David Orlin Hestenes (born May 21, 1933) is an American theoretical physicist and science educator. He is best known as chief architect of geometric algebra as a unified language for mathematics and physics,D. Hestenes: A Unified Language for Mathematics and Physics. In: J.S.R. Chisholm/A.K. Common (eds.): Clifford Algebras and their Applications in Mathematical Physics (Reidel: Dordrecht/Boston, 1986), pp. 1–23. and as founder of Modelling Instruction, a research-based program to reform K–12 Science, Technology, Engineering, and Mathematics (STEM) education.Home page on Modeling Instruction http://modeling.asu.edu/
For more than 30 years, he was employed in the Department of Physics and Astronomy of Arizona State University (ASU), where he retired with the rank of research professor and is now emeritus.
Life and career Education and doctorate degree David Orlin Hestenes (eldest son of mathematician Magnus Hestenes) was born 1933 in Chicago, Illinois. Beginning college as a pre-medical major at UCLA from 1950 to 1952, he graduated from Pacific Lutheran University in 1954 with degrees in philosophy and speech. After serving in the U.S. Army from 1954 to 1956, he entered UCLA as an unclassified graduate student, completed a physics M.A. in 1958 and won a University Fellowship. His mentor at UCLA was the physicist Robert Finkelstein,Robert Finkelstein who was working on unified field theories at that time.D. Hestenes:Clifford algebra and the interpretation of quantum mechanics. In: J.S.R. Chisholm, A.K. Commons (eds.): Clifford Algebras and their Interpretations in Mathematical Physics, Reidel, 1986, pp. 321–346 A serendipitous encounter with lecture notes by mathematician Marcel Riesz inspired Hestenes to study a geometric interpretation of Dirac matrices. He obtained his Ph.D. from UCLA with a thesis entitled Geometric Calculus and Elementary Particles.D. Hestenes: Geometric Calculus and Elementary Particles, –~~~~ University of California, Los Angeles Shortly thereafter he recognized that the Dirac algebras and Pauli matrices could be unified in matrix-free form by a device later called a spacetime split.D. Hestenes, Spacetime Physics with Geometric Algebra, American Journal of Physics 71: 691–714 (2003). Then he revised his thesis and published it in 1966 as a book, Space–Time Algebra,D. Hestenes, Space-Time Algebra (Gordon & Breach: New York, 1966). now referred to as spacetime algebra (STA). This was the first major step in developing a unified, coordinate-free geometric algebra and calculus for all of physics.
Postdoctorate research and career From 1964 to 1966, Hestenes was an NSF Postdoctoral Fellow at Princeton with John Archibald Wheeler. In 1966 he joined the physics department at Arizona State University, rising to full professor in 1976 and retiring in 2000 to Emeritus Professor of Physics.
In 1980 and 1981 as a NASA Faculty Fellow and in 1983 as a NASA Consultant he worked at Jet Propulsion Laboratory on orbital mechanics and attitude control, where he applied geometric algebra in development of new mathematical techniques published in a textbook/monograph New Foundations for Classical Mechanics.D. Hestenes, New Foundations for Classical Mechanics (Kluwer: Dordrecht/Boston, 1986), Second Edition (1999).
In 1983 he joined with entrepreneur Robert Hecht-Nielsen and psychologist Peter Richard Killeen in conducting the first ever conference devoted exclusively to neural network modeling of the brain. In 1987, he became the first visiting scholar in the Department of Cognitive and Neural Systems (Boston University) and worked on neuroscience research for a period.D. Hestenes, How the Brain Works: the next great scientific revolution. In C.R. Smith and G.J. Erickson (eds.), Maximum Entropy and Bayesian Spectral Analysis and Estimation Problems (Reidel: Dordrecht/Boston, 1987). pp. 173–205.D. Hestenes, Invariant Body Kinematics: I. Saccadic and compensatory eye movements. Neural Networks 7: 65–77 (1994).D. Hestenes, Invariant Body Kinematics: II. Reaching and neurogeometry. Neural Networks 7: 79–88 (1994).D. Hestenes, Modulatory Mechanisms in Mental Disorders. In Neural Networks in Psychopathology, ed. D.J. Stein & J. Ludik (Cambridge University Press: Cambridge, 1998). pp. 132–164.
