One of the most intriguing claims among believers in paranormal phenomena is the allegation that extraterrestrial spacecraft are visiting the Earth. According to various polls taken in the late 1990s, between 30 and 50 percent of Americans are convinced that unidentified flying objects (UFOs) are alien spacecraft. Their beliefs are often based on the accounts of credible eyewitnesses who claim to have seen unusual objects that defy the laws of ordinary physics, moving in ways that no manmade aircraft could move. Moreover, some UFO reports are bolstered by persuasive photographs and films of odd-looking objects that hover, zigzag, or fly away at incredible speeds.

One event that some believe offers proof of the existence of alien spacecraft is the “Phoenix lights” incident of 1997. On March 13, between 7:30 and 10:30 in the evening, thousands of Phoenix-area residents observed a large arc of six lights floating over...