“It’s woven into every play,” said Bradford Mahon, a cognitive neuroscientist at Carnegie Mellon.

His partner, Adnan Hirad of the University of Rochester, held out the possibility that a better helmet might help in the margins. But that’s it. “It’s a dangerous sport, and we can’t mince words about a technology. There’s no El Dorado.”

I asked Dr. Goldstein what sort of technological breakthrough would protect a player against C.T.E.? He peered at me. “A force field that keeps a player from blocking or tackling you,” he said.

He did not smile.

I mentioned to Dr. Camarillo this upwelling of skepticism. He nodded with the confidence of a true believer. He and several of these scientists know each other and plan to collaborate on research. If his proposed helmet reduces concussions, he said, logically it might reduce the force of subconcussive hits that cause long-term damage to the brain. In this way, he said, it’s analogous less to a cigarette filter than to technological changes that have made surviving car crashes progressively safer.

I mentioned that claim to Dr. Goldstein and his head started to wag. He insisted the evidence on C.T.E. and the toll taken by even small hits did not support Dr. Camarillo’s optimism. “This is hope-and-a-prayer science,” he said.

Evidence could take years, at the very least, to accumulate. For now, there is no way to diagnose C.T.E. in the living; it can be found only with an autopsy.

And yet Dr. Camarillo is not deterred. “I hope this is like the seatbelt,” he said of his new helmet design, with a jauntiness that would warm the heart of an N.F.L. executive. “And the day will come when you think it’s just crazy we didn’t have it sooner.”