Hestenes has been a principal investigator for NSF grants seeking to teach physics through modeling and to measure student understanding of physics models at both the high school and university levels.
In the 2020s, Hestenes backed an anti-gravity propulsion company formed by Joe Firmage, an investor and former founder of USWeb.
Work Hestenes has worked in mathematical and theoretical physics, geometric algebra, neural networks, and cognitive research in science education. He is the prime mover behind the contemporary resurgence of interest in geometric algebras and in other offshoots of Clifford algebras as ways of formalizing theoretical physics.Abel Diek, R. Kantowski: Some Clifford algebra history, in: Rafal Ablamowicz, P. Lounesto (eds.): Clifford Algebras and Spinor Structures: A Special Volume Dedicated to the Memory of Albert Crumeyrolle (1919–1992), Mathematics and Its Applications, Kluwer Academic, 1995, , pp. 3–12, p. 9Chris J. L. Doran, Anthony Lasenby: Geometric Algebra for Physicists, Cambridge University Press, 2003, , p. 123
Geometric algebra and calculus Spacetime algebra provided the starting point for two main lines of research: on its implications for quantum mechanics specifically and for mathematical physics generally.
The first line began with the fact that reformulation of the Dirac equation in terms of spacetime algebra reveals hidden geometric structure.D. Hestenes, Real Spinor Fields, Journal of Mathematical Physics 8: 798–808 (1967). Among other things, it reveals that the complex factor in the equation is a geometric quantity (a bivector) identified with electron spin, where specifies the spin direction and is the spin magnitude. The implications of this insight have been studied in a long series of papersD. Hestenes and R. Gurtler, Local Observables in Quantum Theory, American Journal of Physics 39: 1028 (1971).D. Hestenes, Local Observables in the Dirac Theory, Journal of Mathematical Physics 14: 893–905 (1973).D. Hestenes, Observables, Operators and Complex Numbers in the Dirac Theory, Journal of Mathematical Physics. 16 556–572 (1975).D. Hestenes (with R. Gurtler), Consistency in the Formulation of the Dirac, Pauli and Schroedinger Theories, Journal of Mathematical Physics 16: 573–583 (1975).D. Hestenes, Spin and Uncertainty in the Interpretation of Quantum Mechanics, American Journal of Physics 47: 399–415 (1979).D. Hestenes, Geometry of the Dirac Theory. Originally published in A Symposium on the Mathematics of Physical Space-Time, Facultad de Quimica, Universidad Nacional Autonoma de Mexico, Mexico City, Mexico (1981), pp. 67–96. with the most significant conclusion linking it to Schrödinger's zitterbewegung and proposing a zitterbewegung interpretation of quantum mechanics.D. Hestenes, The Zitterbewegung Interpretation of Quantum Mechanics, Foundations of Physics 20: 1213–1232 (1990). Research in this direction is still active.
