COURTS and legal scholars love quoting legal maxims in Latin. One of the most famous is fiat justitia ruat caelum. The phrase is a resolute affirmation of the rule of law. It means "Let justice be done though the heavens fall".

It was intended as hyperbole. But, ironically, courts may now have to confront these words on literal terms. In various countries, plaintiffs have sought court orders to halt the operation of the Large Hadron Collider at CERN near Geneva, Switzerland, with the most extraordinary of allegations: that the experiment may create a black hole that will devour the Earth.

Up until now, the various lawsuits filed against the LHC have faltered. But if the right kind of claim is filed in the proper court, a judge may soon have to face the question of whether an injunction might be needed to save the world.

Injunctions are court orders that command persons to do or refrain from doing something. They are relatively routine, for example when a building of historic significance is threatened with demolition. But wading into the world of particle physics to shut down the LHC would be a forbidding proposition for anyone in judges' robes.

In deciding whether or not to issue an injunction, courts engage in what lawyers refer to as a "balancing test". The idea is that the court weighs the hardships that would be endured by both parties if the injunction were or were not issued, taking into account the likelihood and severity of the alleged consequences. The test closely resembles what is portrayed by courthouse statues around the world - Lady Justice holding up scales to measure the relative weight of the plaintiff's and defendant's cases.

So let's do the balancing test for the LHC case. The hardship CERN would suffer from an injunction is enormous - idling thousands of workers and equipment worth billions of euros, and upending a great scientific adventure. That weighs on the scales heavily. But on the other side is an Earth-mass black hole. That not only tips the scales, it eats them up.

The remaining task is to determine whether the questions raised are sufficiently serious. For that, a court must take a careful look at the scientific controversy. Yet the physics involved is difficult terrain even for physicists. A judge with maybe just a few days to ponder has scant chance of learning the science well enough to confidently decide who is right and who is wrong.

Usually when complex scientific issues are involved, courts turn to expert witnesses. But there is a problem with using experts in this case: none would seem to be without bias. CERN employs half of the world's particle physicists; the other half are their friends. All of them are anxiously awaiting data from the LHC to advance their field. The LHC is not just a particle physics experiment, it is the particle physics experiment. So what is a court to do?

Courts can maintain the rule of law in a fair and principled way by looking at the human context surrounding the scientific debate. While the physics may be largely impenetrable to the court, the human factors are not.

One question a court can investigate is how likely it is that the theoretical underpinnings of the scientific work are defective. Those seeking an injunction could, for example, ask a court to consider the history of shifting arguments for why the LHC is safe.

In 1999, physicists said no particle accelerator for the foreseeable future would have the power to create a black hole. But theoretical work published in 2001 showed that if hidden extra dimensions in space-time did exist, the LHC might create black holes after all. Thereafter, the argument for safety was changed. In 2003, it said that any black holes created would instantly evaporate. But when subsequent theoretical work suggested otherwise, the argument changed again. In 2008, CERN issued a report arguing a safety case based, ultimately, on astrophysical arguments and observations of eight white dwarf stars. These flip-flops on safety might cause a court to find current assurances less persuasive than they would otherwise be.

In addition, a court could look at the sociological and psychological context in which the disputed scientific work was carried out. Social scientists have identified a number of phenomena that can skew attempts to reach objective assessments of risk. For instance, cognitive dissonance describes the tendency of people to seek information that is consistent with their beliefs and to avoid information that is inconsistent. "Groupthink" describes a process by which intelligent individuals, working in a group, can reach a worry-free outlook that is not justified by the facts. And the phenomenon of confirmation bias - the tendency to filter information so as to confirm working hypotheses - was cited by the Columbia Accident Investigation Board as one explanation for why space shuttle programme managers ignored sure signs of trouble.

A court charged with deciding whether an injunction should be issued could consider whether these sorts of social effects plausibly undermine the conclusion that the LHC is safe.

These lines of inquiry might strike physicists as unfair. Many will argue that scientific work should be debated on its scientific merits alone. That objection is well put in a purely academic dispute, but the question of whether the LHC is safe is not academic - it is a real-world question with the highest possible stakes. Evaluating the science from a real-world perspective, and understanding scientific work to be a fallible human enterprise, is not merely fair - where justice is concerned, it is essential.