It’s good now and then to let the imagination soar. Don Wilkins has been poking into the work of Carlo Rovelli at the Perimeter Institute, where the physicist and writer explores unusual ideas, though perhaps none so exotic as white holes. Do they exist, and are there ways to envision a future technology that can exploit them? A frequent contributor to Centauri Dreams, Don is an adjunct instructor of electronics at Washington University, St. Louis, where he continues to track research that may one day prove relevant to interstellar exploration. A white hole offers the prospect of even a human journey to another star, but turning these hypothesized objects into reality remains an exercise in mathematics, although as the essay explains, there are those exploring the possibilities even now.

by Don Wilkins

Among the many concepts for human interstellar travel, one of the more provocative is an offspring of Einstein’s theories, the bright twin of the black hole, the white hole. The existence of black holes (BH), the ultimate compression stage for aging stellar masses above three times the mass of our sun, is announced by theory and confirmed by observation. White holes, the matter spewing counterparts of BHs, escape observation but not the explorations of theorists.

Carlo Rovelli, an Italian theoretical physicist and writer, now the Distinguished Visiting Research Chair at the Perimeter Institute, discusses all this in a remarkably brief book called, simply, White Holes (Riverhead Books, 2023) wherein he travels in company with Dante Alighieri, another author with experience at descents into perilous places. Rovelli makes two remarkable assertions. [1]

1) Rovelli states that another scientist, Daniel Finkelstein, demonstrated that Einstein and other analysts are incorrect when they depict what occurs as one enters a black hole. From the Finkelstein paper (citation below):

The gravitational field of a spherical point particle is then seen not to be invariant under time reversal for any admissible choice of time coordinate. The Schwarzschild surface, r=2m is not a singularity but acts as a perfect unidirectional membrane: causal influences can cross it but only in one direction. [2]

In other words, no time dilation, no spaghettification of trespassers entering a black hole. Schwarzchild’s solution only applies to distant observers; it does not describe the observer crossing the event horizon of the black hole.

2) Rovelli believes in the existence of white holes. His white hole births when the black hole compresses its constituent parts into the realm of quantum mechanics. Rovelli speculates “… a black hole … quantum tunnels into a white one on the inside – and the outside can stay the same.”

In Figure 1 and Rovelli’s intuition, a quantum mesh separates the black hole and white hole. At these minute dimensions, quantum tunneling effects surge matter away from the black hole, into the mouth of the white hole and back into the Universe.

Figure 1. Relationship between a black hole and a white hole. Credit: C. Rovelli/Aix-Marseille University; adapted by APS/Alan Stonebraker.

The outside of a black hole and a white hole are geometrically identical regardless of the direction of time. The horizon is not reversible under the flow of time. As a result the interiors of the black hole and white hole are identical.

In a paper he co-authored with Hal Haggard, Rovelli writes:

We have constructed the metric of a black hole tunneling into a white hole by using the classical equations outside the quantum region, an order of magnitude estimate for the onset of quantum gravitational phenomena, and some indirect indications on the effects of quantum gravity. [3]

Haggard and Rovelli acknowledge that the calculations do not result from first principles. A full theory of quantum gravity would supply that requirement.

Figure 2: Artist rendering of the black-to-white-hole transition. Credit: F. Vidotto/University of the Basque Country. [9]

Efforts to design a stable wormhole require buttressing the entrance or mouth of the wormhole with prodigious amounts of a hypothesized material, negative matter. Although minute amounts have been claimed to form in the narrow confines of a Casimir device, ideas on how to manufacture planetary-sized masses of negative matter are elusive. [4]

According to recent research, the stability of the WH is dependent upon which of the two major families of matter, bosons or fermions, forms the WH. Bosons are subatomic particles which obey Bose-Einstein statistics and whose spin quantum number has an integer value (0, 1, 2, …). Photons, gluons, the Z neutral weak boson and the weakly charged bosons are bosons. The graviton, if it exists, is a boson. Theoretic analysis of stable traversable WHs founded on bosonic fields demonstrates a need for vast amounts of negative matter to hold open the mouth of a WH.

The other family, the fermions, have odd half-integer (1/2, 3/2, etc.) spins. These particles, electrons, muons, neutrinos, and compound particles, obey the Pauli Exclusion Principle. It is this family that is employed by a team of researchers to describe a two fermion stable white hole [5]. Their configuration produces John Wheeler’s “charge without charge”, where an electric field is trapped within the structure without any physical electrical charge present. The opening in the white hole would be too small, a few hundred Planck lengths (a Planck length is 1.62 x 10-35 meters) to pass gamma rays.

