In 1901, Nikola Tesla began work on a global system of giant towers meant to relay through the air not only news, stock reports and even pictures but also, unbeknown to investors such as J. Pierpont Morgan, free electricity for one and all. It was the inventor’s biggest project, and his most audacious.

The first tower rose on rural Long Island and, by 1903, stood more than 18 stories tall. One midsummer night, it emitted a dull rumble and proceeded to hurl bolts of electricity into the sky. The blinding flashes, The New York Sun reported, “seemed to shoot off into the darkness on some mysterious errand.”

But the system failed for want of money, and at least partly for scientific viability. Tesla never finished his prototype tower and was forced to abandon its adjoining laboratory.

Today, a fight is looming over the ghostly remains of that site, called Wardenclyffe...