The original derivation of Einstein’s laws of gravitation (general relativity) was based on the notion of curved spacetime. The same equations can be derived assuming flat spacetime, taking a particle physics viewpoint. Does it matter, since the equations are the same? Evidently yes – this is from Misner, Thorne, and Wheeler’s 1973 classic Gravitation, also known simply as MTW:
| Einstein derivation | Spin-2 derivation | |
| Nature of primordial spacetime geometry? | Not primordial; geometry is a dynamic participant in physics | “God-given” flat Lorentz spacetime manifold |
| Topology (multiple connected-ness) of spacetime? | Laws of physics are local; they do not specify the topology | Simply connected Euclidean topology |
| Vision of physics? | Dynamic geometry is the “master field” of physics | This field, that field, and the other field all execute their dynamics in a flat spacetime manifold |
| Starting points for this derivation of general relativity | 1. Equivalence principle (world lines of photons and test particles are geodesics of the spacetime geometry) 2. That tensorial conserved quantity which is derivedfrom the curvature (Cartan’s moment of rotation) is to be identified with the tensor of stress-momentum-energy (see Chapter 15). | 1. Begin with field of spin two and zero rest mass in flat spacetime. 2. Stress-energy tensor built from this field serves as a source for this field. |
| Resulting equations | Einstein’s field equations | Einstein’s field equations |
| Resulting assessment of the spacetime geometry from which derivation started | Fundamental dynamic participant in physics | None. Resulting theory eradicates original flat geometry from all equations, showing it to be unobservable |
| View about the greatest single crisis of physics to emerge from these equations: complete gravitational collapse | Central to understanding the nature of matter and the universe | Unimportant or at most peripheral |
From Misner, Thorne, Wheeler, Gravitation. p. 437 ©1973