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A Supermassive Lens on the Constants of Nature

What this year’s Nobel-winning discovery of the black hole at our galaxy’s center reveals.

The 2020 Nobel Prize in Physics went to three researchers who confirmed that Einstein’s general relativity predicts black holes,…By Sidney Perkowitz

The 2020 Nobel Prize in Physics went to three researchers who confirmed that Einstein’s general relativity predicts black holes, and established that the center of our own galaxy houses a supermassive black hole with the equivalent of 4 million suns packed into a relatively small space. Besides expanding our understanding of black holes, the strong gravitational field around the supermassive black hole is a lab to study nature under extreme conditions. Researchers, including one of the new Nobel Laureates, Andrea Ghez at UCLA, have measured how the intense gravity changes the fine structure constant, one of the constants of nature that defines the physical universe, and in this case, life within it. This research extends other ongoing efforts to understand the constants and whether they vary in space and time. The hope is to find clues to resolve issues in the Standard Model of elementary particles and in current cosmology.

NOBEL LAUREATE: Andrea Ghez won science’s biggest prize for her co-discovery of a supermassive black hole in the center of our galaxy. She has also precisely defined the elliptical paths of stars orbiting the galactic center.Wikimedia Commons

Besides Ghez, the other Nobel Laureates honored in 2020 are Roger Penrose at Cambridge University, who deepened our theoretical understanding of black holes; and Reinhard Genzel, of the Max Planck Institute for Extraterrestrial Physics in Garching, Germany. Ghez and Genzel carried out parallel but separate observations and analysis that led each to deduce the presence of our galactic supermassive black hole. At 27,000 light-years away, obtaining good data required huge telescopes. Ghez worked with the Keck Observatory on Mauna Kea in Hawaii, and Genzel used the Very Large Telescope in Chile. Each researcher found that the motion of the stars they observed arose from an enormous mass at the center of the galaxy. They obtained the same value, 4 million times the mass of our sun, in a region only as big as our solar system—definitive evidence of a supermassive black hole.

Ghez’s research at Keck made her a co-author in a paper published this year, in which Aurélien Hees of the Paris Observatory and 13 international colleagues presented results for the fine structure constant near our galactic supermassive black hole. Remarkably, Ghez’s Nobel Prize-winning results supporting this research combined today’s theories and astronomical techniques with ideas dating back to Johannes Kepler and Isaac Newton to examine the motion of stars near the supermassive black hole. This is another example of Newton’s insight about how science advances when he wrote in 1675, “If I have seen further it is by standing on the shoulders of giants.”

The constant in the strong gravity near the black hole could be a clue to modifying the Standard Model.

German astronomer Kepler is one such giant who changed science when he presented his laws of planetary motion in 1609. He was the first to show that the planets do not orbit the sun in divinely inspired perfect circles, as had been assumed. The orbits are ellipses with the sun at a focus of the ellipse, one of the two points symmetrically offset from the center that define how to construct an ellipse. Kepler also found a mathematical relation between the size of a planetary orbit and how long it takes the planet to complete a circuit.

In 1687 Newton gave Kepler’s laws a deeper, more coherent physical basis. Newton’s law of gravitation, based on mutual attraction between bodies, showed that a celestial object in a closed orbit around a mass follows an elliptical path that depends on that mass. This result, which today is taught in introductory astronomy, is the heart of how Ghez found the mass of the supermassive black hole. Her years of careful observations precisely defined the elliptical paths of stars orbiting the galactic center; then she used Newton’s theory to calculate the mass at the center (general relativity, which replaces Newton’s law, predicts black holes but Newton’s approach is sufficiently accurate for the stellar orbits around the supermassive black hole). Knowledge of these orbits would be crucial for measuring the fine structure constant in the strong gravity near the supermassive black hole. How that constant depends on gravity could be a clue to modifying the Standard Model or general relativity to deal with dark matter and dark energy, the two great puzzles of contemporary physics.


This particular examination fits into a bigger, long-term examination of the fundamental constants of nature, each of which tells us something about the scope or scale of our deepest theories. Along with other constants, the fine structure constant (denoted by the Greek letter α), appears in the Standard Model, the quantum field theory of elementary particles. The numerical value of α defines how strongly photons and electrically charged particles interact through the electromagnetic force, which controls the universe along with gravity and the strong and weak nuclear forces. Among its effects, electromagnetism determines the degree of repulsion between protons and how electrons behave in an atom. If the value of α were much different from the one we know, that would affect whether nuclear fusion within stars produces the element carbon or whether atoms can form stable complex molecules. Both are necessary for life, another reason α is significant.

