Physicists Nail Down the “Magic Number” That Shapes the Universe
Reprinted with permission from Quanta Magazine’s Abstractions blog.
As fundamental constants go, the speed of light, c, enjoys all the fame, yet c’s
numerical value says nothing about nature; it differs depending on
whether it’s measured in meters per second or miles per hour. The
fine-structure constant, by contrast, has no dimensions or units. It’s a
pure number that shapes the universe to an astonishing degree—“a magic
number that comes to us with no understanding,” as Richard Feynman
described it. Paul Dirac considered the origin of the number “the most
fundamental unsolved problem of physics.”
Numerically, the fine-structure constant, denoted by the Greek letter α (alpha), comes very close to the ratio 1/137. It commonly appears in formulas governing light and matter. “It’s like in architecture, there’s the golden ratio,” said Eric Cornell, a Nobel Prize-winning physicist at the University of Colorado, Boulder and the National Institute of Standards and Technology. “In the physics of low-energy matter—atoms, molecules, chemistry, biology—there’s always a ratio” of bigger things to smaller things, he said. “Those ratios tend to be powers of the fine-structure constant.”
“A factor of three is a big deal. Let’s not be shy about calling this a big accomplishment.”
The
constant is everywhere because it characterizes the strength of the
electromagnetic force affecting charged particles such as electrons and
protons. “In our everyday world, everything is either gravity or
electromagnetism. And that’s why alpha is so important,” said Holger
Müller, a physicist at the University of California, Berkeley. Because
1/137 is small, electromagnetism is weak; as a consequence, charged
particles form airy atoms whose electrons orbit at a distance and easily
hop away, enabling chemical bonds. On the other hand, the constant is
also just big enough: Physicists have argued that if it were something
like 1/138, stars would not be able to create carbon, and life as we
know it wouldn’t exist.
Physicists have more or less given up
on a century-old obsession over where alpha’s particular value comes
from; they now acknowledge that the fundamental constants could be
random, decided in cosmic dice rolls during the universe’s birth. But a
new goal has taken over.
Physicists want to measure the fine-structure constant as precisely as possible. Because it’s so ubiquitous, measuring it precisely allows them to test their theory of the interrelationships between elementary particles—the majestic set of equations known as the Standard Model of particle physics. Any discrepancy between ultra-precise measurements of related quantities could point to novel particles or effects not accounted for by the standard equations. Cornell calls these kinds of precision measurements a third way of experimentally discovering the fundamental workings of the universe, along with particle colliders and telescopes.
In a new paper in Nature, a team of four physicists led by Saïda Guellati-Khélifa at the Kastler Brossel Laboratory in Paris reported the most precise measurement yet of the fine-structure constant. The team measured the constant’s value to the 11th decimal place, reporting that α = 1/137.035999206.
With a margin of error of just 81 parts per trillion, the new measurement is nearly three times more precise than the previous best measurement in 2018 by Müller’s group at Berkeley, the main competition. (Guellati-Khélifa made the most precise measurement before Müller’s in 2011.) Müller said of his rival’s new measurement of alpha, “A factor of three is a big deal. Let’s not be shy about calling this a big accomplishment.”
Guellati-Khélifa has been improving her experiment for the past 22 years. She gauges the fine-structure constant by measuring how strongly rubidium atoms recoil when they absorb a photon. (Müller does the same with cesium atoms.) The recoil velocity reveals how heavy rubidium atoms are—the hardest factor to gauge in a simple formula for the fine-structure constant. “It’s always the least accurate measurement that’s the bottleneck, so any improvement in that leads to an improvement in the fine-structure constant,” Müller explained.
The Paris experimenters begin by cooling the rubidium atoms almost to absolute zero, then dropping them in a vacuum chamber. As the cloud of atoms falls, the researchers use laser pulses to put the atoms in a quantum superposition of two states—kicked by a photon and not kicked. The two possible versions of each atom travel on separate trajectories until more laser pulses bring the halves of the superposition back together. The more an atom recoils when kicked by light, the more out of phase it is with the unkicked version of itself. The researchers measure this difference to reveal the atoms’ recoil velocity. “From the recoil velocity, we extract the mass of the atom, and the mass of the atom is directly involved in the determination of the fine-structure constant,” Guellati-Khélifa said.
