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N. David Mermin
N. David Mermin
N. David Mermin
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Nathaniel David Mermin (/ˈmɜːrmɪn/; born 30 March 1935) is a solid-state physicist at Cornell University best known for the eponymous Hohenberg–Mermin–Wagner theorem, his application of the term "boojum" to superfluidity, his textbook with Neil Ashcroft on solid-state physics, and for contributions to the foundations of quantum mechanics and quantum information science.[2]

Key Information

Education and career

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Mermin was born in 1935 in New Haven, Connecticut. He obtained a bachelor's degree in mathematics from Harvard University in 1956, graduating summa cum laude. He remained at Harvard for his graduate studies, earning a PhD in physics in 1961.[3] After holding postdoctoral positions at the University of Birmingham and the University of California, San Diego, he joined the Cornell University faculty in 1964.[3] He became a Cornell professor emeritus in 2006.

Early in his career, Mermin worked in statistical physics and condensed-matter physics, including the study of matter at low temperatures, the behavior of electron gases, the classification of quasicrystals, and quantum chemistry. His later research contributions included work in quantum information science and the foundations of quantum mechanics.[4]

Mermin was the first to note how the three-particle GHZ state demonstrates that no local hidden-variable theory can explain quantum correlations,[5][6] and together with Asher Peres, he introduced the "magic square" proof, another demonstration that attempting to "complete" quantum mechanics with hidden variables does not work.[7] Richard Feynman described another paper by Mermin in this area as "one of the most beautiful papers in physics".[8] In collaboration with Charles Bennett and Gilles Brassard, he made a significant early contribution to quantum cryptography.[9] Starting in 2012, he has advocated the interpretation of quantum mechanics known as Quantum Bayesianism, or QBism.[10]

In 2003, the journal Foundations of Physics published a bibliography of Mermin's writing that included three books, 125 technical articles, 18 pedagogical articles, 21 general articles, 34 book reviews, and 24 "Reference Frame" articles from Physics Today.[4]

Mermin was elected a Fellow of the American Physical Society in 1969,[11] and he was elected a member of the National Academy of Sciences in 1991.[12] He was also elected a member of the American Philosophical Society in 2015.[3]

Word and phrase coinages

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Inspired by Lewis Carroll's comic poem The Hunting of the Snark, Mermin introduced the term boojum into the vocabulary of condensed-matter physics.[13]

In his book It's About Time (2005), one of several expository pieces on special relativity, he suggests that the English foot (0.3048 meters) be slightly modified to approximately 29.98 cm. This adaptation of a physical unit is one of several ploys that Mermin uses to draw students into spacetime geometry. In the book, Mermin writes:

Henceforth, by 1 foot we shall mean the distance light travels in a nanosecond. A foot, if you will, is a light nanosecond (and a nanosecond, even more nicely, can be viewed as a light foot). ... If it offends you to redefine the foot ... then you may define 0.299792458 meters to be 1 phoot, and think "phoot" (conveniently evocative of the Greek φωτος, "light") whenever you read "foot".[14]

Though it is often misattributed to Richard Feynman, Mermin coined the phrase "shut up and calculate!" to characterize the views of many physicists regarding the interpretation of quantum mechanics.[15]

Books

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  • 1968: Space and Time in Special Relativity, McGraw Hill ISBN 0-88133-420-0
  • 1976: (with Neil Ashcroft) Solid State Physics, Holt, Rinehart and Winston ISBN 0-03-083993-9[16]
  • 1990: Boojums All the Way Through, Cambridge University Press ISBN 0-521-38880-5[17]
  • 2005: It's About Time: Understanding Einstein's Relativity, Princeton University Press ISBN 978-0-691-12201-4[18]
  • 2007: Quantum Computer Science, Cambridge University Press ISBN 978-0-521-87658-2[19]
  • 2016: Why Quark Rhymes with Pork: and Other Scientific Diversions, Cambridge University Press ISBN 978-1-107-02430-4[20]

