Quantum Tunneling of Dark Matter

According to the uncertainty principle of quantum mechanics, a car can in principle pass through a brick wall intact. But since the car is a massive object, the chance of that happening is negligibly small. However, elementary particles have a higher likelihood for quantum tunneling through a barrier. This is because they are not localized as well as a massive object, and the wave function that characterizes the probability distribution of their uncertain location has an extended tail that could surpass the obstacle.

Thankfully, nuclear fusion in stellar interiors is made possible by quantum tunneling through the electric-repulsion barrier between the fusing nuclei. Heavy elements, like oxygen and carbon, that are essential for life, would have never been created in stellar interiors without the uncertainty principle of quantum mechanics at play. In short, we owe our existence to quantum mechanics.

But could quantum tunneling also be of cosmological significance? In a new paper, I showed that if dark matter was made of ultra-light particles, then quantum tunneling would have allowed these particles to evaporate from the gravitational potential wells that bind them to dwarf galaxies within the halo of the Milky-Way.

In classical physics, the tidal gravity of the Milky-Way can rip apart dark matter particles only if they reside in the outskirts of these satellite galaxies. But in quantum mechanics, even particles that are gravitationally bound interior to the cores of these satellites, could tunnel through the gravitational barrier that binds them. The tunneling probability is high for low-mass particles whose wave function is spread by the uncertainty principle over a large distance.

The popular paradigm of cold-dark-matter predicts divergence of the mass density through so-called “cusps” at the centers of all galaxies, but observations imply smoother density profiles than expected. To relieve the tension between theory and observations, it was suggested that perhaps dark matter is made of very light particles for which the uncertainty principle is smoothing the innermost density profile at the centers of galaxies.

For that to be the case, the dark matter particles must have a mass that is 31 orders of magnitude smaller than that of a proton. My new paper shows that if the dark matter particles had this mass, they would have tunneled out of the potential well of dwarf galaxies within the Milky-Way halo.

Quantum mechanics was constructed to explain the behavior of the smallest systems we know, such as elementary particles bound in atoms. But its universal principles can be used to study some of the largest bound systems we know, galaxies. This is no surprise, since the small and the big are all obeying the same universal principles of physics.

We could in principle detect quantum tunneling in our daily routines. If we hit enough tennis balls with a racket, we will find that one of them goes through the racket because of quantum tunneling. But this would require many more balls than we can bounce over the age of the universe. Some events are just too rare for us to witness them. But just as with winning the lottery, we know that they could happen in principle, as they do for fusing nuclei or dark matter particles.

According to the Ancient Greek legend, Sisyphus was condemned by the gods for eternity to repeatedly roll a boulder up a hill only to have it roll down again once he got it near the top. In his philosophical essay titled “The Myth of Sisyphus”, Albert Camus used this story as a metaphor for our persistent struggle against the essential absurdity of life. In enabling tunneling, Quantum Mechanics removes the need for this existential struggle. It asserts that if we just keep waiting with patience, the boulder will end up on the other side of the hill by itself. Perhaps we should just relax, enjoy life at the bottom of the hill and let nature do the rest.

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 chairs the advisory board for the Breakthrough Starshot project, and 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.

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Avi Loeb

Avi Loeb is the Frank B. Baird Jr Professor of Science and Institute director at Harvard University and is the bestselling author of “Extraterrestrial”.