Wave-Particle Duality Considered as a Relativistic Paradox
Keywords: wave-particle duality, special relativity, blackbody radiation, photoelectric effect, single-photon experiments, harmonic oscillator, radiating charge
When the velocity of a point harmonic vibrator becomes very high, the product amplitude times frequency of the vibration tends to a limit that is equal to c/4. If the motion is free, without damping, amplitude is preserved, and the observed frequency tends to an upper limit. Applied to an electron on the wall of a blackbody, this cutoff frequency can remove the ultraviolet catastrophe, and a relation between amplitude and temperature is derived. When the motion is maintained, frequency is preserved and the observed amplitude tends to a lower limit, which can be used to show that a particle cannot absorb less than a certain quantity of energy, proportional to the frequency. The wave properties of a relativistically vibrating particle are deduced. Finally, the change in the angular distribution of radiation emitted by an accelerated charge, the velocity of which becomes relativistic, is used to explain the particle properties of light as they are exhibited in the so-called single-photon experiments.
