University at Albany (SUNY)

Project Title

An Information-Theoretic Approach to Identical Particles in Quantum Theory

Project Summary

In ancient Greece, Democritus theorized that everything in the phenomenal world consists of atoms and void, there being an infinite number of atoms, and kinds of atoms, which differ in shape, and size. The diverse appearances and properties of the things around us is then ultimately due to these atoms clustering in different shapes, arrangements, and positions. In modern physics, our atoms are elementary particles: electrons, quarks, photons, and many others. But are all the electrons in the universe exactly the same as one another? Does it matter? Astonishingly, the answer is yes: unless we treat all electrons as identical, so that it is impossible to tell any two of them apart, our best theory of the microscopic world, quantum theory, gives completely the wrong answer. The mathematical rule through which we express the idea that a set of particles are identical is called the Symmetrization Postulate. Even though we have successfully applied this rule to understand so much of the physical world, we still have no clear explanation of it. The purpose of this Project is use the concept of information to build a bridge between the intuitive idea that particles are identical and the symmetrization postulate.

Technical Abstract

Our understanding of the chemical behavior of multi-electron atoms would be impossible if we did not treat the electrons in these systems as indistinguishable. Formally, indistinguishability is expressed through the symmetrization postulate of quantum theory, which stipulates that the wavefunction describing a set of identical particles is either symmetric or antisymmetric. Remarkably, the physical origin of this postulate has not yet been established. The two most widely-known approaches to the origin of the symmetrization postulate are due to Messiah & Greenberg, and to Leinaas & Myheim. They differ greatly in the way that they formalize the notion of indistinguishability, in the additional assumptions that they make, and in the degree to which they are able to account for the symmetrization postulate. The informational approach to the foundations of physical theory provides a perfect opportunity to investigate precisely how we conclude from measurement-derived information that two particles are indistinguishable, and to thereby understand how this notion is properly formalized. In this Project, the primary goal is to develop my own recent derivation of the symmetrization postulate, and to create a unifying framework in which the three different approaches to the symmetrization postulate can be compared and related.

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Our understanding of the chemical behavior of multi-electron atoms would be impossible if we did not treat the electrons in these systems as indistinguishable. Formally, indistinguishability is expressed through the symmetrization postulate of quantum theory, which stipulates that the wavefunction describing a set of identical particles is either symmetric or antisymmetric. Remarkably, the physical origin of this postulate has not yet been established. The two most widely-known approaches to the origin of the symmetrization postulate are due to Messiah & Greenberg, and to Leinaas & Myheim. They differ greatly in the way that they formalize the notion of indistinguishability, in the additional assumptions that they make, and in the degree to which they are able to account for the symmetrization postulate. The informational approach to the foundations of physical theory provides a perfect opportunity to investigate precisely how we conclude from measurement-derived information that two particles are indistinguishable, and to thereby understand how this notion is properly formalized. In this Project, the primary goal is to develop my own recent derivation of the symmetrization postulate, and to create a unifying framework in which the three different approaches to the symmetrization postulate can be compared and related.

Hide Technical Abstract

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