(\cfrac{m_{\small{Q}}}{m}=1\)
that entanglement is collision in the time dimension of similar particles of equal mass. The time dimension became accessible at light speed. In which case, the new constant,
\(A_{\small{D}}=\cfrac{32}{3}*\pi*(299792458)^3=9.029022e26\)
shall be called the Durian constant.
Have a nice day.
