Gravity is the least understood of all the forces. It is often said that we have a successful theory of gravity in General Relativity. General Relativity, certainly, enables us to predict accurately a number of effects and physical phenomena – light deflection, time delay, redshift, perihelion precession, gravitational waves, etc – but it doesn’t help us to understand what gravity is or how it relates to the rest of physics.
We are told, frequently, that the theory tells us that the effect equivalent to gravitational ‘force’ in Newtonian theory is ‘caused by’ a local curvature of space-time, but this is not the real difference between the theories. It is well-known that Cartan in 1924 showed that any field theory, including Newtonian gravity, could be represented by the mathematics of curvature. In effect, terms added to the space and time derivatives (to create the covariant derivatives that describe the presence of the field) can be either physical field terms or curvature terms. In using geometric methods to calculate perturbed orbits, Newton himself provided a case in which the effect of a perturbing force could be replaced by the curvature of an equivalent orbit varying in space and time (Principia, Book I, Proposition 44, Corollary 6). In addition, General Relativity requires Newtonian theory, including the Newtonian potential to make sense of its local solutions.
In principle, the field equations of General Relativity are an abstract description of mathematical curvature with no additional physical meaning unless we equate it via the Newtonian gravitational constant to the energy-momentum tensor (the stress tensor in Newtonian theory). In Cartan’s presentation, the Newtonian version of this process is equivalent to Rab= 8πTabby comparison with the General Relativistic Rab= 8π(Tab− gabT/2), where the extra terms on the right-hand side originate in the Lorentzian or relativistic connection of space and time.
In fact, I believe it is meaningless to talk about physics as though there is a ‘real’ ontology apart from the abstractions. Physics is, in its foundations, a totally abstract subject in which the seeming tangibility of material objects is simply an emergent property. The properties of the four parameters which determine the entire content of physics have an entirely algebraic origin. Newton’s ‘gravitational force’ was as much an abstraction as Einstein’s curvature, an effect capable of mathematical exposition, not a mechanism. As the first physicist to base the subject on a totally abstract methodology, he went out of his way to avoid specifying ‘physical’ causes as necessary to his explanation.
The most remarkable thing about the Newtonian and Einsteinian theories is that they are, in principle, both totally abstract, and this is the source of their success in explaining many phenomena. What they don’t tell us is what gravity is, only what it does, and in strongly similar ways. The difference between them has nothing to do with any metaphor used to describe them. It concerns rather the natureof the force involved. The space-time used to describe General Relativity is that of a LOCAL interaction, that of Newtonian gravity is of a NONLOCAL one. All other differences stem from this.
As the work described in the Nilpotent Quantum Mechanics section demonstrates, however, local and nonlocal descriptions of forces are not in mutual contradiction. They are complementary aspects of the same phenomena. All interactions are simultaneously both local and nonlocal. A nilpotent bracket defines everything inside as local and everything outside as local, and all interactions have both local and nonlocal manifestations. Significantly, the local is discrete while the nonlocal is continuous. The weak, strong and electric interactions define the localised particle as real and the nonlocal vacuum as virtual. Gravity, which acts like a cancellation of the sum of these interactions, defines the localised particle as virtual and the vacuum as real. The local (virtual) version of gravity manifests itself as INERTIA, and is a repulsive (positive energy) force, like the forces between identical discrete weak, strong and electric sources. The attractive force of gravity requires negative energy, like that of (the continuous) vacuum in quantum mechanics.
My view of gravity is conditioned by the fact that mass is a continuous parameter in the Klein-4 group, as it is in the Higgs field, zero-point energy, the cosmic microwave background and other phenomena. There is no point in space without mass. I have, therefore, always questioned the idea that gravity is a purely local interaction, like those based on discrete charges.