In such precise experiments, every detail matters. Table 1 of the new paper is an “error budget” listing 16 sources of error and uncertainty that affect the final measurement. These include gravity and the Coriolis force created by Earth’s rotation—both painstakingly quantified and compensated for. Much of the error budget comes from foibles of the laser, which the researchers have spent years perfecting.
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For Guellati-Khélifa, the hardest part is knowing when to stop
and publish. She and her team stopped the week of February 17, 2020,
just as the coronavirus was gaining a foothold in France. Asked whether
deciding to publish is like an artist deciding that a painting is
finished, Guellati-Khélifa said, “Exactly. Exactly. Exactly.”
Surprisingly, her new measurement differs from Müller’s 2018 result in the tenth digit, a bigger discrepancy than the margin of error of either measurement. This means—barring some fundamental difference between rubidium and cesium—that one or both of the measurements has an unaccounted-for error. The Paris group’s measurement is the more precise, so it takes precedence for now, but both groups will improve their setups and try again.
Though the two measurements differ, they closely match the value of alpha inferred from precise measurements of the electron’s g-factor, a constant related to its magnetic moment, or the torque that the electron experiences in a magnetic field. “You can connect the fine-structure constant to the g-factor with a hell of a lot of math,” said Cornell. “If there are any physical effects missing from the equations [of the Standard Model], we would be getting the answer wrong.”
Instead, the measurements match beautifully, largely ruling out some proposals for new particles. The agreement between the best g-factor measurements and Müller’s 2018 measurement was hailed as the Standard Model’s greatest triumph. Guellati-Khélifa’s new result is an even better match. “It’s the most precise agreement between theory and experiment,” she said.
And yet she and Müller have both set about
making further improvements. The Berkeley team has switched to a new
laser with a broader beam (allowing it to strike their cloud of cesium
atoms more evenly), while the Paris team plans to replace their vacuum
chamber, among other things.
What kind of person puts such a vast effort into such scant improvements? Guellati-Khélifa named three traits: “You have to be rigorous, passionate and honest with yourself.” Müller said in response to the same question, “I think it’s exciting because I love building shiny nice machines. And I love applying them to something important.” He noted that no one can single-handedly build a high-energy collider like Europe’s Large Hadron Collider. But by constructing an ultra-precise instrument rather than a super-energetic one, Müller said, “you can do measurements relevant to fundamental physics, but with three or four people.”
Natalie Wolchover is a senior writer and editor at Quanta Magazine covering the physical sciences.
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Larry David and the Game Theory of Anonymous Donations
In a Curb Your Enthusiasm episode from 2007, Larry David and his wife Cheryl and their friends attend a ceremony to celebrate his public donation to the National Resources Defense Council, a non-profit environmental advocacy group. Little does he know that the actor Ted Danson, his arch-frenemy, also donated money, but anonymously. “Now it looks like I just did mine for the credit as opposed to Mr. Wonderful Anonymous,” David tells Cheryl. David feels upstaged, as if his public donation has been transformed from a generous gesture to an egotistical one. Cheryl says, about Danson, “Isn’t that great? He donated the whole wing. Didn’t want anybody to know.” “I didn’t need the world to know either!” David says. “Nobody told me I could be ‘anonymous’ and tell people!” He would have done it Danson’s way, he says, but, realizing the contradiction, he fumes, “You can’t have it halfway! You’re either anonymous, or you’re not.” What Danson did, David concludes, is “fake philanthropy and faux anonymity!”
I thought of this scene after reading a 2018 study in Nature Human Behavior. “People sometimes make their admirable deeds and accomplishments hard to spot, such as by giving anonymously or avoiding bragging,” write the authors—Moshe Hoffman, Christian Hilbe, and Martin A. Nowak, evolutionary biologists from Harvard University and the Institute of Science and Technology Austria. But if “we give to gain reputational benefits, why would we ever wish to hide the fact that we gave?”
