4 Dualities Between Bosons and Fermions

It has been shown in [1] that energy of mass particles is constant from the dimensional viewpoint of $X_5$ while it is measured proportional to $\gamma$ from $X_4$ . Similarly, the energy of a photon is independent of its direction in 3D space from the dimensional viewpoint of $X_4$ but will be measured as variable from $X_3$ . Other parallels between mass particles and photons are found in their universal speed $c$ in null geodesics in, respectively, $X_5$ and $X_4$ , and potentially in the absorption process by, respectively, black holes and electrical charges. Yet, in view of these many parallels between mass particles and photons, one of the conclusions may now be that mass particles themselves are to be regarded the bosons for 5D gravity in $X_5$ , in addition to their role as fermions in $X_4$ (which is related to their electrical charge). Their invariant 4D momentum in $X_5$ , $m_0c$ or $E/c$ should be ranked hierarchically in line with the expression $p=E/c$ for the photon in $X_4$ . An inevitable conclusion from the previous Section must than be that black holes form the corresponding fermions in $X_5$ .

It is very tempting to think of the geometrical hierarchy and dualities between gravity and electromagnetism as a general principle, covering also the nuclear forces in the lower-dimensional spaces $X_3$ and $X_2$ . The author has the intention to elaborate this in future work at www.euclideanrelativity.com.