An infantry officer for much of his career, he is best known as a leading advocate for the development of non-lethal weapons and of military applications of the paranormal.

Alexander figures prominently in journalist Jon Ronson's book The Men Who Stare At Goats (2004), which was later made into a Hollywood film starring George Clooney (2009).

A "mustang," Alexander was selected to attend Officer Candidate School as a sergeant first class and was the honor graduate.

[2][3][4] Alexander describes his assignment in 1972 as an infantry officer at Schofield Barracks, Hawaii, before which time he went diving in the Bimini Islands in search of the mythological continent of Atlantis.

During his career in the Army he showed considerable interest in esoteric techniques with his colleague Lieutenant Colonel Jim Channon in his First Earth Battalion manual.

[5] In 1985, Alexander founded the Advanced Theoretical Physics Project, an informal cadre of "government officials" (including "people from the Army, Navy, and Air Force, plus several from the defense aerospace industries and some members from the Intelligence Community") who "took it upon themselves to find out whether there was a secret federal UFO project."