Danson’s anonymity seems calculated despite his profession of noble intent.
The answer to this question may seem less mysterious for anyone who’s seen that Curb episode, “The Anonymous Donor.” We “hide” the fact that we gave precisely for
the reputational benefits. For example, at the ceremony, when Danson
pops over to David, who’s chatting with then-California Senator Barbara
Boxer, she calls Danson a “hero” and stands in awe of the altruism of
his “anonymous” donation. Danson playfully shushes her—he’s meant to
have only told one or two people but everyone seems to know. David can’t
believe it, and later resolves to always donate anonymously for the
sake of his reputation.
The episode hits on exactly what Hoffman, Hilbe, and Nowak describe in their paper. “Donations are never fully anonymous,” they write. “These donations are often revealed to the recipient, the inner circle of friends or fellow do-gooders,” and these “few privy observers, in turn, do not only learn that the donor is generous” but are “also likely to infer that the generosity was not motivated by immediate fame or the desire for recognition from the masses…”—exactly what everyone seemed to figure was true of David, to his chagrin.
What’s intriguing about anonymous giving, and other behaviors apparently designed to obscure good traits and acts, like modesty, is that it’s “hard to reconcile with standard evolutionary accounts of pro-social behavior,” the researchers write. Donations fall under a form of cooperation called “indirect reciprocity.” “Direct reciprocity is like a barter economy based on the immediate exchange of goods, while indirect reciprocity resembles the invention of money,” Nowak wrote in his highly cited 2006 paper “Five Rules for the Evolution of Cooperation.” “The money that fuels the engines of indirect reciprocity is reputation.” Donation evolved, in other words, because it granted a good reputation, which helped humans in securing mates and cementing alliances. But if that’s true, how did the practice of anonymous giving arise? The title of the new paper suggests a solution: “The signal-burying game can explain why we obscure positive traits and good deeds.”
The signal-burying game is one of the latest examples of scientists gaining insight into human behavior from game theoretic models and signalling theory. These games, the authors write, make sense of “seemingly counterintuitive behaviors by carefully analyzing which information these behaviors convey in a given context.” Geoffrey Miller, an evolutionary psychologist at the University of New Mexico, said on Sam Harris’ podcast, Making Sense, “Signalling theory is probably the part of game theory I use most often. The idea there is: How do you credibly demonstrate what kind of organism you are through the signals you give out? And what makes those signals honest, and hard to fake, rather than easily faked, like cheap talk?”
In the signal-burying game, a sender and a receiver pair up randomly, and are rewarded for the kind of match that is made. There are three types of senders (or donors)—low, medium, and high—and two types of receivers—weakly selecting and strongly selecting, or weak and strong for short. A strong receiver corresponds to one of the donor’s close friends or a fellow altruist, and a weak receiver to a member of the general public. The best payoff results from a strong receiver partnering with a high sender, while the worst payoff results from a weak receiver partnering with a high sender.
However, the players know their own type but not each other’s. So the sender aims for an optimum pairing by choosing the kind of signal to send, and the receiver chooses whether to partner with the sender based on the signal. The sender can choose to reveal their type by the costliness of their signal (the donation amount) and how it’s sent (buried or clear, anonymous or public), or whether they send one at all (for simplicity, the authors assume low senders can’t signal, because the cost is prohibitive). Clear signals are always spotted by strong and weak receivers. Buried signals are more likely to be revealed by receivers, and tagged as buried, if they’re sent by a high sender. The end game is for the players to partner up for “some economic interaction,” the authors write. The payoffs for each player in that interaction depend on the sender-receiver types paired (high sender, strong receiver, for example), not the signals sent and received. Senders always want to partner up, no matter the receiver, since the payoff is always positive, but “strong receivers get a positive payoff only from interacting with high senders, and weak receivers get a positive payoff only from interacting with high or medium senders.”
