The Virtues and Risks of Slow Aging by Gravitational Time Dilation
On April 2, 2024, the Office of Science and technology Policy (OSTP) at the White House issued a memo in which it acknowledged the difference in the ticking rates of clocks between the Moon and Earth owing to gravitational time dilation.
Einstein’s General Relativity implies that time is ticking slower in a gravitational potential well. At a distance R from the center of a spherical Newtonian object of mass M, the passage of time is slowed down by a fraction GM/Rc² relative to an observer at a much larger distance, where G is Newton’s constant and c is the speed of light.
Since the Moon has a shallower potential than Earth, the lunar time ticks faster relative to an Earth-based clock by an average of 58.7 microseconds per Earth-day, with additional periodic variations. The resulting time difference must be included when synchronizing technological infrastructure on the lunar surface with Earth-based clocks. The OSTP memo tasked NASA to establish a unified standard time for the Moon and other celestial bodies by December 31, 2026.
The slight difference between the flow of time at the top and bottom of the Harvard Physics building as a result of Earth’s gravity, was measured in 1960 by Professor Robert Pound and his student Glen Rebka. They used a gamma-ray line from the radioactive decay of an iron-57 isotope, measured to a part in a quadrillion thanks to the Mössbauer effect (recoil-free nuclear resonance absorption) which was discovered by the Nobel Laureate Rudolf Mössbauer two years earlier.
Humans transported to Mars by SpaceX under the leadership of Elon Musk, will age faster than earthlings. There are two important contributions to their faster aging. One originates from the shallower gravitational potential on the surface of Mars, which causes a time drift relative to the surface of Earth by 48 microseconds per day. The second and bigger effect stems from the fact that Mars is 1.5 times farther from the Sun than Earth is, causing an additional relative drift of 284 microseconds per day or a tenth of a second per year. The relative motion of the Earth and Mars as they both orbit the Sun, adds periodic drifts in their time standards as a result of Special Relativity, but those average out over the Martian orbital period of 687 days (1.88 Earth years) around the Sun.
The Solar system offers even slower aging than can be found on Earth. For example, at the surface of the Sun, aging is slowed down by 0.18 seconds per day or 1.1 minutes per year. Of course, life-as-we-know-it cannot survive at the boiling Solar photosphere temperature of 5,800 degrees Kelvin.
Once the Sun will consume its nuclear fuel, its core will contract into a white dwarf, a metallic ball the size of Earth with a mass of about 60% that of the Sun. The white dwarf surface will cool down steadily with time and offer the benefit of aging more slowly by 11 seconds per day or 1.1 hours per year.
Stars with a mass larger than 8 solar masses collapse to a neutron star, typically with 1.4 solar masses and a radius of 12 kilometers, roughly the size of a city like Boston. On the neutron star surface, aging is slowed down by 4.1 hours per day or 2.1 months per year. This starts to offer a sizable advantage to those among us who wish to live longer than their friends.
The most massive stars with tens of solar masses collapse after a few million years into a black hole. Close to the event horizon of a black hole, time dilation can reach arbitrarily large values relative to a distant observer. This offers a great benefit to self-centered astronauts who wish to appear forever young in Instagram posts sent to their terrestrial friends. Upon returning to Earth, they could visit the graves of descendants of their friends who are long gone.
Of course, getting close to a black hole’s horizon does not come without a severe existential risk. Crossing the line of the event horizon would result in inevitable death within less than a minute even for the largest black hole in the Milky-Way galaxy, Sagittarius A*, where the horizon radius is roughly a tenth of the Earth-Sun separation.
Inside the event horizon, the radial space coordinate is transformed into time and the progression of time forward means the inevitable infall towards the black-hole singularity, where the divergent tidal force will rip apart any material body.
It is ironic that the tempting slow-aging surface of the event horizon hides an inescapable death machine inside of it. Perhaps this explains why black holes are so fascinating to humans, especially those of us who love horror movies.
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.
