“And remember that General Relativity was correct, from all the vast space of possibilities.”
The Einstein field equation itself is actually extremely simple:
G = 8piT
where G is the Einstein tensor and T is the stress-energy tensor. Few serious competitors to GR have emerged for a very good reason; what sane modifications could you make to this equation? G and T have to be directly proportional, because everyone knows that the curvature of spacetime (and hence the effect of gravity) is directly proportional to the quantity of matter/energy. The constant of proportionality is fixed by direct measurement of g. G must vanish when T vanishes, as there must be no gravity in the absence of matter. T itself cannot be modified, because it’s the only sane way to measure mass, energy, and momentum in the Lorentzian manifold framework. G cannot be modified, because it must be constructable from the metric tensor (a property of spacetime), it must be directly proportional to the amount of curvature, and it must be invariant with respect to the choice of coordinate system (the full derivation is left as an exercise to the reader in my textbook).
“And remember that General Relativity was correct, from all the vast space of possibilities.”
The Einstein field equation itself is actually extremely simple:
G = 8piT
where G is the Einstein tensor and T is the stress-energy tensor. Few serious competitors to GR have emerged for a very good reason; what sane modifications could you make to this equation? G and T have to be directly proportional, because everyone knows that the curvature of spacetime (and hence the effect of gravity) is directly proportional to the quantity of matter/energy. The constant of proportionality is fixed by direct measurement of g. G must vanish when T vanishes, as there must be no gravity in the absence of matter. T itself cannot be modified, because it’s the only sane way to measure mass, energy, and momentum in the Lorentzian manifold framework. G cannot be modified, because it must be constructable from the metric tensor (a property of spacetime), it must be directly proportional to the amount of curvature, and it must be invariant with respect to the choice of coordinate system (the full derivation is left as an exercise to the reader in my textbook).