In September 2011, the OPERA experiment at CERN reported that neutrinos travel faster than light. Nearly two hundred papers tried to make sense of the results in terms of new physics. In July 2012, the experimentalists corrected their conclusion after further analysis and declared that the speed of neutrinos is consistent with the speed of light. The mistake was traced to the experimental hardware. The error resulted from a loose fiber cable that linked a GPS receiver to the OPERA master clock, increasing the time delay through the link.
In retrospect, this correction should have been anticipated. The discovery of stable black holes demonstrates that neutrinos cannot travel faster than light. The argument, as explained below, is straightforward.
Black holes are extreme structures of spacetime that form when matter collapses towards a point and leaves behind empty space. Karl Schwarzschild derived in January 1916 the final state of such a collapse as a static solution to Albert Einstein’s equations of General Relativity, which were published just a couple of months earlier. The central point singularity is surrounded by an event horizon, a spherical surface at a radius of GM/c^2, where M is the mass that fell in and c is the speed of light. The Schwarzschild radius of the event horizon is 3 kilometers for a solar mass. Schwarzschild’s solution implies that no particle moving below or at the speed of light can escape the interior of the event horizon.
However, faster-than-light neutrinos would be able to escape from this spacetime prison. What would be the consequences of that?
After the core of a massive star consumes its nuclear fuel, it loses pressure support and collapses under its own gravity. For pedagogical simplicity, let us imagine this stellar core to be a sphere with a uniform density of matter. As the sphere collapses, it would remain uniform as long as the contraction speed of each interior shell is proportional to its distance from the center. This means that all parts of the sphere will reach the center at the same time in a Big Crunch. This synchronized fate resembles the time reversal of cosmic expansion after the Big Bang.
Once the outer boundary of the collapsing sphere shrinks below the Schwarzschild radius, a black hole is born, surrounded by an event horizon. Interior to the horizon, the shrinking sphere will continue to collapse until all matter reaches the central singularity at the Big Crunch. As the sphere collapses, it will follow in reverse the standard milestones of cosmic history after the Big Bang. While the collapsing sphere gets denser and hotter by gravitational compression, all particles in it will heat up to temperatures well above their rest mass and their energetic collisions would produce radiation. Eventually, the radiation would dominate the energy-mass budget and include photons, neutrinos and relativistic particles like electron-positron pairs. Eventually, protons and neutrons will break up into a hot dense soup of quarks and gluons which will heat up further as contraction continues.
If neutrinos could travel faster than light, they would be able to escape this spacetime prison. The escape of faster-than-light neutrinos would leak energy out of the black hole horizon and reduce the interior mass steadily. As neutrinos leak out, the contracting sphere of radiation at ever increasing temperature would replenish them and restore thermal equilibrium through particle collisions, possibly up to the Planck temperature. As a result, more energy would leak continuously in neutrinos out of the black hole. The steady leakage of faster-than-light neutrinos would imply that the black hole will keep losing mass.
The timescale for such an evaporation process is short since a black hole with ten solar masses has a Schwarzschild radius of 30 kilometers, the size of a large city. The light crossing time of this spatial scale is very short, merely a tenth of a milli-second. Such a time is shorter by 21.6 orders of magnitude than the age of the Universe. Faster-than-light neutrinos can quickly drain the mass of a stellar-mass black hole after the collapse of the parent stellar core, making the black hole disappear as a ghost before astronomers can observe it.
Since September 14, 2015, a century after Schwarzschild’s solution was derived, we know for certain that black holes with the masses of stellar cores are stable. The proof came from the LIGO detection of gravitational waves by a merger of such black holes. By now, there are nearly a hundred black-hole mergers detected by the LIGO-KAGRA-Virgo observatories. These stable black holes would not exist if neutrinos could travel faster than light and drain their mass.
Naively, we tend to assume that fundamental physics is best revealed by laboratory experiments on Earth. However, since fundamental physical principles are universal, whatever we conclude by looking down towards Earth must be consistent with what we discover by looking up towards the Universe.
If Karl Schwarzschild could have lived for 150 years, he would have been delighted to know that, as he predicted, stable black holes exist as a result of the collapse of massive stars. But as a Jewish German patriot, he died in World War I on May 11, 1916, merely four months after his black hole solution was published. Was the sacrifice of his life for the sake of German patriotism worth it given the holocaust of his fellow Jews just two decades later? One thing is clear: the Schwarzschild event horizon was much too short.
The discovery of a loose fiber cable in the OPERA experiment demonstrates how ingenious the Schwarzschild black hole solution is. In celebration of stable black holes as the ultimate prisons from which nothing can escape, I raised a toast last night at a restaurant dinner with my wife. The waiter recognized me and asked, “Are you Avi Loeb, the astrophysicist? I saw you on podcasts. What brand of wine would you like to have tonight?”
In celebration of stable black holes as spacetime prisons, I replied by requesting one my my favorite choices: “The Prisoner.”
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.