Mysterious forces may be a reliable trope in science fiction, but in reality, physicists have long agreed that all interactions between objects evidently arise from just four fundamental forces. Yet that has not stopped them from ardently searching for an additional, as-yet-unknown fifth fundamental force. The discovery of such a force could potentially resolve some of the biggest open questions in physics today, from the nature of dark energy to the seemingly irreconcilable differences between quantum mechanics and general relativity. Now, a recent experiment carried out at the National Institute of Standards and Technology (NIST) is offering fresh hints about a fifth force’s possible character. An international collaboration of researchers used neutrons and a silicon crystal to set new limits on the strength of a potential fifth fundamental force at atomic scales. Published in Science in September, the study also includes measurements of the precise structure of both silicon crystals and neutrons themselves.

“This work of ‘fifth force’ searches actually goes on over the entire length scale of human observation,” says NIST physicist Benjamin Heacock, the study’s lead author. Because different theories predict different fifth force properties, he says, physicists have looked for its subtle effects in everything from surveys of astronomical objects like galaxies to the miniscule motions of custom-built microscopic instruments. So far, however, all searches have come up empty.

“There’s a reason to think we're missing something,” notes Eric Adelberger, a physicist at the University of Washington who was not involved with the study. His own team has previously looked for some of the proposed new forces and, with great experimental certainty, found nothing at all. In work recognized in 2021 with a Breakthrough Prize, they concluded that the fifth force must be much weaker than some theories predicted, or that it simply does not exist. The NIST experiment follows a similar idea but uses a novel experimental technique. “The goal from the experimentalist perspective is to make strides forward in limiting [the strength of] new forces, wherever the experiment can do it, and for us that happens to be on the atomic scale,” Heacock says.

Gauging relevant interactions at such scales is uniquely challenging, according to Adelberger, in part because in the atomic realm a typical object is about a million times smaller than the width of an average human hair. “You have to ask, how much matter can you get within a little volume associated with that length scale? It's absolutely tiny,” he says. And even the barest influence from other, known forces such as electromagnetism can easily scuttle the delicate measurements. To solve that problem, the NIST team relied on neutrons, the neutrally charged subatomic particles usually found in atomic nuclei, as neutrons are barely swayed by electromagnetic effects.

Further, the even smaller particles that make up neutrons, called quarks, are “glued” together so intensely by the strong interaction (one of the four known fundamental forces) that it is exceedingly difficult to physically disturb them. “The strong interaction that holds quarks together in a neutron is insanely strong, so the neutron gets almost no distortion when it gets close to [other] matter,” explains W. Michael Snow, a physicist at Indiana University who was also uninvolved with the new experiment. Studying the behavior of neutrons is consequently well-suited for seeking out new forces because there are not many easily measurable effects influencing these subatomic particles to begin with. One of the new study’s co-authors, Albert Young, a physicist at North Carolina State University, puts it simply: “At present, at our [atomic] length scale, neutrons kind of rule.”

In their experiment, researchers observed neutrons that had traveled through a specially machined, nearly perfect silicon crystal made by collaborators at the RIKEN Center for Advanced Photonics in Japan. “Silicon is a common material, but precision machining of silicon is a super difficult thing,” underlines Michael Huber, a NIST physicist and another of the study’s co-authors. Inside this perfect crystal—shielded from light, heat, vibrations and other sources of external noise thanks to special NIST facilities—silicon atoms are arranged in predictable grid-like patterns.

Neutrons traveling through that grid collided with some silicon atoms and evaded others. However, as the neutrons’ journey took place at the atomic scale where laws of quantum mechanics dictate that all particles behave like waves, their collisions with silicon atoms were similar to breakers crashing into a shore dotted with large, evenly spaced rocks. When a neutron bumped into a silicon atom then, this interaction created something like a neutron wave ripple. This ripple overlapped with other neutron wave ripples originating near adjacent silicon atoms, resulting in a wave interference pattern not unlike rough, choppy water along a rocky coast.

Most crucially, through clever experimental design, the researchers ensured that some of the neutron “waves” lapping on the silicon atom “shores” overlapped in a very specific way that resulted in so-called Pendellösung oscillations. These oscillations are roughly analogous to beats, and are best thought of as pulsing, alternating low-then-loud auditory effects that happen when two nearly identical sound waves are played simultaneously. In the case of this new experiment, they are akin to a distinctive but difficult to detect ripple pattern within the neutron waves breaking along the silicon seashore. “Although Pendellösung interference was discovered and demonstrated a long time ago, in the 1960s at MIT, it's rarely used and most experiments are not sensitive to it,” Huber explains.

His team carefully analyzed these special ripples, looking for key details about the silicon “rocks” and the neutron waves that crashed into them. It was as if they could tell how much “water” each “wave” carried, whether any “rocks” moved in the collision and more. Importantly, had an atomic-scale fifth-force interaction been at play, the details of the neutron wave interference pattern would have revealed its presence, much like how ripples in surf can follow the outline of a submerged sea wall. Although the researchers found no signs of a fifth force, they did determine a new limit, 10 times stricter than before, on how strong such a force could be.

The NIST team believes that their innovative experimental setup will allow them to make even more precise measurements in the future. They already managed, for instance, to infer details of the arrangement of quarks inside a neutron, as well as some precise motions of silicon atoms, which could prove useful for the manufacture of fine-tuned electronics. However, their quest to constrain the strength of the fifth force, a task they accomplish by combining multiple separate neutron-property measurements under certain assumptions, remains the most promising and the most difficult part of their work. “We can keep and should keep searching [for the fifth force],” says Yoshio Kamiya, a physicist at Tokyo University who was uninvolved with the new study. “This is just one step.”

Adelberger agrees, and he is eager see new results from the next phase of experimentation. “There's a lot of stuff that has to go into getting this kind of a result,” he says. “It’s a tiny effect, and researchers have to keep accounting for all other tiny effects.” Both Kamiya and Adelberger think that there is room for debate on how strongly the new work should make physicists reconsider their theories about the strength of a possible fifth force. Based on the current study, Adelberger says, too many potential sources of error remain; even if the NIST team had found positive evidence of a new force, he says, it could not be considered truly definitive.

Heacock notes that his team already has ideas for advancing their work, for instance by using germanium crystals instead of silicon, in which atoms are arranged in different structures that could be even more advantageous for precise observations of neutron interference. Another goal is to seriously expand the available catalog of precise atomic scale measurements for any and all fifth force–hunting physicists to consult in their own independent work. Ideally, Heacock notes, the measurements in the new study are just a first few opening the door for the dozens more to come. “I think any experiment will eventually hit a wall, but I also think we're pretty far from it,” he says.