Measurement as Absorption of Feynman Trajectories: Collapse of the Wave Function Can Be Avoided

We define a measuring device (detector) of the coordinate of quantum particle as an absorbing wall that cuts off the particle's wave function. The wave function in the presence of such detector vanishes on the detector. The trace the absorbed particles leave on the detector is identifies as the absorption current density on the detector. This density is calculated from the solution of Schrödinger's equation with a reflecting boundary at the detector. This current density is not the usual Schrödinger current density. We define the probability distribution of the time of arrival to a detector in terms of the absorption current density. We define coordinate measurement by an absorbing wall in terms of 4 postulates. We postulate, among others, that a quantum particle has a trajectory. In the resulting theory the quantum mechanical collapse of the wave function is replaced with the usual collapse of the probability distribution after observation. Two examples are presented, that of the slit experiment and the slit experiment with absorbing boundaries to measure time of arrival. A calculation is given of the two dimensional probability density function of a free particle from the measurement of the absorption current on two planes.