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Volume 12: Pages 226-241, 1999

The Question of Theoretical Self‐Consistency in General Relativity: On Light Bending, Duality, Photonic Energy‐Stress Tensor, and Unified Polarization of Plane‐Wave Forms

C. Y. Lo

Applied and Pure Research Institute, 17 Newcastle Drive, Nashua, New Hampshire 03060 U.S.A.

In gravity, a seeming paradox is that although the gravity of the static electromagnetic energy is intrinsically distinct from that of massive matter, the motion of light is also a geodesic. This means that free radiation should have an energy‐stress tensor distinct from that of electromagnetism with material charges and current. Moreover, existing solutions of gravity for electromagnetic waves are unbounded, in addition to violating the equivalence principle; and therefore are incompatible with the light‐bending calculation. Assuming the theoretical framework of general relativity is valid, analysis based on physical principles shows that the related Einstein equation has no physical solution unless another energy tensor with an antigravity coupling is included. Such a tensor is identified to be the energy‐stress tensor for photons. It generates the geodesic equation, and has the sum of the electromagnetic and the gravitational energy. The gravitational and electromagnetic components have the same speed of propagation. For monochromatic plane waves, a gravitational wave solution has the polarization matching that of the electromagnetic wave, while their frequency ratio is 2. For a circularly polarized wave, the gravitational wave component can be zero. The existence of a distinct energy tensor for photons clarifies and explains further (i) the meaning of duality and (ii) the behavior of radiative electromagnetic energy. Then, not only is the bending of light self‐consistently calculated but it would also be established as the earliest experimental proof for the existence of gravitational waves.

Keywords: bending of light, duality, principle of causality, photonic energy‐stress tensor, antigravity coupling, inconsistency, gravitational waves, unified polarization of plane‐wave forms, nonexistence of dynamic solutions, complex Einstein equation

Received: March 20, 1998; Published online: December 15, 2008