In this paper we demonstrate duality between matter and light. Through mathematical derivation we show that every fundamental matter particle with non-zero rest mass can be represented by a pair of photons. The photons in the representation are not normal photons but a special kind of continuously generating and annihilating virtual photons, whose wave functions super impose to give the wave function of the non-zero rest mass particle and the representation is in agreement with the spin of the particle. We use this duality to derive De Broglie wavelength. We show that a moving matter wave has two frequency components, one of it is with De-Broglie wavelength h/P and the other one is with wavelength hc/E. We also correct the De-Broglie wavelength for v = 0 where we show that there is only one frequency component for v = 0 with wavelength hc/E. Later in the paper we derive that every photon can be represented by a non-zero rest mass particle pair, one going below the speed of light and the other going above the speed of light.
One of the most intriguing quantum phenomena of light is the wave–particle duality which is related to the inability of the classical wave and particle concepts to fully describe the behavior of quantum objects. Theoretically, the wave features of the electromagnetic field, such as interference, follow from the solution of Maxwell's equations while particle features are a consequence of the field quantization, in which the electromagnetic field is described to consist of discrete energy packets, photons. Due to the wave–particle duality, for example, simultaneous description of optical absorption, emission, and interference of propagating fields has conventionally not been considered feasible using local optical models but has required using Maxwell's equations with stochastic source terms accounting for the wave–particle duality. Also the description of the momentum of light in a medium has been problematic. In the research described in this thesis, the quantized fluctuational electrodynamics (QFED) model is derived based on combining the electromagnetic Green's functions to the field quantization to describe the position dependence of the photon number and local thermal balance in general non-equilibrium conditions, and to separate the electromagnetic field into parts propagating in different directions in resonant structures, which has conventionally been problematic due to interference effects. The QFED method is shown to resolve the previously found anomalies in the canonical commutation relations of photon ladder operators. The QFED method is also used to derive quantum optical field–matter interaction parameters fully capturing the interference, emission, damping, and scattering of propagating photons in stratified media leading to an interference-exact radiative transfer equation (RTE) model. Therefore, the derived interaction parameters solve the problem of simultaneously describing interference and losses in the widely used RTE framework. The particle aspects of light are also studied by directly applying the conservation laws of nature and the special theory of relativity to show that light propagating in a medium must be described as mass-polariton (MP) quasiparticles, covariant coupled states of the field and matter. These quasiparticles are shown to have momentum of the Minkowski form and a nonzero mass that is carried by a mass density wave associated with light. The field–matter interaction related to the MP quasiparticles also leads to the dissipation of photon energy. These particle model results are also derived using a wave-based optoelastic continuum dynamics (OCD) approach following from the electrodynamics of continuous media and the continuum mechanics. The obtained results verify the full agreement between the wave and particle models when they are correctly applied. The key finding that a light pulse propagating in a medium is inevitably associated with an experimentally measurable mass implies a fundamental change in the prevailing perceptions of light.