Rovelli reenters the discussion here. [6] The James Webb Space Telescope has identified large numbers of black holes in the early Universe, more black holes than anticipated. Rovelli describes white holes forming from these black holes as Planck-length sized, chargeless entities, unable to interact with the matter except through gravity. In other words, the descendants of the early black holes manifest as the material we describe as dark matter. Rovelli is working on a quantum sensor to detect these white holes.

Once the white holes are detected, it might be possible to capture a white hole. John G. Cramer, professor emeritus of physics at the University of Washington in Seattle, Washington, suggests accelerating the wormhole to almost the speed of light. [7] Aimed at Tau Ceti, he predicts:

The arrival time as viewed through a wormhole is T’ = T/γ , where γ is the Lorentz factor [γ= (1- v/c)] and v is the wormhole-end velocity after acceleration. For reference, the maximum energy protons accelerated at CERN LHC have a Lorentz factor of 6,930. Thus, the arrival time at Tau Ceti of an LHC-accelerated wormhole-end would be 15 hours….Effectively, the accelerated wormhole becomes a time machine, connecting the present with an arrival far in the future.

Spraying accelerated electrons through the wormhole could expand the mouth to a size where it could be used as a sensor portal into another star system. The wormhole becomes a multi light-year long periscope, one that scientists could bend and twist to study up close and in detail the star and its companions. Perhaps the wormhole could be expanded enough to pass larger, physical bodies.

Constantin Aniculaesei and an international team of researchers may have overcome the need for an accelerator as large as the LHC to accelerate the white hole to useful size [8]. Developing a novel wakefield accelerator, wherein an intense laser pulse focused onto a plasma excites nonlinear plasma waves to trap electrons, the team’s machine produced 10 Giga electron Volt (GeV) electron bunches. The wakefield accelerator was only ten centimeters long, although a petawatt laser was needed to excite the wakefields.

Cramer hypothesizes that fermionic white holes formed immediately after the Big Bang and in cosmic rays. The gateways to the stars could be found in the cosmic ray bombardment of the Earth or possibly trapped in meteorites. The heavy particles, if ensnared on Earth, would probably sink to the center of the planet.

All that is needed to find a fermionic white hole, Cramer suggests, is a mass spectrometer. But let me quote him on this:

[Wormholes] might be a super-heavy components of cosmic rays….They might be trapped in rocks and minerals….In a mass spectrograph, they could in principle be pulled out of a vaporized sample by an electric potential but would be so heavy that they would move in an essentially undeflected straight line in the magnetic field. …wormholes might still be found in meteorites that formed in a gravity free environment.

The worm hole is essentially unaffected by a magnetic field. A mass detector would point to an invisible mass. The rest, as non-engineers like to say, is merely engineering.

If this line of reasoning is correct – a very large if – enlarged white holes could pass messages and matter through tunnels in the sky to distant stars.

References

1. Carlo Rovelli, translation by Simon Carnell, White Holes, Riverhead Books, USA, 2023

2. David Finkelstein, Past-Future Asymmetry of the Gravitational Field of a Point Particle, Physical Review, 110, 4, pages 965–967, May 1958, 10.1103/PhysRev.110.965

3. Hal M. Haggard and Carlo Rovelli, Black hole fireworks: quantum-gravity effects outside the horizon spark black to white hole tunneling, 4 July 2014, https://arxiv.org/pdf/1407.0989.pdf

4. Matt Visser, Traversable wormholes: Some simple examples, arXiv:0809.0907 [gr-qc], 4 September 2008.

5. Jose Luis Blázquez-Salcedo, Christian Knoll, and Eugen Radu, Traversable Wormholes in Einstein-Dirac-Maxwell theory, arXiv:2010.07317v2, 12 March 2022.

6. What is a white hole? – with Carlo Rovelli, The Royal Institution, https://www.youtube.com/watch?v=9VSz-hiuW9U

7. John G. Cramer, Fermionic Traversable Wormholes, Analog Science Fiction & Fact, January/February 2022.

8. Constantin Aniculaesei, Thanh Ha, Samuel Yoffe, et al, The Acceleration of a High-Charge Electron Bunch to 10 GeV in a 10-cm Nanoparticle-Assisted Wakefield Accelerator, Matter and Radiation at Extremes, 9, 014001 (2024), https://doi.org/10.1063/5.0161687

9). Rovelli, “Black Hole Evolution Traced Out with Loop Quantum Gravity,” Physics 11, 127 (December 10, 2018).
https://physics.aps.org/articles/v11/127