Realistic classical charge from an asymmetric wormhole

TL;DR

This work presents a classical mechanism to realize SM-scale mass and charge from a Planck-scale bare mass by coupling a complex spinor field and electromagnetic fields to gravity in an asymmetric, rotating wormhole setup. By solving the coupled Einstein-Dirac-Maxwell equations with a small throat and enforcing a one-particle normalization, the authors show that one wormhole end can exhibit masses and charges of SM particles while the other end remains at Planck scales. The configurations are inherently spinning, with total angular momentum obeying J = 1/2 Q_psi, and the gyromagnetic ratio g can differ significantly from the standard electron value, depending on throat size. This provides a classical analog of Wheeler’s ideas of ‘‘mass without mass’’ and ‘‘charge without charge’’ within a two-universe topology, highlighting a potential link between topology and observed particle properties.

Abstract

Within Einstein-Dirac-Maxwell theory, we consider a wormhole solution supported by a complex non-phantom spinor field with a bare mass of the order of the Planck mass (which provides a nontrivial spacetime topology and an intrinsic angular momentum), an electric field (which provides a charge of the system), and a magnetic field. This solution describes an asymmetric wormhole connecting two different asymptotically flat spacetimes (two universes) in which there are in general different observed masses and charges. It is shown that, by suitably adjusting the values of free system parameters, at one end of the wormhole, one can obtain the values of the observed mass and charge typical of the Standard Model particles, whereas at the other end of the wormhole these physical quantities acquire the Planck values. Such a configuration incarnates Wheeler's idea of ``mass without mass'' and ``charge without charge'', and can be thought of as a model of a classical charge possessing a spin.

Figures (3)

• Figure 1: The typical distributions of lines of force of the dimensionless electric, $\mathbf{\bar{E}}\equiv\sqrt{4\pi G}/m_s \mathbf{E}$, and magnetic, $\mathbf{\bar{H}}\equiv\sqrt{4\pi G}/m_s \mathbf{H}$, fields Dzhunushaliev:2025ntr. The top plots correspond to the subspace with $x>0$, while the bottom plots are for the subspace with $x<0$.
• Figure 2: The masses $M_+$ and $M_-$ (the left panel) and the electric charges $Q=Q_+=-Q_-$ (the right panel) vs. the mass of the spinor field $m_s$ are shown for different values of the throat parameter $x_0$ and with $\bar{e}=0$. The solid lines correspond to the systems in the subspace with $x>0$, while the dashed lines are for the configurations in the subspace with $x<0$. The leftmost points of the curves correspond to the systems with $\bar{\Omega}=-0.9$, while the rightmost points are for the systems with $\bar{\Omega}\to -1$ (cf. Fig. \ref{['fig_J_g']}). The bold dots label the configuration with the mass and charge of a positron.
• Figure 3: The ratio of the angular momentum $J$ to the Noether charge $Q_\psi$ (the left panel) and the gyromagnetic ratio $g$ (the right panel) vs. the spinor frequency $\bar{\Omega}$ are shown for different values of the throat parameter $x_0$ and with $\bar{e}=0$. The solid lines correspond to the systems in the subspace with $x>0$, while the dashed lines are for the configurations in the subspace with $x<0$. The bold dots label the configuration with the mass and charge of a positron.