Other constants represent other major physical theories: c, the speed of light in vacuum, is crucial in relativity; h, the constant derived by Max Planck (now taken as “h-bar,” or ħ = h/2π), sets the tiny size of quantum effects; and G, the gravitational constant in Newton’s theory and general relativity, determines how astronomical bodies interact. In 1899 Planck used just these three to define a universal measurement system based on natural properties and not on any human artifacts. This system, he wrote, would be the same “for all times and all civilizations, extraterrestrial and non-human ones.”

It raises the notion that out of many multiverses, the one where we exist is the one with the winning value.

Planck derived natural units of length, time, and mass from c, ħ, and G: LP = 1.6 x 10-35 meters, TP = 5.4 x 10-44 seconds, and MP = 2.2 x 10-8 kilograms. Too small to be practical, they have conceptual weight. In today’s universe the gravitational interaction between elementary particles is too weak to affect their quantum behavior. But place the bodies a tiny Planck length LP apart, less than the diameter of an elementary particle, and their gravitational interaction becomes strong enough to rival quantum effects. This defines the “Planck era” 10-44 seconds after the Big Bang, when gravitational and quantum effects were of similar strength and would require a combined theory of quantum gravity instead of the two separate theories we have today.

Nevertheless, to some physicists, c, ħ, and G are not truly fundamental because they depend on units of measurement. Consider for instance that c is 299,792 km/sec in metric units but 186,282 miles/sec in English units, This shows that physical units are cultural constructs rather than inherent in nature (in 1999, NASA’s Mars Climate Orbiter fatally crashed because two scientific teams forgot to check which measurement system the other had used). Constants that are pure numbers, however, would translate perfectly between cultures and even between us and aliens with unimaginably different units of measurement.

The fine structure constant α stands out as carrying this favored purity. In 1916 it appeared in calculations for the wavelengths of light emitted or absorbed as the single electron in hydrogen atoms jumps between quantum levels. Niels Bohr’s early quantum theory predicted the main wavelengths but spectra showed additional features. To explain these, the German theorist Arnold Sommerfeld added relativity to the quantum theory of the hydrogen atom. His calculations depended on a quantity he called the fine structure constant. It includes ħ, c, and the charge on the electron e, another constant of nature; and the permittivity ε0  that represents the electrical properties of vacuum. Remarkably, the physical units in this odd collection cancel out, leaving only the pure number 0.0072973525693.

GIANT SHOULDERS: This year’s Nobel winners drew on astronomical techniques dating back to Isaac Newton, who wrote of scientific advances, “If I have seen further it is by standing on the shoulders of giants.”Nicku / Shutterstock

Sommerfeld used α just as a parameter, but it gained fame in the late 1920s when it reappeared in advanced work on relativistic quantum mechanics by the French physicist Paul Dirac, and then in what the English astronomer Arthur Eddington hoped would be a Theory of Everything. He planned to merge quantum theory and relativity to derive the properties of the universe such as the number of elementary particles in it, and its constants, α among them.

One twist in Eddington’s approach was that he considered the quantity 1/α rather than α, because his analysis showed that it must be an integer as well as a pure number. This was consistent with a contemporary measurement that yielded 1/α = 137.1, tantalizingly near 137 exactly. Eddington’s calculations gave instead 136, close enough to raise interest. Further measurements however confirmed that 1/α = 137.036. Eddington’s attempts to justify his different result were unconvincing and for this and other reasons his theory has not survived.

But α and “137” remain linked, which is why Richard Feynman called 137 a “magic number.” What he meant has nothing to do with numerology. Rather it is that we know how to measure the value of α but not how to derive it from any theories we know. This is true also for the other fundamental constants, including pure numbers such as the ratio of the proton and electron masses, and is a lack in the Standard Model. Nevertheless, the value of α is critical in quantum electrodynamics, the quantum theory of electromagnetism. Feynman fully understood this, since he earned the 1965 Nobel Prize with two other theorists for developing quantum electrodynamics.

So α is accepted as one of the important constants of nature. Now, with the values of these quantities accurately known, physicists ask, are they truly constant? In 1937, considerations about the forces in the universe led Dirac to speculate that α and G change with time as the universe ages. Another suggestive and even older speculation is to wonder whether the constants vary across the universe. In 1543, when the Polish astronomer Nicolaus Copernicus put the sun and not the Earth at the center of the universe, he moved humanity from its special cosmic location. This implies that the universe is the same everywhere, but this is only an assumption.


