The history of the belief in the existence of elements from which all matter is formed begins more than two millennia ago with the writings of the ancient Greeks and Romans. Developments in the late 17th century pioneered by Robert Boyle led to the modern concept of elemental balance, according to which the number and type of various atoms remains exactly the same in the course of a chemical reaction. The concept of the creation and annihilation of matter changed all that. According to Einstein’s relativity theory, elements can be converted entirely into energy and therefore no longer exist. The present study examines this theoretical interpretation by looking in detail at the process of positronium decay. It is suggested that the electron and positron constituents of positronium are actually bound so tightly together after decay that they form a massless lower-energy state which can be identified with the photon itself. The Breit-Pauli Hamiltonian is adjusted through the addition of momentum-dependent exponential damping factors so that it possesses eigenfunctions which correspond to such a tightly bound state with 2moec2 binding energy. The success which the corresponding Schrödinger-type calculations achieves calls into question the creation-annihilation hypothesis on a completely general basis.