Conférence du vendredi 11 septembre 2026

The Born rule in quantum mechanics - N.D. Hari Dass (Chennai Institute of Mathematical Sciences)

Abstract: In this talk I shall discuss various aspects and nuances of the Born rule for probabilities in QM. After stating this indispensable rule and various versions of it, I shall examine Born's original paper of 1926 and its various weaknesses. I shall then discuss Heisenberg's own role in the genesis
of this rule. von Neumann was very critical of what he saw as an essentially arbitrariness in Born's approach, and wanted a more systematic understanding. I shall give a brief overview of von Neumann's ideas.
The Born rule discussed so far is only applicable to the so called Projective Measurements where the possible outcomes are orthogonal. I shall brie y discuss what form the rule takes for more general measurements where the states after dierent outcomes are not necessarily orthogonal. These are
called Generalized Measurements, also Positive Operator Valued Measurements(POVM).
Contrary to what is mostly propagated in QM courses, probabilities are not the only observables. I shall brie y discuss Aharonov's Weak Values to illustrate this.
Finally, I analyse the relation between the Born rule and the Quantum Superposition Principle and will try to answer why superposition principles in classical physics do not mandate any probability interpretation. I will end with a few remarks on the Superselection Rules in QM which dramat-
ically restrict the scope of the quantum superposition principle, essentially trivialising the Born Rule.

Bio : N.D. Hari Dass is currently residing in Mysore, INDIA. He obtained his BSc(Hons) and MSc in Physics from Delhi University, and his Ph.D. from UCSB. Subsequently he worked at UCLA, Niels Bohr Institute, RRI, and NIKHEF,Amsterdam before joining the Institute of Mathematical Sciences in Chennai. He retired from there as a Senior Professor and became the DAE Raja Ramanna Chair Professor at Indian Institute of Science, Bangalore, and Adjunct Professor at Chennai Mathematical Inst. He is a fellow of the National Academy of Sciences, Allahabad. His current research interests are in high energy physics,astrophysics,and foundations of quantum mechanics. He is passionate about teaching in general and in raising awareness about science.
In 2004 he built India’s fastest supercomputer in academia, KABRU, which was among the top 500 supercomputers in the world. He has authored the book “The Essentials of Thermodynamics” (SRI Publishers, Singapore). His second book 'From Strings to Strings' on Yang-Mills Flux Tubes has appeared as  Springer Lecture Notes in Physics 1018.