The force we experience most intimately remains the most mysterious. Physicists understand how vast migrations of particles called photons light up our homes, and how swarms of “gluon” particles hold together the cores of our atoms. But they can’t say what gravity particles, if any, delight us as babies by enabling our spoons to plummet to the floor. The force of gravity has proved so difficult to account for in terms of particles that many physicists have abandoned that approach altogether. They consider the possibility that gravity and with it, reality as a whole might instead be made of tiny strings or other strange things. But in one corner of the theoretical-physics world, the particle approach is staging a comeback. A growing band of physicists has been using the typical approach to particle physics, known as quantum field theory, for gravity. Although this use of the theory was long considered fatally flawed, these physicists are now finding that it works far better than their predecessors expected. “So far there is no hint telling us that we should throw quantum field theory away; actually, it’s the opposite,” said Luca Buoninfante, a theoretical physicist at Radboud University in the Netherlands whose calculations have helped shore up the old theory. When you apply the standard quantum field theory to gravity, you don’t just get a unique theory called quadratic gravity, he said. “You also get new predictions.” Those predictions have not yet been tested. And on purely theoretical grounds, quadratic gravity has eerie features that still spook many physicists. But quadratic gravity enthusiasts aren’t put off by its abnormalities. On the contrary, they view these features as previously unappreciated possibilities that may be permitted by quantum field theory. Perhaps effects occasionally sneak ahead of their causes at the microscopic level, for instance. And perhaps negative-energy “ghost” particles that arise in quadratic gravity can exist safely in the equations without creating paradoxes in experiments. Ghosts, Buoninfante said, may be “new objects that appear when we try to understand gravity and quantum field theory at a deeper level.” More Constants, More Problems From the moment physicists tried to fit gravity into quantum field theory (the framework they use to describe all the other fundamental forces), it was obvious the union was going to be a rocky one. Quantum fields are rippling substances that suffuse space. A ripple in a quantum field is a particle. By exchanging streams of these particle-ripples, one object can push or pull on another, exerting a force. The electromagnetic force, for instance, is conveyed through disturbances in the electromagnetic field that we call photons. A deeply inconvenient truth of quantum field theory is that what a field does depends on each and every one of the ripples it can conceivably support. And those ripples come in an unending number of shapes and sizes. When physicists first invented quantum field theory and tried to use it to ask questions about electrons and photons, their calculations went infinite because each term in a sum tried to account for a never-ending continuum of ever-smaller ripples. But a sum of infinite terms was no answer at all. In the late 1940s, the physicists Richard Feynman, Julian Schwinger and Sin-Itiro Tomonaga independently hit on a workaround that would turn those endless ripples into clear answers, earning themselves a Nobel Prize. They realized that they could reexpress the unknowable, infinite-seeming parts of their calculations in terms of their net effect on two known constants that had already been measured in the lab: the electron’s mass and charge. Doing so fixed the values of the terms, after which physicists could predict anything they liked about the electromagnetic field. This trick, known as renormalization, seemed like an algebraic hack. But over the following decades, physicists came to understand why it worked. Renormalization was a way of blurring out the smallest ripples in a field and including only their net effects. In the case of the electromagnetic field, this works because the impact of the small ripples is limited; the smaller the ripples get, the less they influence the larger ripples. Gravity, however, works differently. Gravity too has a field: the fabric of space-time itself. Albert Einstein, in his general theory of relativity, described gravity as a consequence of objects “falling” along curves in this space-time fabric. This gravitational field is not a rippling thing that fills space, per se, but rather a rippling thing that is space. Physicists have detected “gravitational waves” traveling through this field. And the tiniest ripples in this field cause no end of trouble. When Feynman and a colleague by the name of Bryce DeWitt tried to renormalize gravity, they found that the tinier the space-time ripples, the more they matter. They influence the rippling of space-time at higher levels in innumerable subtle ways that can’t be summed up only in terms of a few measurable constants. The trick failed. The tiny space-time ripples refused to be blurred out. “Everyone was concerned about this,” said John Donoghue, an expert in quantum field theory at the University of Massachusetts, Amherst. “This is the reason that quantum general relativity was considered a problem.” Birth of Quadratic Gravity In the mid-1970s, the late Kellogg Stelle, then a graduate student at Brandeis University, saw that there was a way and only one way to stop the inundation of infinities that had plagued earlier attempts to “quantize” general relativity. General relativity can be written as an equation that has a single term representing space-time’s curvature. Apply Feynman and DeWitt’s renormalization procedure to this equation and you get one type of particle-ripple, the graviton, rippling in unignorably infinite ways. But Stelle figured out that he could modify Einstein’s equation so that space-time more closely resembled the electromagnetic field, with ripples that became less significant as they got smaller. Their overall effects could then be captured in just a few measurable constants, analogous to the electron’s charge and mass in electromagnetism. This theory of gravity, which came to be known as quadratic gravity because it contained two new terms related to the square of the curvature, was renormalizable. It made just as much sense as electromagnetism. “That gives you a indefinite article quantum theory of gravity,” said Stelle, who was a professor at Imperial College London until his death last month. “Then of course the question is: Do you like it?” Most physicists, Stelle among them, did not. “I was also aware that not everything was going to be hunky-dory about this,” he said during an interview in April. The problem was that this enhanced fabric of space-time could now host three types of ripples. The first term represents the normal gravitons. But the two curvature-squared terms bring two new particles into the picture. One is inoffensive, what Stelle called a “sweet little scalar” particle. But the other is a ghoul. An unwelcome minus sign stemming from the third term unleashes chaos. The associated particle has negative energy, so the space-time fabric actually gains energy by creating it. This means that more and more of such a particle will spontaneously appear, whipping space itself into an increasingly energetic inferno. Worse, events involving this third particle may have a negative probability of taking place a meaningless proposition. Physicists call such particles ghosts and say that theories haunted by ghosts are “sick” mathematically inconsistent. Shortly after Stelle published his research in 1977, physicists stumbled across a healthier quantum gravity theory called supergravity. It solved a handful of problems by positing that each known elementary particle teams up with an as-yet-undiscovered “superpartner” particle. Supergravity immediately captured the attention of theoretical physicists, including Stelle. The theory would eventually merge with string theory and dominate the field for decades. Quadratic gravity, with its ghosts and inconsistencies, couldn’t compete. Physicists paid it little attention, citing Stelle’s paper just 10 to 20 times per year. Ghostly Revival The theory never completely faded away, however. Theorists returned to it here and there. Interest rose in the 2010s as string theory failed to deliver the spectacular breakthroughs its early practitioners had promised, and superpartners failed to materialize in experiments at the Large Hadron Collider. In 2014, the Italian physicists Alberto Salvio and Alessandro Strumia wondered whether quadratic gravity could solve a puzzle that many had expected the superpartners to address. The puzzle, known as the hierarchy problem, asks why gravity seems impossibly weak compared to the other three fundamental forces. Why is there one “scale” for those forces, and a special, dramatically different one for gravity? Salvio and Strumia found that the two extra particles from Stelle’s theory could help push the two scales apart. That got them wondering whether the ghost was truly a deal-breaker.
https://www.quantamagazine.org/old-ghost-theory-of-quantum-gravity-makes-a-comeback-20251117/
