Physics has all but surrendered to mathematics in the last hundred years. I believe this has been detrimental, and nowhere more than in gravitation theory. The general theory of relativity was conceptual in origin, mathematical in its corroboration. The theory has represented gravitation as a product of the “curvature” or deformation of spacetime in the presence of mass, and both the evidence and the supportive mathematics have been entirely adequate to justify its acceptance. Gravitation is nevertheless described in terms of the mathematics of quantum theory as a force and associated with a hypothetical particle, without either an explicit dissension from the geometric conception or empirical evidence of the particle.
Conceptual physics, which I take to be roughly coextensive with pre-quantum physics, involved the initial development of coherent hypotheses and secondarily the employment of mathematics (or experiments) to support their plausibility. A mathematical formalism without conceptual coherence would be regarded as irremediably provisional, if not unsatisfactory, in the former methodology. With respect to the former physics, two thought-experiments will be employed here, without resort to mathematics, to demonstrate that the quantum interpretation of gravitation is conceptually flawed and without empirical support.
A description of the first experiment may be unnecessary, but the pre-relativistic association of gravitation with inertia and of inertia with universal mass is still maintained on occasion, if only tacitly, and may be the ultimate basis of the continued identification of gravitation with force. The identification may also be a residue of one of our most familiar experiences on the earth's surface: The pressure we feel between ourselves and the surface is fundamental to our original concept of gravitation; we tend to regard the pressure as a force (“the force of gravity”) and our surface station as being at rest. The following experiment may therefore be helpful toward more clearly dispelling the identification of gravitation with force and inertia, and also in prefacing the second experiment (actually a thought-investigation) of the force-free continuity between astronomical gravitation and gravitation at the surface of a massive body:
Imagine a spacecraft traveling a uniform path relative to the "fixed stars" which comes under the influence of a stellar object nearby and begins to deviate toward it, while continuing in uniform motion by the evidence of free-floating objects inside. In order to maintain the original course a thruster is fired and inertial effects are experienced onboard as the craft accelerates just enough to counter the influence of the local gravitational field.
Note that in this experiment inertial effects are associated with uniform motion relative to the distant stars, contrary to the pre-relativistic Machian expectation. Aside from the discrimination of inertia from any influence of the overall mass of the universe (an association that is seldom explicitly defended now anyway), the experiment demonstrates what I hold to be most significant, that at least in the situation just described, force becomes evident in conjunction with gravitation only when gravitation is being resisted.*
Now consider an experiment that comprehends the transition from astronomical gravitation along a geodesic to an involvement with force and inertia at the surface of a massive body:
Imagine two test bodies gravitating toward the earth from some considerable distance. For the sake of simplicity, consider the earth to be at rest and the test bodies to be gravitating directly toward its center of mass. (They appear to be simply “falling” from a perspective on the earth’s surface.) One body is an immense hollow sphere of negligible mass, the other is relatively small in size -- an extra-vehicular scientist, let's say -- and also of negligible mass. Notice that while the test bodies are falling toward the earth (or more accurately, while the three bodies are converging) there is among them a purely relative transformation of potential energy to kinetic energy as each moves uniformly in its own frame of reference -- there is, at least as yet, no occasion for an exchange of mass-energy in the form of the supposed gravitational energy. Let the sphere and the scientist be placed initially close together so that as they approach the earth their geodesics converge enough to bring their surfaces in contact some time before the larger impact. (It is the fantastic size of the hollow sphere that allows the surfaces of the two bodies to meet somewhere above the earth's surface). From the moment the sphere and the scientist come in contact until they reach the surface of the earth an inertial acceleration between them will intensify as each tries to conform to its own geodesic at an ever greater angle to the normal. The situation will, if viewed in isolation, come to resemble the gravitation of a small body pressing against a planetary surface (although the gravitation between them is actually insignificant due to their negligible masses) and the scientist will even be able to stand upon the sphere. This development of an increasing inertial acceleration between the test bodies is the only aspect of the situation which changes from the moment they meet; the earthward component of their motion continues as before, a relative gravitation. In a way similar to the first experiment, force has developed in the resistance to what is in this case a convergent gravitation of two bodies toward another. And once the two reach the earth the situation remains essentially the same: Each one, now in conjunction with the entire conglomerate of the earth, presses toward the center of mass with the same sort of conflict of geodesics as was observed between them when they were gravitating from a distance. Along with the other components of the earth at and below the surface, they are resisted, and thereby accelerated, by those further below, due to the coincidence of the common inclination toward the center of mass and the subordinate obstructions.
This second experiment demonstrates that it is only in the inertial conflict of geodesics (or as in the first experiment, in a singular inertial acceleration) that force can be observed in association with gravitational phenomena. The intersection of geodesics and the consequent inertial effects constitute the interruption of gravitation, and what is commonly conceived as “the force of gravity” at a surface would be more accurately described as anti-gravitation.
Gravity has to be considered absolute in the aspect that a geometric vertex exists at a center of mass that cannot be transformed, either conceptually or mathematically. But unless the geodesic of a body brings it to a massive obstruction, such as the surface of a planetary body, gravitation involves uniform motion with only relative accelerations -- no force can be attributed.
There remains a most significant aspect of the situation disclosed in the second experiment to be comprehended, although its full implications must be left outside the scope of this discussion. The energy expressed in the continuous static acceleration of bodies at or below a surface toward a center of mass is rendered inexplicable in purely geometric terms when gravitation is finally discriminated from force. If there is no “force of gravity”, what accounts for the persistent energy of the inertial acceleration at a surface after a body has come to a relative state of rest? Recall that in the initial appearance of force in the second experiment only a conflict of geodesics is present and resistant against the otherwise uniform motion of the test bodies. No extrinsic source of energy can be identified, yet there is a static acceleration between the two, while the gravitation with the earth remains relative. I believe the only available explanation is that motion as-such, the motion of matter in general, must be regarded as absolute, although relative in the various incidental trajectories between individual bodies. I wish to maintain that the source of the energy usually identified as gravitational energy must be attributed to an intrinsic and ceaseless dynamic of mass-energy, independent of gravitation but uniquely revealed by its coincidence.
Having briefly acknowledged the implications of a consistent geometric theory of gravitation, that gravitation and motion in general are each in their own way both relative and absolute, that mass-energy is somehow intrinsically dynamic and the source of the energy disclosed in the opposition of gravitation and its occasional resistance, I will consolidate the findings with regard to quantum theory in the following summation:
Gravitation is evidently a deformation of spacetime in the presence of mass, its effects the product of the concentration of spacetime at vertices, at centers of mass. As such, gravitation cannot be a force, and cannot therefore be mediated by a particle. The assimilation of gravitation by quantum theory and its derivatives (e.g., string theory) as a field of force, and the positing of a gravitational quantum of action where none is apparent, theoretically necessary, or conceptually coherent is entirely without justification.
This is admittedly an unsettling proposition, but in consolation its acceptance would make one of the principal projects of quantum theory less complicated, as gravitation with all its peculiarities could be disregarded in the pursuit of a unified field theory. I hope that it might also signal the need to rely more upon conceptualization, and not so heavily on mathematical formalisms, in the development of physical hypotheses.
* Incidentally, there may also be evidence of force if the gradient of a gravitational field is severe enough to produce tidal stresses to a body’s molecular binding energies.