Although quantum theory is very successful in the microscopic domain, it is unable to satisfactorily describe the outcome of a quantum measurement, and adopts the collapse postulate and Born rule in an ad hoc manner. The present project proposes an innovative approach towards the resolution of this problem. Quantum theory depends on an external classical time for its formulation. However it can be argued that there ought to exist an equivalent but more fundamental reformulation which does not depend on this classical time. Such a reformulation can be shown to be a limiting case of a theory which becomes nonlinear on the Planck mass/energy scale. This nonlinearity could possibly explain why the wave-function of a quantum system collapses during a measurement, thereby resolving the measurement problem. The purpose of this project is (i) to develop a concrete mathematical description of the nonlinear theory using the languages of Trace Dynamics and Noncommutative Differential Geometry, (ii) to derive the consequent stochastic nonlinear Schrodinger equation which describes and explains the measurement process, (iii) to make experimentally verifiable predictions which will test departures of this theory from standard linear quantum mechanics, and (iv) to compare and contrast the results of this project with results obtained in the Continuous Spontaneous Localization model and in Trace Dynamics. The key outputs and outcomes of the project will include published research articles and a review article in peer-reviewed journals, which we hope will have a marked influence on the future development of the subject of quantum measurement. If it turns out to be correct that quantum theory is a limiting case of a deeper theory, it is the latter theory which will have to be used for constructing a quantum theory of gravity, and for developing a unified description of gravity and particle physics.
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