  Our Universe is described jointly by Einstein's relativity principle and the
quantum principle; there the existence of the smallest units of matter, such as
electrons, neutrinos, quarks, and photons, is well established and the smallest
units of matter are described by the Standard Model. Based on these, we have a
clear picture for the propagation of ultra high energy cosmic rays (UHECR's),
for energies greater than $E > 10^{13}\, eV$ but less than $E < 10^{26}\, eV$,
in the cosmic medium of the Cosmic Microwave Background (CMB) and of the cosmic
background neutrinos (CB$\nu$'s). We find that the CMB plays a pivot role in
this energy range, so that the observed "knee(s)" and the "ankle" could be
understood in reasonable terms. What we might observe at the energy near
$10^{25}\,eV$', the so-called "$W^\pm$ bursts" or "$Z^0$ bursts", is briefly
discussed. Meanwhile, in the early Universe, the CB$\nu$'s, in view of the tiny
neutrino mass, gave rise to the clustering phenomenon, resulting in a neutrino
halo attached to each visual ordinary-matter object, such as the Earth, the
Sun, and stars - with the $PeV$ neutrinos near the surface of the Fermi-Dirac
sphere of the neutrino halo of the Earth playing the most fundamental role.