In their paper, Hoffman, Hilbe, and Nowak show the conditions under which signal-burying can be maintained. “First, high senders need to prefer sending a buried signal to a clear signal,” they write. “In equilibrium, burying allows high senders to gain access to some strong receivers (who would have rejected the clear signal but accept buried signals when they are revealed). However, burying also causes high senders to lose some weak receivers (who would have accepted the clear signal, but now may fail to notice the buried signal).” Second, medium senders need to prefer signalling clearly over burying. Third, medium and high senders need to be willing to pay the signalling cost.
David is a medium sender. He tries to signal his wealth, generosity, and public concern by publicly incurring a substantial cost via donation to an important cause, like protecting the environment. In their paper, the authors suggest that burying this signal—anonymizing the donation—is another way to signal the same thing, but in a way that’s harder to fake, or more difficult for receivers to find dishonest. Their explanation of why someone like Danson would obscure his good deed “is based on the intuition that making a positive signal harder to spot can serve as a signal in itself,” they write. By burying it, Danson may be showing that he doesn’t care about wide public recognition, even if it would come off as impressive; or, “alternatively, burying may also signal confidence that receivers are liable to find out anyway.”
Part of what’s so amusing about the
“The Anonymous Donor” is that, to David, Danson’s anonymity seems
calculated despite his profession of noble intent. “I kept my name off
because it’s the exhibit, it’s the issue, that needs to stand forward,
not me,” he tells Senator Boxer. Perhaps it’d be cynical to assume that
anonymous donors are all as covertly egotistical as Danson seems. This
year, at least 17 donations in the United States of more than $10
million were given anonymously.
But these signal buriers aren’t necessarily being shrewd about their
reputation, the authors write. Self-effacing strategies are not
necessarily consciously chosen, and can become natural and stable in a
population if they prove adaptive, “as is arguably the case for our
ideologies, tastes and emotions, including our artistic sense or moral
intuitions related to anonymous giving.”
Brian Gallagher is an associate editor at Nautilus. Follow him on Twitter @bsgallagher.
This classic Facts So Romantic post was originally published in June 2018.
The Problem with a New Study on Mentorship in Science
The increasing visibility of women in leadership roles is one of the few success stories in the struggle for equality in science. But a new study, which connects how often scientists’ later publications get cited with the gender of their early coauthors, threatens to throw cold water on even that modest success. The authors, computer science and public policy researchers at New York University Abu Dhabi, two of whom are women, claim the evidence is clear that having women as mentors is harmful to their mentees’ long-term citation rates. The paper, published in Nature Communications, goes on to suggest that working with senior women coauthors is perhaps best avoided, especially by junior women scientists, because it could leave a stain that marks a researcher for her academic life and diminishes her overall “scientific impact.” Diversity policies specifically “promoting female-female mentorships, as well-intended as they may be,” the authors write, “could hinder the careers of women who remain in academia in unexpected ways.”
It would take a stronger word than “controversial” to describe this paper adequately, in part because the scientists in its target audience are also its subjects. An open letter with 17,000 likes on Twitter called for it to be retracted “for the good of the global scientific community.” Scientists across disciplines have threatened to stop reviewing for the journal. Many have also pushed back against calls for retraction, recommending that comments on the paper’s alleged flaws be submitted to the journal instead. And this idea has, of course, itself received criticism for being an ineffective half-measure. (The journal’s editors have added a note that they are “investigating the concerns raised” by the paper and planning an editorial response.)
To recap where things stand in the year 2020: For a variety of reasons, including cultural and structural impediments, far more men than women today have careers in science, technology, engineering, and mathematics (STEM). In the United States, only one in three bachelor’s degrees in physical sciences, engineering, and computing go to women, and fewer than one in five doctoral degrees in those fields. This can create a feedback effect: the fewer women there are, the harsher the environment can be for those who remain. Women in male-dominated scientific fields are subject to insults and abuses ranging in severity from subtle verbal cues, like their employers using male pronouns to refer to potential new hires, to outright sexual harassment and employment discrimination. Even once established in their careers, female academics are paid less than their male counterparts, cited less often, and expected to do more time-consuming service work, like participating in committees. Recent research has shown that female mentors may help address some—but certainly not all—of these problems. Contact with a woman in a more advanced role inoculates younger women against threats to their scientific identity and reinforces that perhaps they, too, can thrive in science.
