The last and longest phase in Finkelstein's scientific life is best described by him as spent working on 'reconciling the fundamental concepts and principles of quantum theory and space-time theory, Einstein and Heisenberg.' He used quantum set theory, his extension of classical set theory, to do so and presented the then state of his work in his 1996 book Quantum Relativity: A Synthesis of the Ideas of Einstein and Heisenberg. He continued to work on the fundamental question of the structure of space-time for the rest of his life.
Throughout his career Finkelstein published over 100 scientific articles, some of them seminal. In 1958, as a young man, he published his paper about the 'unidirectional membrane,' which would be renamed five years later the 'black hole.' He was the first to discover kinks, topological charges and topological spin-statistics theorems, with Misner (1959) and Rubenstein (1962). The 1962–63 papers with Jauch, Schiminovich and Speiser were the first to introduce the Higgs mechanism before Higgs. Inspired by John von Neumann, Finkelstein was a pioneer in considering logics as physical. He understood the peculiarities of quantum physics as demonstrating quantum logics, which unlike classical Boolean logics is non-commutative. Later in his life he also explored the implications of non-associativity. Between 1969 and 1972 Finkelstein published his series 'Space-time code' in which he considered the universe as a quantum computer and studied the fundamental unit of time, which he named the 'chronon.' He also was a pioneering voice when he argued the feasibility of quantum computing in 1969.
He earned his PhD in theoretical physics from the Massachusetts Institute of Technology in 1953. He taught at Stevens Institute of Technology, was a professor of physics and department chair at Yeshiva University, and after more than twenty years of service retired as an emeritus professor of physics at the Georgia Institute of Technology. For over two decades, Finkelstein edited the International Journal of Theoretical Physics.
He is survived by his first wife Helene Cooper and their three children Dan Finkelstein, Beth Bosworth, and Eve Finkelstein, and by his second wife Shlomit Ritz Finkelstein and their daughter Aria Ritz Finkelstein.