The Accurate Tests of General Relativity Verified Flat Spacetime —-flat-spacetime Covariant Gravity, Its Quantization and Solar Application

Only when space is flat does there exist one coordinate system which has direct meaning of distances or angles, and if one coordinate system has direct meaning of distances or angles then the space must be flat. This is the famous Riemann theorem when he pioneered the concept of curved space. General relativity (GR) claims curved spacetime. However, when testing GR with data, all relativists consider Schwarzschild coordinates to have direct meaning of distances or angles. The gravitational wave calculation and the theoretical preparation for the forthcoming Gravity Probe B data play the same trick. Therefore, GR verified flat spacetime where the metric has no geometric meaning at all! For example, on a curved space, the sum of all angles of a triangle is not π, either greater or less than π. Two famous general relativity tests are about angles. All mainstream textbooks and papers calculate angles by directly using the coordinate φ. They indirectly assume the variance range of φ is 2π. Therefore, the sum of all angles of a triangle is π. That is, they assume flat space! All coordinate systems on a curved space are curvilinear. All coordinates are merely parameters. Real angles and distances have to be calculated by employing the coefficients of the space metric. Only when the space is flat will the metric reduce to the Pythagoras theorem. That is, only when the space is flat will the coordinates have direct meaning of spatial distances or angles. 1 Introduction Gravity is the oldest known interaction yet the least understood. Gravitational force is generally considered a static force, a stereotype of " action-at-a-distance " which implies infinite velocity of propagation. One of the foundational theories discovered in the twentieth century is the theory of special relativity which requires any force be transmitted with velocity less than or equal to c, the light speed. The theory assumes flat background spacetime of Minkowski metric and requires a covariant four-dimensional form for all laws of mechanics. For example (Goldstein, 1950), the Lagrangian of any force should be an invariant property of the corresponding system only, independent of the particular coordinate system used, and we expect it to be a world scalar, invariant under all Lorentz transformations. Specifically, we should not treat time t as a parameter entirely distinct from the spatial coordinates. An invariant parameter p must be chosen and the common velocity ˙ x i must be …