The formidable problem with double-slit experiments is: if electrons and photons exhibit wave properties (seen as interference patterns), then what is waving? What is the medium for transmission of ‘electron waves’? Such a medium has been disproved experimentally, in the case of the photon, and not even conceivable for the electron. Erwin Schrodinger was on the right track with his view of the electron as a ‘smeared’ object, rather than as a point particle. Then how is a wave possible without a medium? How can a wave property and a particle property co-exist in a single physical entity (wave- particle duality)? Nature uses a simple and subtle trick : the average electron mass density at a given region of space is directly proportional to the root mean square (RMS) intensity of oscillation (velocity) of the electron (the electron wave) in that region. The instantaneous mass density of the electron at a given point is directly proportional to the instantaneous magnitude of vibrational velocity of the electron at that point. The average photon energy density in a given region of space is directly proportional to the root mean square of rate of change of the electric and magnetic fields in that region. The instantaneous energy density of the photon at a given point of space and time is directly proportional to the magnitude of rate of change of the electric and magnetic fields at that point. The rate of change of electric and magnetic fields in turn depends on the frequency, amplitude and phase of the wave. The electron mass and photon energy will always be concentrated at regions of high wave amplitude. This means that the electron and the photon are dragged by their respective waves. The new theory provides a hint on the mystery behind Planck’s relation: E=h.f. Higher frequency photons have higher energy than lower frequency photons just because higher frequency photons also have higher amplitudes of electric and magnetic field oscillations. If we assume that ordinary waves also have the same fundamental properties as electron waves, then we may be able to explain the lack of backward propagation in Huygens’ principle. We may be able to explain why the bouncing oil droplet in the Couder-Fort oil bath experiment starts to go in the direction of the wave propagation.