References

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Further reading

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N. David Mermin

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N. David Mermin is an American theoretical and Horace White Professor of Physics Emeritus at , best known for his foundational work in , including the Hohenberg–Mermin–Wagner theorem, which demonstrates the impossibility of spontaneous breaking of continuous symmetries in one- and two-dimensional systems at finite temperatures, and for his influential contributions to the foundations of and . Born on March 30, 1935, in , Mermin earned his A.B. in mathematics summa cum laude from in 1956, followed by an A.M. in physics in 1957 and a Ph.D. in physics in 1961, all from Harvard. After completing postdoctoral fellowships at the (1961–1963) and the (1963–1964), he joined in 1964 as an , advancing to in 1967, full professor in 1972, and Horace White Professor in 1990, a position he held until his retirement in 2006. During his tenure, he also served as director of Cornell's Laboratory of Atomic and from 1984 to 1990. Mermin's research spans solid-state physics, statistical mechanics, and quantum foundations, with early work focusing on low-temperature physics and many-body problems, later shifting toward quantum Bayesianism (QBism) and interpretations of quantum phenomena, such as his seminal 1981 essay "Is the Moon There When Nobody Looks?" which popularized discussions of quantum reality and observer dependence. He has also made significant pedagogical contributions through textbooks like Solid State Physics (1976, co-authored with N. W. Ashcroft), a standard reference translated into multiple languages, and Quantum Computer Science: An Introduction (2007), which elucidates quantum computing concepts for broader audiences. Other notable books include It's About Time: Understanding Einstein's Relativity (2005) and Why Quark Rhymes with Pork and Other Scientific Diversions (2016), the latter compiling his essays on physics and language. Throughout his career, Mermin received numerous accolades, including the first Prize from the in 1989 for outstanding contributions to physics, election to the in 1991, and the Klopsteg Memorial Award from the American Association of Physics Teachers in 1994 for excellence in . He was also elected to the American Academy of Arts and Sciences in 1988 and the in 2015, reflecting his impact as both a researcher and communicator of complex scientific ideas. In his autobiographical reflections, Mermin has emphasized his role in advancing through unconventional perspectives and interactions with leading physicists.

Biography

Early life and education

Nathaniel David Mermin was born on March 30, 1935, in , to Jewish parents John Mermin, a power engineer, and Eva Mermin, a school teacher. His paternal grandparents had immigrated from to New Haven to escape pogroms, and his father was one of ten siblings who grew up in the city, attending . Mermin grew up in an urban East Coast environment, where his family's working-class background emphasized education. From an early age, Mermin developed a strong interest in mathematics, though he felt challenged by talented peers and eventually shifted toward physics. He attended high school in New Haven, the same institution his father and uncles had, where teachers still recalled his relatives; this local education, combined with self-study, nurtured his aptitude for abstract thinking and scientific inquiry. Mermin pursued undergraduate studies at Harvard University, earning an A.B. in mathematics in 1956, summa cum laude. His coursework initially focused on pure mathematics but transitioned toward physics, where he encountered influential peers like Kenneth G. Wilson and Richard Friedberg. He received an A.M. in physics from Harvard in 1957 before continuing directly into doctoral studies. For his Ph.D. in physics, completed at Harvard in 1961, Mermin initially worked under before completing his thesis under . The dissertation explored through a theoretical model analogous to gas-to-liquid condensation, addressing foundational quantum mechanical aspects of many-body systems. Following his doctorate, Mermin held postdoctoral positions that marked his entry into solid-state theory. From 1961 to 1963, he served as an NSF Postdoctoral Fellow at the in , collaborating with . He then spent 1963 to 1964 as a Postdoctoral Associate at the (), working with .

Academic career

N. David Mermin joined the faculty of as an assistant professor of physics in 1964, following postdoctoral positions at the and the . He advanced to in 1967 and to full professor in 1972, serving in that role until 1990. In 1990, he was appointed the Horace White Professor of Physics, a position he held until his retirement in 2006, after which he became Horace White Professor of Physics Emeritus. Even after retirement, Mermin has remained active in research and writing, contributing to discussions in and , including autobiographical reflections published in 2024. During his tenure, Mermin served as director of Cornell's Laboratory of Atomic and Solid State Physics (LASSP) from 1984 to 1990, overseeing operations in a key center for condensed matter research. He also held various administrative roles, including chairing the physics department's admissions and participating in university-wide reviews. Mermin's emphasized clarity and conceptual understanding, spanning undergraduate and courses in , , and . He taught a popular non-majors course on relativity for several decades starting in the , using innovative approaches to demystify concepts for students outside physics. His pedagogical style influenced generations of students, prioritizing exposition over rote computation in advanced topics like and . Mermin mentored numerous PhD students, shaping careers in theoretical physics. Among his notable advisees was Susan Coppersmith, who completed her 1983 thesis on nonlinear dynamics and chaos theory in condensed matter systems under his supervision (with computational elements facilitated at Bell Laboratories); she later became a distinguished professor at the University of New South Wales, advancing quantum computing and glass theory. Anupam Garg earned his 1983 PhD exploring quantum measurement and macrorealism, contributing to the Leggett-Garg inequality; he is now a professor at Northwestern University, specializing in quantum foundations and nanomagnetism. Tin-Lun Ho received his 1977 doctorate on superfluid helium-3 phases, co-developing the Mermin-Ho relation for superfluid dynamics; Ho advanced to a distinguished professorship at Ohio State University, pioneering ultracold atomic gases. Daniel S. Rokhsar completed his 1986 thesis on quasicrystals and topological defects (co-advised with James Sethna), later transitioning to biological physics; he holds a professorship at UC Berkeley in molecular and cell biology. Sandra Troian finished her 1987 PhD on mean field theories of icosahedral quasicrystals, applying symmetry principles to such systems; she is now a professor of applied physics at Caltech, focusing on microfluidics and surface science. As documented in a 2003 bibliography, Mermin's scholarly output up to that point included approximately 125 technical papers on topics from to , 18 pedagogical articles clarifying complex concepts for broader audiences, and 21 general essays on and .

