**Articles & Reviews**

###### Authored by RSF Research Staff

# Black holes as elementary particles — revisiting a pioneering investigation of how particles may be micro black holes.

By: William Brown

The idea of particles being tiny black holes may at first pass seem strange, yet even within the canonical model of particle physics elementary particles like electrons and quarks are taken to have mass yet occupy zero-dimension. In fact, because of the self-energy of a point-particle, leptons have infinite bare mass and infinite bare charge -- vacuum fluctuations are needed to shield these infinite values. Such a point-particle is a singularity, or in more common parlance a black hole.

So why then are elementary particles not commonly viewed as micro black holes? One reason is that quantum field theory treats particles as extended probabilistic objects, which do not exist except as a superposition of states -- so they are not truly point-particles since they don't actually occupy any specific point in space. Yet, the same theory stipulates that upon collapse of the wavefunction a particle will return to a point-like position, and we are back at a singularity. Even within string theory, there are close parallels between strings, their behavior as branes, and singularities or black holes.

Another argument is that micro black holes could not possibly exhibit any of the characteristics observed of elementary particles -- and while this is taken as a basic assumption, actual investigations into the matter have shown that micro black holes can in fact exhibit many of the characteristics observed in elementary particles.

For example, in the study Hadrons as Kerr-Newman Black Holes, by Robert Oldershaw of Amherst College, the logical argument and empirical self-consistency of a 'particles-as-black holes' model is evaluated (note, a hadron is a "composite" subatomic particle, such as a proton, neutron, or meson):

*The scale invariance of the source-free Einstein field equations suggests that one might be able to model hadrons as “strong gravity” black holes, if one uses an appropriate rescaling of units or a revised gravitational coupling factor.*

*For the case of hadrons, it is at least logically possible that the gravitational coupling between matter and the geometry of space-time is much stronger than for macroscopic systems. The value of the gravitational coupling factor has never been measured within an atom or a subatomic particle. The standard use of the Newtonian value in this domain is based purely on an untested assumption.*

*One might well ask whether there are observational data or theoretical results that support the “strong gravity” hypothesis. In fact there is some interesting evidence that is consistent with this unorthodox idea. As discussed in detail by Sivaram and Sinha (1977), hadrons and Kerr-Newman black holes share an intriguing set of similarities.*

*Both hadrons and Kerr-Newman black holes are almost entirely characterized by just three parameters: mass, charge and angular momentum.**Both hadrons and Kerr-Newman black holes have magnetic dipole moments, but do not have electric dipole moments.**Typical hadrons and Kerr-Newman black holes have gyromagnetic ratios of 2.**Hadrons and Kerr-Newman black holes have similar linear relationships between angular momentum and mass squared.**When Kerr-Newman black holes interact, their surface areas may increase but can never decrease, which is potentially analogous to the increase of cross-sections found in hadron collisions.*

*Given these curious similarities between the fundamental characteristics of hadrons and Kerr-Newman black holes, there appears to be sufficient motivation for considering the “strong gravity” approach to hadrons.*

### Einstein's Singularity and Wheeler's Quantum Geometrodynamics

In 1935, Albert Einstein and Nathaniel Rosen addressed the issue of the "particle as singularity" in the renowned paper "the particle problem in the general theory of relativity". Einstein and Rosen wanted a theory that got rid of the point-particle singularity and described material particles purely from the gravitational solution of general relativity and Maxwell's solutions of electromagnetism -- a unified theory.

To this end, they imagined a path tracing radially inward to the singularity. Instead of trying to cross the event horizon and proceed down to the center, Einstein and Rosen showed how to match the path onto another track that emerges outward again–but into a separate section of spacetime. Imagine funnel shapes pulled out of two adjacent rubber sheets and connected at their necks, providing a continuous, tube-shaped path from one surface to the other. This construction makes a smooth connection or bridge between two distinct pieces of spacetime. The Einstein-Rosen bridge was formed.

Nearly 20 years later the preeminent physicist John Archibald Wheeler revisited Einstein and Rosen's unification scheme, and formed the field of quantum geometrodynamics. Wheeler described how an extremely stong electromagnetic field would curve spacetime to such a strong degree it would curve back on itself, forming a torus (like a photon ring), and at the dimensions of the quantum scale would form a micro black hole.

Such an object would be indistinguishable from a particle: what Wheeler termed a gravitational electromagnetic entity, or Geon. It would have mass and charge even though these were not intrinsic characteristics of the field before forming the micro black hole, they would become an effective consequence of the spacetime geometry.

Similar to the Einstein-Rosen bridge, Wheeler described these geons as particle pairs connected by a spacetime bridge, or wormhole: the Wheeler wormhole was formed. Recently, in a study investigating the geometry of entanglement (ERb = EPR) calculations have predicted the formation of a Wheeler wormhole particle pair via the holographic Schwinger effect.

While the majority of physicists in the unification regimes veered away from quantum geometrodynamics in favor of string theories, work continued on the idea. In 1968 Brandon Carter showed that a black hole with the same mass, charge, and angular momentum as an electron would match the observed magnetic moment of the electron. This is an important finding because calculations that do not include general relativity and treat the electron as a small rotating sphere of charge give a magnetic moment that is off by roughly a factor of 2.

In 2008 a study investigating "a scenario for strong gravity in particle physics" found that Unruh-Hawking evaporating black holes will undergo a type of phase transition resulting in variously long-lived quantized objects of reasonable sizes, including those of particles within the quantum domain. Again, this led to speculation that perhaps everything is made of micro black holes.

in 2012, Nassim Haramein discovered (continuing from earlier work) that the confinement force of a hadron and nucleus can be exactly described from the gravitational force of a Schwarzschild proton (a black hole with the same diameter of a proton), with no need for the *post hoc* addition of a contrived strong force.

Even though such calculations demonstrate that micro black holes recapitulate the characteristics observed of elementary particles, and can actually described the generation of intrinsic characteristics like mass, charge, and spin from first principles -- the idea of micro black holes receives strong criticism.

In a 1992 paper, Christoph Holzhey and Frank Wilczek investigated how certain black holes can reasonably be interpreted as behaving like normal elementary particles:

"Is there a fundamental distinction between black holes and elementary particles? The use of concepts like entropy, temperature, and dissipative response in the description of black hole interactions makes these objects seem very different from elementary particles. This has helped inspire some suspicion that the description of the holes may require a departure from the fundamental principles of quantum mechanics. However a more conservative attitude is certainly not precluded. In the bulk of this paper, we shall analyze a particular class of black hole solutions (extremal dilaton black holes) in some detail, and argue that some of these do in fact appear to behave very much as elementary particles." -- Black Holes as Elementary Particles

While our discussion here does not by any means exhaust the entirety of the sources and information that can be presented on this topic, it should give general insight into the work that has been performed investigating the question of micro black holes as elementary particles.

Note: Frank Wilzcek has a recent article posted on Quanta magazine discussing topological quantum computing with anyons.

Read more at: https://arxiv.org/pdf/hep-th/9202014.pdf

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