PRINCETON JUNCTION, N.J.—Welcome aboard the Tension Train.

"As a reminder, folks, this train has two quiet cars," announces a conductor on a NJ Transit train. "Please refrain from cellphone usage and keep all conversations down to a quiet tone."

In theory, and often in reality, the quiet car has been a haven for commuters seeking peace. Passengers who desire quiet stay in a designated car, and chatty types in the rest.

Tell that to the passengers on the 8:07 p.m. NJ Transit express train out of New York City late last year. In an extreme example of the kind of scene that has played out regularly on train lines nationwide, two passengers mistakenly got on an express train at Newark, N.J., instead of the local—and then stood in the quiet car as they discussed their dilemma. A stranger on the train told them to shush. A shoving match ensued. Police were called in. The train was delayed on its route for 30 minutes.

Some people, the conductor explained to riders, "didn't know how to behave like adults."