Modern developments of atomic theory have required alterations in some of the most fundamental physical ideas. This has resulted in its being usually easier to discover the equations that describe some particular phenomenon than just how the equations are to be interpreted. The quantum mechanics of Heisenberg and Schrodinger was first worked out for a number of simple examples, from which a general mathematical scheme was constructed, and afterwards people were led to the general physical principles governing the interpretation, such as the superposition of states and the indeterminacy principle. In this way a satisfactory non-relativistic quantum mechanics was established. In extending the theory to make it relativistic, the developments needed in the mathematical scheme are easily worked out, but difficulties arise in the interpretation. If one keeps to the same basis of interpretation as in the non-relativistic theory, one finds that particles have states of negative kinetic energy as well as their usual states of positive energy, and, further, for particles whose spin is an integral number of quanta, there is the added difficulty that states of negative energy occur with a negative probability. With electrons the negative-probability difficulty does not arise, and one can get a sensible interpretation of the negative-energy states by assuming them to be nearly all occupied and an unoccupied one to be a positron. This model, however, is excessively complicated to work with and one cannot get any results from it without making very crude approximations. The simple accurate calculations that one can make would apply to a world which is almost saturated with positrons, and it appears to be a better method of interpretation to make the general assumption that transition probabilities obtained from these calculations for this hypothetical world are the same as those for the actual world. With photons one can get over the negative-energy difficulty by considering the states of positive and negative energy to be associated with the emission and absorption of a photon respectively, instead of, as previously, with the existence of a photon. The simplest way of developing the theory would make it apply to a hypothetical world in which the initial probability of certain states is negative, but transition probabilities calculated for this hypothetical world are found to be always positive, and it is again reasonable to assume that these transition probabilities are the same as those for the actual world.