The second line of research was dedicated to extending geometric algebra to a self-contained geometric calculus for use in theoretical physics. Its culmination is the book Clifford Algebra to Geometric CalculusD. Hestenes and G. Sobczyk, Clifford Algebra to Geometric Calculus, a unified language for mathematics and physics (Kluwer: Dordrecht/Boston, 1984). which follows an approach to differential geometry that uses the shape tensor (second fundamental form). Innovations in the book include the concepts of vector manifold, differential outermorphism, vector derivative that enables coordinate-free calculus on manifolds, and an extension of the Cauchy integral theorem to higher dimensions.D. Hestenes, Multivector Calculus, Journal of Mathematical Analysis and Applications 24: 313–325 (1968)
Hestenes emphasizes the important role of the mathematician Hermann GrassmannD. Hestenes, Grassmann's Vision. In G. Schubring (Ed.), Hermann Günther Grassmann (1809–1877) — Visionary Scientist and Neohumanist Scholar (Kluwer: Dordrecht/Boston, 1996), pp. 191–201D. Hestenes, Grassmann’s Legacy. In H-J. Petsche, A. Lewis, J. Liesen, S. Russ (eds.) From Past to Future: Grassmann’s Work in Context (Birkhäuser: Berlin, 2011) for the development of geometric algebra, with William Kingdon Clifford building on Grassmann's work. Hestenes is adamant about calling this mathematical approach “geometric algebra” and its extension “geometric calculus,” rather than referring to it as “Clifford algebra”. He emphasizes the universality of this approach, the foundations of which were laid by both Grassmann and Clifford. He points out that contributions were made by many individuals, and Clifford himself used the term “geometric algebra” which reflects the fact that this approach can be understood as a mathematical formulation of geometry, whereas, so Hestenes asserts, the term “Clifford algebra” is often regarded as simply “just one more algebra among many other algebras”,D. Hestenes: Differential forms in geometric calculus. In: F. Brackx, R. Delanghe, H. Serras (eds.): Clifford Algebras and their Applications in Mathematical Physics: Proceedings of the Third Conference Held at Deinze, Belgium, 1993, Fundamental Theories of Physics, 1993, , pp. 269–286, p. 270 which withdraws attention from its role as a unified language for mathematics and physics.
Hestenes' work has been applied to Lagrangian field theory,A. Lasenby, C. Doran and S. Gull, A Multivector Derivative Approach to Lagrangian Field Theory, Foundations of Physics 23: 1295–12327 (1993) formulation of a gauge theory of gravity alternative to general relativity by Lasenby, Doran and Gull, which they call gauge theory gravity (GTG),A. Lasenby, C. Doran, & S. Gull, Gravity, gauge theories and geometric algebra, Philosophical Transactions of the Royal Society (London) A 356: 487–582 (1998)C. Doran & A. Lasenby, Geometric Algebra for Physicists (Cambridge U Press: Cambridge, 2003) and it has been applied to spin representations of Lie groups.C. Doran, D. Hestenes, F. Sommen & N. Van Acker, Lie Groups as Spin Groups, Journal of Mathematical Physics 34: 3642–3669 (1993) Most recently, it led Hestenes to formulate conformal geometric algebra, a new approach to computational geometry.D. Hestenes, Old Wine in New Bottles: A new algebraic framework for computational geometry. In E. Bayro-Corrochano and G. Sobczyk (eds), Advances in Geometric Algebra with Applications in Science and Engineering (Birkhauser: Boston, 2001). pp. 1–14 This has found a rapidly increasing number of applications in engineering and computer science.L. Dorst, C. Doran and J. Lasenby (Eds.), Applications of Geometric Algebra in Computer Science and Engineering, Birkhauser, Boston (2002)L. Dorst, D. Fontjne and S. Mann, Geometric Algebra for Computer Science (Elsevier: Amsterdam, 2007)D. Hestenes & J. Holt, The Crystallographic Space Groups in Geometric Algebra, Journal of Mathematical Physics 48: 023514 (2007)H. Li, Invariant Algebras and Geometric Reasoning. (Beijing: World Scientific, 2008)E. Bayro-Corrochano and G. Scheuermann (eds.), Geometric Algebra Computing for Engineering and Computer Science. (London: Springer Verlag, 2009)L. Dorst and J. Lasenby, Guide to Geometric Algebra in Practice (Springer: London, 2011)
He has contributed to the main conferences in this field, the International Conference on Clifford Algebras (ICCA) and the Applications of Geometric Algebra in Computer Science and Engineering (AGACSE) series.
Modeling theory and instruction