In the mind of Christopher Caputo, a pilot, each moment signals a paradigm shift in aviation.

"You're looking at history," Mr. Caputo said recently, speaking from the cockpit of a plane trailing the Alia at close distance. It had an exotic, almost whimsical shape, like an Alexander Calder sculpture, and it banked and climbed in near silence.

It is, essentially, a flying battery. And it represented a long-held aviation goal: an aircraft with no need for jet fuel and therefore no carbon emissions, a plane that could take off and land without a runway and quietly hop from recharging station to recharging station, like a large drone.

The Alia was made by Beta Technologies, where Mr. Caputo is a flight instructor. A five-year-old start-up that is unusual in many respects, the company is the brainchild of Martine Rothblatt, the founder of Sirius XM and pharmaceutical company United Therapeutics, and Kyle Clark, a Harvard-trained engineer and former professional hockey player. It has a unique mission, focused on cargo rather than passengers. And despite raising a formidable treasure chest in capital, it is based in Burlington, Vt., population 45,000, roughly 2,500 miles from Silicon Valley.

A battery-powered aircraft with no internal combustion has been a goal of engineers ever since the Wright brothers. Larry Page, the Google co-founder, has been funding electric plane start-ups for over a decade. Electric motors have the virtue of being smaller, allowing more of them to be fitted on a plane and making it easier to design systems with vertical lift. However, batteries are heavy, planes need to be light, and for most of the last century, the e-plane was thought to be beyond reach.