In a saner world, where science and the law meshed more precisely, a case like Firstenberg v. Monribot would have been dead on arrival in court. But that is not what happened.

Earlier this month, five years after the lawsuit was filed, the New Mexico Court of Appeals upheld a lower court’s ruling that Arthur Firstenberg, an outspoken opponent of wireless technology, could not seek $1.43 million in damages from his neighbor, Raphaela Monribot, for damaging his health by using her iPhone and a Wi-Fi connection.

The electromagnetic signals that go from cellphone to cellphone and computer to computer lie quietly on the spectrum between radio broadcast waves and the colors of light. From the perspective of science, the likelihood of the rays somehow causing harm is about as strong as the evidence for ESP. But the law proceeds by its own logic, in which concepts like evidence and proof take on meanings of their own. This case in New Mexico shows how two of civilization’s great bodies of thought — the scientific and the legal — can make for an uneasy mix.

Mr. Firstenberg and Ms. Monribot, the record shows, were once on good terms. He had hired her in 2008 to cook for him, and after she left for Europe, he rented and then purchased her small house in a densely populated old neighborhood in Santa Fe, N.M. When she returned to town, she moved into a house adjacent to the one he owned.