The “Havana Syndrome” health cases are gut-wrenching. As the U.S. government gathers information, there’s growing speculation that the attackers may be Russians. But there’s no proof. It’s an assault case with no hard evidence — other than the suffering of the victims.

These mysterious attacks are a policymaker’s nightmare. You can’t accuse another country of warlike assaults without solid facts; the Iraqi WMD fiasco taught a generation of intelligence analysts that lesson. But if you don’t hold rogue actors accountable, how do you deter future attacks? That’s the conundrum facing the Biden administration.

U.S. officials have analyzed about 200 cases in which Americans have experienced symptoms of what are officially known as “anomalous health incidents” such as the ones first reported in Havana in 2016. It’s a government-wide effort, driven by the Central Intelligence Agency, which employed many of those experiencing symptoms.

The information gathered has fostered suspicion about a Russian role, officials say. A significant number of those affected, more than 100, have U.S. intelligence connections. Of that group, many were involved in activities related to Russia and its close partners, though there’s no precise pattern. There may be a Russia nexus here, but there’s no smoking gun.

Investigators believe that the concussion-like damage may have been caused by mobile directed energy weapons, such as ones Russia, China and other adversaries have been developing for more than a decade. An investigation last year by the National Academies of Science, Engineering, and Medicine concluded that directed energy was “the most plausible mechanism in explaining these cases.” Despite speculation that cases may reflect mass hysteria, the report said the acute symptoms “cannot be ascribed to psychological and social factors” based on current evidence.

Microwaves, lasers and other directed energy systems are hardly new in the spy business. Intelligence collectors (including U.S. agencies) have bathed target locations with radio waves or beams, and then tried to tune the vibrations of particular objects — a pane of window glass, say, or the filament in a lightbulb — to produce what amounts to an invisible microphone. The CIA sometimes describes this as “ubiquitous technical surveillance,” or UTS.

The Havana cases could be collateral damage from intelligence collection, but many experts believe that unlikely. Investigators have explored whether the attacks come from mobile directed energy transmitters that could be small enough to fit into a backpack. These could be easily transported to the disparate locations where Americans have reported symptoms, including Australia, Austria, Bulgaria, China, Colombia, Georgia, Germany, India, Kyrgyzstan, Poland, Russia, Syria, Taiwan, Uzbekistan and Vietnam, as well as Cuba. But the delivery mechanism could be airborne, like a drone, officials caution.

Here’s how the attacks began, according to last year’s study by the National Academies: “An individual assigned to the U.S. Embassy in Cuba was awakened one night at home in Havana in 2016 by severe pain and a sensation of intense pressure in the face, a loud piercing sound in one ear … and acute disequilibrium and nausea.” Similar symptoms were reported in the scores of cases since then.

Russia has denied any involvement in such attacks, including in private conversations with U.S. officials. Some U.S. officials speculate that Russian mercenaries or criminal groups may have obtained weapons originally developed by the Russian government and used them without explicit official authorization, but there’s no proof of that, either.

The Russian playbook has emphasized deniable “gray zone” operations over the last decade. Networks of “illegal” operatives, such as those the KGB sent abroad a generation ago, are now reportedly used by the GRU and FSB, Russia’s military and domestic security agencies. Mark Galeotti, a Russia analyst who heads an intelligence consulting firm, describes the networks of criminal organizations that operate in Europe to support the Kremlin’s interests as the “Crimintern.” Russia analyst A.E. Goldberg has used the Russian word bespredel to describe these reckless operations. It’s a word used by Russian criminal gangs that means “anything goes.”

With its freewheeling network of mercenaries, hackers and thugs, Russia is an obvious suspect. But that’s not the same thing as having proof. So, what should the Biden administration do about these anomalous health incidents to make sure they stop, when it lacks the evidence to support a potential military confrontation?

The first task is to keep investigating. That’s what CIA Director William J. Burns is doing aggressively, assigning the probe to one of the targeters who found al-Qaeda leader Osama bin Laden a decade ago. While this investigation continues, it might also make sense to draw Russia into a discussion about “rules of the road” for directed energy systems.

Like hypersonic missiles, space weapons and cyberattacks, these directed energy systems will be weapons of the future, regardless of what emerges in the investigation of Havana Syndrome. They’re double-edged swords — as dangerous to Russia as to America.

Message to the Kremlin: We’re not making any allegations. But we need to talk.