Alvin Andreas Herborg Nielsen was born to Knud Herborg Nielsen and Maren Nielsen in Menominee, Michigan on May 30, 1910. His parents immigrated from just outside Herning, Denmark to the United States in the late 19th century. He had an older brother, Harald Herborg Nielsen (1903-1973).

Nielsen majored in physics at the University of Michigan, where he earned his Bachelor of Arts (1931), Master of Science (1932), and Doctorate (1934) degrees. He began his professional career as a post doctorate research fellow at Ohio State University shortly after graduating in 1934, where his brother worked as a physics professor. Nielsen left OSU in 1935 to teach as a physics instructor at the University of Tennessee. He served as a professor of physics (1946-1980), as head of the Department of Physics (1956-1969), and as the dean of the College of Liberal Arts (1962-1977). He was also honored as a Mace Bearer and as a Phi Kappa Phi Distinguished Faculty lecturer in 1963.

Nielsen's academic and professional research focused on molecular spectroscopy, the study of the interaction between atoms or molecules and radiated energy. He conducted research on infrared spectroscopy in detection work for the U.S. Air Force at Ohio State University (with his brother, Harald) from 1944-1946. He was selected as the University of Tennessee's first Fulbright Research Scholar, which granted him time during the 1951-1952 academic year to develop his infrared research and work with Marcel Migeotte of the Astro-Physicial Institute of the University of Liége, Belgium. He also served as one of the first consultants for the Oak Ridge National Laboratory and the Oak Ridge Gaseous Diffusion Plant Laboratories post-WWII (1947-1980). He published eighty-five publications throughout his career.

When Nielsen retired from his dean position in 1977, the City of Knoxville and the university held an Alvin Nielsen Appreciation Week. In addition, the College Scholars Scholarship, a program he planned as dean, began in his name. In 1980, when he retired from his professorship, the university dedicated the Alvin H. Nielsen Physics Building in his honor. He continued to teach physics as a professor emeritus until 1988. He continued his community involvement after his retirement, including serving on the board of directors for the Knoxville Symphony Orchestra, among other organizations that promoted the arts, music and theater.

Nielsen married his wife Jane Ann Evans Nielsen (circa 1914-October 18, 2003), of Columbus, Ohio, on December 29, 1942. They had one daughter, Margaret Arthur Nielsen Wayne (1947- ). Nielsen died on November 3, 1994 in Knoxville, Tennessee.