This papers introduces axioms for von Neumann’s theory of quantum measurement in a differential geometric framework. Our visual perception places us (observers) at the origin of a 3-dimensional cartesian coordinate system. So the first axiom is that Observers can be regarded as point objects/particles. Our second axiom is that perceptual experiences can be regarded as occurring on a tangent space at the point where the Observer is located. Due to our psychological experience of time asymmetry, we have the third axiom that, the observer is traversing irreversibly along the future time-like direction, on the (3+1) dimensional space-time manifold. Interaction between Observers is discussed at classical and quantum mechanical levels. Quantum mechanical experiments such as those of Schrodinger’s Cat, and the Quantum Zeno Effect, are examined; keeping in view, the information processing and flicker rate, with in the brain. It is anticipated that as the spatial and temporal resolution, of real time brain investigation techniques, such as the functional Magnetic Resonance Imaging (fMRI), Superconducting Quantum Interference Device (SQUID), Magneto-Encephalo-Gram (MEG), Electro-Encephalo-Gram (EEG), reach a critical level — the Quantum Measurement Processes within the brain, would be open to study experimentally.