Quantum Measurement and Quantum Gravity

At present, there are two possible, and equally plausible, explanations for the physics of quantum measurement. The first explanation, known as the many-worlds interpretation, does not require any modification of quantum mechanics, and asserts that at the time of measurement the Universe splits into many branches, one branch for every possible alternative. The various branches do not interfere with each other because of decoherence, thus providing a picture broadly consistent with the observed Universe. The second explanation, which requires quantum mechanics to be modified from its presently known form, is that at the time of measurement the wave-function collapses into one of the possible alternatives. The two explanations are mutually exclusive, and up until now, no theoretical reasoning has been put forward to choose one explanation over the other. In this article, we provide an argument which implies that the collapse interpretation is favored over the many-worlds interpretation. Our starting point is the assertion (which we justify) that there ought to exist a reformulation of quantum mechanics which does not refer to a classical spacetime manifold. The need for such a reformulation implies that quantum theory becomes non-linear on the Planck mass/energy scale. Standard linear quantum mechanics is an approximation to this non-linear theory, valid at energy scales much smaller than the Planck scale. Using ideas based on noncommutative differential geometry, we develop such a reformulation and derive a non-linear Schrödinger equation, which can explain collapse of the wave-function. We also obtain an expression for the lifetime of a quantum superposition. We suggest ideas for an experimental test of this model. Expanded version of arXiv:0705.2357 [gr-qc]. Based on talks given at: [FTAGVI, HRI, Allahabad, 13-18 Nov. 2007]; [Himalayan Relativity Dialog, Mirik, April, 2007]; [Workshop Session on Quantum Gravity, IAGRG, Delhi, Feb. 2007]; [Parmenides Workshop: The present perspectives from physics and philosophy, Wildbad Kreuth, Germany, October, 2006]; [Workshop Session on Quantum Gravity, ICGC, Pune, Dec. 2007]. e-mail address: [email protected]