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

Interference with non-interacting free particles and a special type of detector