Varying “constants” would alter both the Standard Model and the cosmology based on it and general relativity, which among other issues fail to explain dark matter and dark energy. Add the role of α in the notion that the universe is “fine-tuned” to support life and the related idea that out of many multiverses, the one where we exist is the one with that winning value of α. All this spurs research on the constants of nature, much of it focused on α.

Earthly measurements confirm that α is fixed to within parts per tens of billions. A more challenging project is measuring it over astronomical distances. This also determines α at early cosmic times, since light from billions of light-years away took that many years to reach us from a younger universe. Since 1999, John Webb at the University of New South Wales, Australia, with colleagues has been making such measurements by gathering light from the distant galactic cores called quasars where black holes pull in dust that glows. This light traverses interstellar gas clouds and is absorbed at wavelengths characteristic of the atoms in the clouds. Analyzing the wavelengths gives α at the distant location, just as hydrogen wavelengths first defined α on Earth.

The results hint at the Copernican view that on very large scales, the universe looks much the same everywhere.

Webb’s early results showed that α has increased 0.0006 percent over the last 6 billion years or more, and that it depended on distance from the Earth. Results published in 2020 show a smaller change in α between now and 13 billion years ago, when the universe was only 0.8 billion years old, which the authors interpret as “consistent with no temporal change.” The cumulative results also suggest that α varies along different directions in space. Overall, the experimental errors are too large to inspire confidence that any single measured change in α is exactly correct, but the changes are certainly extremely small.

Now α has also been measured within a strong gravitational field, where it can theoretically change. The strongest gravity we know comes from a black hole, where a spacecraft would have to reach the unattainable speed of light to escape. But strong gravity also accompanies a white dwarf, a star that has expelled its outer layers to leave a massive but only planet-sized core. In 2013, J.C. Berengut of the University of New South Wales, with Webb and others analyzed spectral data from a white dwarf and obtained a change in α of 0.004 percent relative to the Earth.

No one, however, had measured α near a supermassive black hole until this year’s work by Hees and co-authors including Ghez. Her results from Keck helped in choosing five stars whose orbits bring them near the supermassive black hole to maximize its gravitational effects, and of a type whose spectra display strong absorption features due to the surrounding stellar atmosphere. This facilitated deriving α from the absorption wavelengths for each star. The final composite result again shows only a small change in α, of 0.001 percent or less compared to Earth.

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Although the measured change in α is small, the results for five stars at different places in the supermassive black hole gravitational field led to a new outcome; they allowed an early test of theoretical predictions that changes in α are proportional to changes in the gravitational potential, the energy stored in the gravitational field. The results confirmed that the two quantities are proportional, but uncertainties in the data supported only a rough estimate of the proportionality constant. A more reliable value could select between several new theories that treat dark matter and dark energy.

For now, the measured changes in α across time and space, and under gravity, are too small or uncertain to guide physicists toward new theories or even to fuel speculation such as the prospects for life far out in the universe or near a black hole. The smallness of the changes hints at the Copernican view that on very large scales, the universe looks much the same everywhere, although more measurements could confirm that there are real if tiny differences across the universe that might be meaningful.

It may be a kind of comfort to know that in a dynamic universe, this particular cosmic number holds steady. But seeing larger changes in α near our galactic supermassive black hole could be the starting point for new physics. As Hees described in an email interview, his goal now is to get deeper into the black hole’s gravitational field. He plans to carry out new optimized measurements in 2021 to “observe stars that are closer to the black hole and therefore that experienced a stronger gravitational potential … But with current technology, it is not easy to get good spectral observations of stars that are super close to the black hole.” Still, he believes he can reduce measurement errors by a factor of 10.

The world-class Nobel Prize work carried out by Ghez depended on vast improvements in observational and spectroscopic techniques. It is a good bet that further improvements building on this successful project will enhance research in the supermassive black hole, a unique arena to study those elusive changes in α and what they mean for how we understand the universe.


Sidney Perkowitz is the Emeritus Charles Howard Candler Professor of Physics, Emory University. His latest books are Physics: A Very Short Introduction, and Real Scientists Don’t Wear Ties. He is at work on Science Sketches.

Lead image: This illustration depicts the frenzied activity at the supermassive black hole in the core of the Milky Way, known as Sagittarius A*, or Sgr A*. Credit: ESA–C. Carreau / NASA

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