An Analysis of R. a. Lyttleton and H. Bondi's Theory of "the Physical Consequences of a General Excess of CHARGE."
Lyttleton and Bondi have developed a theory of relative galactic motions leading to a velocity proportional to the distance from the assigned origin. The theory rests upon a spontaneous creation of matter and accompanying charge, in which the positive charge created exceeds, slightly, the negative. They set up field equations modified from the Maxwell-Lorentz form in such fashion as to permit of such charge creation by providing for a violation of the equation of continuity. However, the solution which they evolve for these equations and regard as applicable to the situation is one in which the electric field is zero, so that there is no force to accelerate the matter with its accompanying charges against the force 6f gravity. They seem to imply that the field equations themselves take care of this matter. However, it is here maintained, and is readily shown, that this cannot be so. The equation of non-continuity evolved from the modified field equations demands the form of motion involved in the velocity-distance law, but no finite field exists to provide for it. To provide for the motion, some motivating agency is necessary. Indeed, Lyttleton and Bondi's preliminary treatment of the problem sets up a picture in which the excess charge provides a repulsive force which exceeds the gravitational attraction and so provides for the motion, but they appear to regard this pictufe as provisional, to be replaced by a more subtle formulation born of the modified electromagnetic equations. In a later section of their paper they formulate the problem on the basis of the general theory of relativity, in order to secure harmony with the cosmological principle to the effect that the universe, apart from local irregularities, looks the same to all observers regardless of where they may be stationed in it. Again the proportionality between v and r appears, but we here maintain that it does not appear as something provided for by the field equations, but as a relation which can be realized only by appeal to the law of the geodesic as the motivating agency responsible for the motion, a motion, moreover, which the de Sitter line element isso well fashioned to provide. However, it remains to provide a basis for the de Sitter line element. This the authors achieve only through the introduction of an electromagnetic energy tensor which has no apparent relation to classical electrodynamics, non-relativistic or relativistic, and can only be said to be designed with no background but in such a manner as to achieve the end desired. The ultimate conclusion is that the relativistic treatment cannot be regarded as a mere generalization of the non-relativistic treatment, as the authors seem to imply.