The Man Who Invented the 26th Dimension

Paul Halpern
Jan 23, 2015 · 7 min read
Calabi Grid, courtesy of Berkeley Center for Cosmological Physics
Image credit: Claude Lovelace with Parakeet (courtesy of Rutgers), via
Image credit: Hadronic String linking two particles, via
Image credit: Abdus Salam via the Alfred Nobel foundation,

“I was a precocious child. I read Einstein and Dirac at 16–17 and made some very amateurish attempts to construct unified field theories. This probably soured me on them later. Salam, who later shared the Nobel for unifying weak and electromagnetic interactions, was my thesis adviser, but I didn’t take much interest in his wilder speculations.”

Never completing his Ph.D., Lovelace left Imperial for a position at CERN, where he began to explore a vexing issue with hadronic string theory. Researchers had started to use open strings, with loose ends, and closed strings, connected in a loop, to model two types of interactions, known then as Reggeons and Pomerons respectively. To construct a realistic field theory of Pomerons required a property called unitarity: a mathematical condition by which the lengths of vectors are preserved during transformations. A unitary operator spins a vector around an abstract space like a needle twirling on a compass. While the needle turns, it keeps the same length.

Image credit: Wikimedia Commons user Dave3457.
Image credit: Philosopher of science John Norton depicts the paradoxical nature of tachyons in this diagram:
Image credit: John Schwarz, via
Image credit: courtesy of Rutgers University, via

    Paul Halpern

    Written by

    Physicist and science writer. Author of The Quantum Labyrinth: How Richard Feynman and John Wheeler Revolutionized Time and Reality

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