  We develop a classical picture of interference for non-interacting individual
classical massive free particles. As long as they remain undetected, particles
carry the information of a phase equal to an action integral along their
trajectory. At the point of their detection, a special type of detector
collects the phases from all individual particles reaching it, adds them up
over time as complex numbers, and divides them by the square root of their
number. The detector announces a number of detections equal to the square of
the amplitude of the resulting complex number. An interference pattern is
gradually built from the collection of particle phases in the detection bins of
the detector after several repetitions of the experiment. We obtain perfect
agreement with three solutions of the Schr\"odinger equation for free
particles: a Gaussian wavepacket, two Gaussian wavepackets approaching each
other, and a Gaussian wavepacket reflecting off a wall.