The paper’s advice could even make matters worse.
According
to the new mentorship study, though, this may come at a cost to their
careers. The authors considered a database of over 200 million
scientific publications from which they identified 3 million
mentor-mentee relationships, defined by one coauthor being within the
first seven years of their career and another being outside that period.
Then they measured the subsequent publication impact of the mentees
according to how often their papers were cited on average. Using a
matching algorithm, they found (among other things) that, all else being
equal, a scientist’s impact was smaller the more women they had as
mentors. (Using similar methods, two of the three authors, in a 2018 study, found that ethnic diversity among research collaborators positively affected their scientific impact.)
Critics have highlighted many potential issues with the mentorship study. There is a definitional problem: Equating mentorship with coauthorship gives an incomplete picture that ignores the mentoring work not involving publications done by women in academia. There are data issues: The database encompasses over 200 years of publications, so it likely reflects gender bias that’s (hopefully) less strong than it once was. More notably, it doesn’t actually include gender identity, so the study used a machine-learning approach to discern gender based on authors’ first names; (as someone whose name comes up as 53 percent likely to be male, according to the algorithm, I may be especially sensitive to this point.) The paper also suggests a causal link between citation rates and mentors’ gender, meaning an individual can improve their expected impact by choosing a male mentor over a roughly equivalent female one. But the data are purely observational, allowing for many other possible explanations for the observed association.
The study controls for several possibly confounding variables: mentors’ citation impact (female mentors themselves would historically be associated with lower citation rates), number of mentors for a given mentee, year of first publication, rank of the mentee’s degree-granting institution, scientific discipline, and others. So, while not being a randomized controlled trial, it perhaps comes about as close as possible to establishing that causal link from the historical record.
What’s upset many scientists about the study is not so much its methodological flaws, nor the finding that the above causal link exists, but rather the hinted-at conclusion for what should be done about it. It’s plausible that coauthoring with female mentors could put a dent in a scientist’s citation numbers for the same reason that being a woman puts a dent in them—bias against women within the academic community. So, it may seem pragmatic to avoid coauthoring too much with women. But this represents a surrender to sexism and a cynical acceptance that such bias should be taken as a given.
It’s also not a conclusion that follows immediately from the data analysis of the paper. Instead, it’s a policy-minded interpretation and recommendation that reflects a particular worldview. As I argued recently in Nautilus, there is an illusion that’s long plagued science—linked to the eugenics movement and the ideas of Francis Galton, the founder of Nature—that objectivity in statistical analysis confers objectivity in interpretation. What’s being measured may be a fact of the world, but what it implies for our decision making depends heavily on our perspective.
For example, if you cut out the abstract and conclusion, the Nature Communications paper could have easily been titled, “Evidence for gender bias in citation rates for senior and junior coauthors in science publications.” That is to say, the paper’s findings are as consistent with a different recommendation than the authors offered—that citation bias extends further than we might previously have thought, and we should work to root out this bias against women mentors and their mentees.
By making it more difficult for women to recruit any coauthors—a crucial ingredient for their career success—the paper’s advice could even make matters worse. As a biologist at McGill University put it, “Imagine if there was a study that found evidence of bias against women in grant review and concluded that, based on that, universities shouldn’t hire female faculty. That’s what this Nature Comms paper does.”
What’s more, by including only the women in science who successfully published papers, the study elides the fact that too few women make it that far because many find academic science inhospitable. Strategically choosing a male coauthor instead of a female one might never have been an option. It’s the equivalent of studying whether milk pasteurization harms the immune systems of children without mentioning the many children before pasteurization was invented who didn’t live long enough to be studied.
When toxic work environments, implicit bias, and a host of other obstacles no longer cause so many women to leave science, we should revisit the question of how best to divvy up mentoring responsibilities. In the meantime, arguably the best prescription to improve the situation facing women in science is for there to be more women in science.
Aubrey Clayton is a mathematician living in Boston and the author of the forthcoming book Bernoulli’s Fallacy.
http://nautil.us/blog/physicists-nail-down-the-magic-number-that-shapes-the-universe
