Gravitational Lensing
Authors: Vegt Wim 
Published: June 2023

Gravitational lensing describes the effect of slowing down of the speed of light within a gravitational field in a comparable way that the speed of light slows down in materials like glass (lenses) determined by the refraction index. Within materials like glass the speed of light slows down because of the interaction of the electromagnetic field around the atoms of the material which interacts with the electromagnetic field of the beam of light, creating in this way an extra amount of electromagnetic mass. (Electromagnetic Interaction).Gravitational lensing describes the effect of slowing down of the speed of light within a gravitational field Within a gravitational field the speed of light slows down because of the interaction of the gravitational field (generated e.g. by a black hole) which interacts with the electromagnetic field of the beam of light, creating in this way an extra amount of Gravitational-Electromagnetic Energy (mass, inertia). (Gravitational-Electromagnetic Interaction).Which has been described in equation (99). A new theory has to be developed to describe “Gravitational-Electromagnetic Interaction”. When the gravitational refraction index has been determined (the mathematical solutions for equation (99)), the calculations for Gravitational lensing will become clearly defined.This article describes a new theory in physics which has been based on the “divergence-free linear 4-dimensional stress-energy tensor in the Minkowski Space”. The difference between Einstein’s General Relativity and this theory is the different approach. Einstein has deformed (non-linear and non-divergence free) the “4-dimensional Stress-Energy Tensor” by introducing the curved 4-dimensional Riemannian Manifold to explain the interaction between Gravity and Light. The new theory describes the interaction between different fields (Electric, Magnetic and Gravitational) by identical interaction terms, generated by the separate divergence and the separate rotation of the different fields. (equation 24) The conclusion of the new theory is that “divergence-free” and “rotation-free” fields do not interact.When Isaac Newton published his 3 famous equations which became the foundation of Classical Dynamics, he was not aware that he was building the first elemental blocks for the Stress-Energy Tensor in the 4-dimensional Minkowski Space.When James Clerk Maxwell published his 4 famous equations which became the foundation for Classical Electrodynamics, he was not aware that he was building new blocks for the Stress-Energy Tensor in the 4-dimensional Minkowski Space.When Paul Dirac published his famous equation which became the foundation of Relativistic Quantum Physics, he was not aware that he was building further on blocks for the Stress-Energy Tensor in the 4-dimensional Minkowski Space.It was Albert Einstein who was one of the first physicists who discovered the importance of the Stress-Energy Tensor to describe in a mathematical way the interaction between Electromagnetic Radiation and a Gravitational Field.But because there was no match, Einstein deformed the Divergence-Free Linear “Stress-Energy Tensor” by deforming Space and Time. He deformed this Tensor in such a way that he found a very special Mathematics to describe the interaction between Electromagnetic Radiation (Light) and a Gravitational Field. The Theory of General Relativity. And that became a problem. Because Einstein deformed the fundamental building block in physics (the Divergence-Free Linear “Stress-Energy Tensor), nothing fits anymore. Classical Mechanics has no match with Classical Electrodynamics. Classical Electrodynamics has no match with Relativistic Quantum Physics. Relativistic Quantum Physics has no match with General Relativity.It is important to distinguish the “Physical Reality” from a Mathematical Description of it (which is in general an approach). The scalar curvature (or the Ricci scalar) is a measure of the curvature of a Riemannian manifold. Einstein used a curved Riemannian manifold to describe “Gravitational-Electromagnetic Interaction”. But the physics beyond this is the interaction between the different fields. It is possible to describe this in different ways. This new theory demonstrates a more direct approach in the force densities acting between different fields expressed by equation (24).This new theory starts with the Divergence-Free Linear “Stress-Energy Tensor” in the 4-dimensional Minkowski Space. And from this unique Divergence-Free “Stress-Energy Tensor” follows Classical Mechanics, Classical Electrodynamics, Relativistic Quantum Physics and General Relativity. Bringing back the necessary unity in physics.