Is quantum linear superposition an exact principle of nature?

The principle of linear superposition is a hallmark of quantum theory. It has been confirmed experimentally for photons, electrons, neutrons, atoms, for molecules having masses up to ten thousand amu, and also in collective states such as SQUIDs and Bose-Einstein condensates. However, the principle does not seem to hold for positions of large objects! Why for instance, a table is never found to be in two places at the same time? One possible explanation for the absence of macroscopic superpositions is that quantum theory is an approximation to a stochastic nonlinear theory. This hypothesis may have its fundamental origins in gravitational physics, and is being put to test by modern ongoing experiments on matter wave interferometry. I. THE ABSENCE OF MACROSCOPIC SUPERPOSITIONS In the year 1927, American physicists Clinton Davisson and Lester Germer performed an experiment at Bell Labs, in which they scattered a beam of electrons off the surface of a nickel plate. In doing so, they accidentally discovered that the scattered electrons exhibited a diffraction pattern analogous to what is seen in the Bragg diffraction of X-rays from a crystal. This experiment established the wave nature of electrons, and confirmed de Broglie’s hypothesis of wave-particle duality. An electron can be in more than one position at the same time, and these different position states obey the principle of quantum linear superposition: the actual state of the electron is a linear sum of all the different position states. The principle of linear superposition is the central tenet of quantum theory, an extremely successful theory for all observed microscopic phenomena. Along with the uncertainty principle, it provides the basis for a mathematical formulation of quantum theory, in which the dynamical evolution of a quantum system is described by the Schrödinger equation for the wave function of the system. The experimental verification of linear superposition for electrons heralded a quest for a direct test of this principle for larger, composite particles and objects. Conceptually, the idea of the necessary experimental set up is encapsulated in the celebrated double slit interference experiment. A beam of identical particles is fired at a screen having two tiny slits separated by a distance of the order of the de Broglie wavelength of the particles, and an interference pattern is observed on a photographic plate at the far end of the screen. Such an experiment was successfully carried out for Helium ions, neutrons, atoms, and small molecules, establishing their wave nature and the validity of linear superposition. When one considers doing such an interference experiment for bigger objects such as a beam of large molecules the technological challenges become enormous. The opening of a slit should