Research contributions

Condensed matter physics

N. David Mermin's contributions to span , , and electron dynamics in metals, with a particular emphasis on low-dimensional systems and . One of his most influential early works was his collaboration with H. Wagner on what is now known as the Mermin-Wagner theorem, which demonstrates that continuous symmetries cannot be spontaneously broken in one- or two-dimensional systems at finite temperatures. The proof relies on analyzing the spin correlation function in the Heisenberg model, showing that associated with Goldstone modes lead to a divergence in the long-wavelength limit. Specifically, for a two-dimensional isotropic Heisenberg ferromagnet, the M\mathbf{M} satisfies ⟨M⟩=0\langle \mathbf{M} \rangle = 0 because the of the ⟨S(0)⋅S(r)⟩\langle \mathbf{S}(0) \cdot \mathbf{S}(\mathbf{r}) \rangle implies an infrared divergence in the integral ∫d2k/k2\int d^2k / k^2, preventing long-range order. This result, building on Pierre Hohenberg's analysis of fluctuations, has profound implications for phase transitions in low-dimensional magnets and superfluids, explaining the absence of or in strictly two-dimensional systems at any finite temperature. In the realm of electron response theory, Mermin extended the Lindhard dielectric function to account for finite-temperature effects and damping in metals. The original Lindhard theory describes the linear response of a degenerate gas to longitudinal at zero temperature, yielding the dielectric function ϵ(q,ω)=1−4πe2q2χ0(q,ω)\epsilon(\mathbf{q}, \omega) = 1 - \frac{4\pi e^2}{q^2} \chi_0(\mathbf{q}, \omega), where χ0\chi_0 is the non-interacting susceptibility. Mermin's generalization incorporates a relaxation-time approximation to include thermal excitations and collision damping, resulting in a form that preserves and sum rules while allowing for damping and at finite temperatures. This Lindhard-Mermin dielectric function, ϵ(q,ω)=1+(ω+iγ)ϵL(q,ω+iγ)−1(ω+iγ)−ωp2/(ω+iγ)\epsilon(\mathbf{q}, \omega) = 1 + \frac{(\omega + i\gamma) \epsilon_L(\mathbf{q}, \omega + i\gamma) - 1}{(\omega + i\gamma) - \omega_p^2 / (\omega + i\gamma)} (with γ\gamma as the damping rate and ϵL\epsilon_L the Lindhard function), provides a more realistic description of plasma oscillations and screening in real metals, influencing calculations of and . Mermin's work on superfluid helium further highlighted his expertise in topological defects and anisotropic phases. In 1976, he introduced the concept of point singularities on the surface of superfluid phases, later termed "boojums," which are singular defects arising from the topology of the order parameter. These boojums manifest as point vortices on the surface where the superfluid velocity field exhibits a π1(S1)=Z\pi_1(S^1) = \mathbb{Z} winding, leading to localized energy concentrations and distinctive textures in the phase. Inspired by Lewis Carroll's , the term "boojum" evocatively captures the elusive, singular nature of these defects, which disrupt uniform superflow and were experimentally verified through observations of critical velocities and scattering in helium films. Later, in collaboration with Tin-Lin Ho, Mermin developed the Mermin-Ho relation for the anisotropic A phase of superfluid 3^3He, providing a theoretical framework that links the superfluid circulation to the orbital texture. The relation states that the vorticity ω=∇×vs=ℏ2ml^(∇×l^)⋅(l^×∇l^)\boldsymbol{\omega} = \nabla \times \mathbf{v}_s = \frac{\hbar}{2m} \hat{l} (\nabla \times \hat{l}) \cdot (\hat{l} \times \nabla \hat{l}), where vs\mathbf{v}_s is the superfluid velocity, l^\hat{l} is the orbital angular momentum vector, and mm is the mass, predicting how disclinations in the l^\hat{l}-texture generate effective magnetic fields and influence vortex dynamics in 3^3He-A. This framework has been essential for understanding the stability and motion of textures in p-wave superfluids. Mermin's theorems and models have had lasting impact on the study of , , and low-dimensional materials. The Hohenberg-Mermin-Wagner theorem underpins modern investigations of two-dimensional systems, such as and transition metal dichalcogenides, where it explains the suppression of long-range order and the role of disorder or in stabilizing phases like at low temperatures. Similarly, his work on dielectric responses and superfluid defects informs applications in , including the design of topological superconductors and the interpretation of excitations in layered systems.

Quantum foundations and information

Mermin's contributions to quantum foundations center on elucidating the tensions between quantum mechanics and classical intuitions of locality, realism, and contextuality through thought experiments and paradoxes that highlight nonlocality without relying on probabilistic inequalities. In 1989, Greenberger, Horne, and Zeilinger proposed the GHZ paradox, a three-particle entangled state that yields a deterministic contradiction with local hidden-variable theories. The state is given by the vector ∣GHZ⟩=12(∣000⟩+∣111⟩)|\text{GHZ}\rangle = \frac{1}{\sqrt{2}} (|000\rangle + |111\rangle)
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