Do particles with negative masses exist? If so, they would have dramatic implications for fundamental physics as well as for technologies of our future.
This morning, it occurred to me that if negative mass particles existed, then the mass of astrophysical black holes would have diverged rapidly in contradiction to observational data.
Astrophysical black holes are born in two families. One stems from the gravitational collapse of the cores of massive stars, after the stars consume the nuclear fuel which supports them against gravity. These stellar-mass black holes span the mass range between a few to a few hundred solar masses based on data collected by gravitational-wave observatories and X-ray telescopes. The second family includes supermassive black holes which form as a result of the flow of gas towards the centers of galaxies. These massive beasts are observed to have masses between a fraction of a million solar masses and up to tens of billions of solar masses.
In 1974, Stephen Hawking realized that black holes evaporate by emitting thermal radiation. This radiation is characterized by a wavelength that is comparable to the size of the black hole horizon. This emission process makes sense, since the spacetime prison bounded by the event horizon of a black hole cannot trap a plump prisoner whose size is bigger than the separation between the prison walls. Vacuum fluctuations with long wavelengths materialize and escape from the event horizon. The leaking radiation carries energy that reduces the black hole mass over time. The temperature of the radiation increases as the black hole mass declines, since the horizon size scales with black-hole mass and corresponds to shorter-wavelengths at lower masses.
When the Hawking temperature reaches the rest-mass energy of massive particles, like the electron or its antiparticle — the positron, the black hole emits electron-positron pairs. However, at lower temperatures the emission of pairs is suppressed exponentially by the ratio between the electron rest-mass energy, mc², and the thermal energy, kT. This exponential suppression factor represents the reduced probability for obtaining a thermal vacuum fluctuation of the required energy, and is called the Boltzmann suppression factor, exp{-mc²/kT}.
But if negative mass particles existed, then their emission probability would have been enhanced exponentially at temperatures below their rest-mass energy, because of the sign reversal in the Boltzmann factor, exp{mc²/kT}. What used to be a Boltzmann suppression factor for positive-mass particles turns into a Boltzmann amplification factor for negative-mass particles. Through the emission of negative mass particles, the black hole mass would have grown and the Hawking temperature decreased, making the Boltzmann amplification factor even larger. As the mass-growth rises and the Hawking temperature declines, the Boltzmann amplification accelerates. This runaway process would have led to the rapid divergence in the masses of astrophysical black holes, which is not observed in the Universe. Hence, particles with a negative mass that is much larger in magnitude than the Hawking temperature of the most massive astrophysical black holes, 10^{-18} degrees Kelvin, do not exist in nature.
The possible existence of exotic matter with negative-mass particles was speculated in the past as a means for constructing traversable wormholes, time machines, or faster-than-light travel. As far as we know, these possibilities are excluded if only matter with positive-mass particles exists.
In a new paper that I wrote with Mark Hertzberg and Aidan Morehouse, just published in the prestigious journal Physical Review, we showed that massive faster-than-light particles, called tachyons, are also ruled out by the stability of astrophysical black holes to Hawking radiation.
As is commonly known, physical reality does not admit all figments of our imagination. This feature distinguishes physics from mathematics or philosophy. Many beautiful ideas lose their vitality under the guillotine of experimental data. To the dismay of science fiction writers, as far as we know — the speed limit for interstellar travel is the speed of light. In contrast to the speed limit on a highway, the laws of physics cannot be broken.
Whether there are other forms of exotic matter that assist interstellar travel might be known to extraterrestrial scientists. The oldest cosmic civilizations might have benefited from billions of years of science and technology that allowed them to figure out the constituents of the Universe by now. We urgently need their advice on the nature of dark matter and dark energy, which are unknown to us earthlings. A week ago, the earliest galaxy from the Webb telescope data was announced in a new paper. The galaxy, named MoM-z14, existed 280 million years after the Big Bang. Its discovery is consistent with the theoretical prediction in my decade-old textbook, that the first stars formed as early as 100 million years after the Big Bang. MoM-z14 formed at least 8.9 billion years before the Sun and any civilization that may have emerged in it, had plenty of time to figure things out before humans appeared on the cosmic scene. With that perspective in mind, it is utterly inappropriate for us to imagine that we are at the top of the cosmic food chain.
ABOUT THE AUTHOR
Avi Loeb is the head of the Galileo Project, founding director of Harvard University’s — Black Hole Initiative, director of the Institute for Theory and Computation at the Harvard-Smithsonian Center for Astrophysics, and the former chair of the astronomy department at Harvard University (2011–2020). He is a former member of the President’s Council of Advisors on Science and Technology and a former chair of the Board on Physics and Astronomy of the National Academies. He is the bestselling author of “Extraterrestrial: The First Sign of Intelligent Life Beyond Earth” and a co-author of the textbook “Life in the Cosmos”, both published in 2021. The paperback edition of his new book, titled “Interstellar”, was published in August 2024.
