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Gravitation, force and energy

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The Principle of Equivalence

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Einstein's original conception of an "equivalence" between gravitation and inertial acceleration pre-dated his recognition of gravitation as a product of spacetime geometry. From the beginning, he expected a generalization of relativity to demonstrate that gravitational and inertial accelerations could be equated as aspects of a single principle, just as uniform motion and non-motion (rest) had been resolved in the Special Theory.

Using a thought experiment with an elevator Einstein sought to illustrate the equivalence "of a gravitational field and the corresponding [inertial] acceleration of [a] reference frame" (1907) by comparing the experience within the elevator in a normal gravitational situation with its being accelerated by a cable attached to a spacecraft somewhere beyond gravitational influence. Although he evidently never revisited the experiment after developing his geometric interpretation of gravity, it should be clear by now that the only reason for the similarity of the two situations is that in the one there is an inertial acceleration and in the other there is " an inertial acceleration.

The notion of equivalence remains a foundational principle in gravitation theory, although its ongoing theoretical relevance and practical application may be questioned. The principle has more recently been interpreted with greater circumscription, sometimes as an axiom that gravitational and inertial masses are equivalent, but more often, as in Dicke's "weak principle of equivalence" (1970), as a dispensation that gravitational effects in most laboratory experiments can be transformed away by regarding the lab as falling freely.

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The subsequent variations on "equivalence" share with the original an implicit identification of gravitation with inertia. The idea of gravitational mass presumes a gravitational force. The "weak principle" is in its common interpretation actually recommending the transformation of inertial (not gravitational) effects at the earth's surface so that experiments can be more clearly and accurately interpreted; the gravitational effects are actually the uniform motion (the "free-fall") being assumed. But even if "equivalence" is formulated in acceptable geometric terms, if it is only claimed that in a sufficiently small region of spacetime gravitational distortions can be ignored for practical purposes, "equivalence" is thereby reduced from a physical principle to a prescription or license for experimental expedience. If it is claimed that the spacetime restriction rescues the principle from the objection that geodesics converge in a gravitational field but not in an inertial acceleration, the expedient becomes a theoretical sleight of hand. It would, after all, be a curious principle that could only be invoked if we agreed to limit the scope of our observations and the precision of our instruments just enough to render its falsification undetectable.

Implicit in the Equivalence Principle (we should say "principles") is its more pertinent antithesis, which may be formulated as follows: First, drawing from the considerations and experiments discussed earlier, there is no intrinsic relationship, and certainly no equivalence, between gravitational and inertial acceleration. Second, however similar the trajectories of a gravitation and an inertial acceleration may appear, it is always possible in principle to distinguish curvilinear motion due to gravitation from that due to a forceful influence; an electrically neutral test body in a container not pressing against a surface will, for example, distinctly express a situation as either gravitational or inertial by either floating freely or tending toward one side of the container. Third, to affirm what "equivalence" is often used to suppress, there is, in principle, no place in the universe, however small, that is truly "flat", and no two coordinate systems, however proximate, that share exactly the same spacetime metric; the fact remains that geodesics converge in a gravitational field, but corresponding inertial accelerations are parallel. Although there are limits to our ability to discern local geometric deformations, and although in many cases we are justified in treating them as insignificant, if there is to be a principle in gravitation theory pertaining to inertial acceleration, it should be a principle of non- equivalence .

Gravitation, relativity, absolutes, and energy

When gravitation is isolated from circumstances where it is being resisted there is only geodesic motion -- curvilinear or straight, energetic or not, according to another frame of reference. In the relative accelerations and decelerations of orbital dynamics, and in the perturbations of orbits due to external gravitational influences, there is no intrinsic indication of force or gravitational energy, there is only the appearance of acceleration and kinetic energy from the perspective of other reference frames.2

The reliance on mathematics for conceptualization and inference discussed earlier is nowhere more striking than in the problem that the Field Equations don't allow gravitational energy to be identified or mathematically expressed in particular circumstances. It isn't questioned whether such energy actually exists, it is said that it can't be "localized" (Misner, Thorne & Wheeler 1973). Thus a theoretical problem is considered nothing more than a mathematical oddity and rendered effectively unproblematic.

From a purely empirical and conceptual perspective, gravity has to be considered absolute in the aspect that a geometric vortex exists at a center of mass that cannot be transformed, either conceptually or mathematically. But unless the geodesic of a body directs it toward a vortex and it becomes obstructed, as at the surface of a planetary body, gravitation involves uniform motion with only relative accelerations. No force or energy can be ascribed.

Given a clear discrimination of gravitation and inertia, a generalization of relativity to include inertial accelerations is untenable. An experiment with a test particle in a container will confirm that an inertial acceleration is absolute, whereas an unobstructed gravitation is not.

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There remains a most significant aspect of the distinction between gravitation and force 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 massive surface is rendered inexplicable in purely geometric terms when gravitation is finally distinguished from force. If gravitation is a warping of spacetime due to the presence of mass, 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 described above, 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, even while their gravitation with the earth remains relative. I believe the only tenable explanation is that motion as-such, the motion of matter in general, must be regarded as absolute, although relative in the incidental trajectories between individual bodies. Evidently, the source of the energy usually identified as gravitational energy should be attributed to an intrinsic and ceaseless dynamic of mass-energy, independent of gravitation, obscured by the conflation of gravitation and inertial acceleration in their incidental coincidence, but revealed by their fundamental distinction.


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 to gravitation in its occasional resistance, I will consolidate the findings with regard to quantum theory and other force-based theories in the following summation:

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A former visitant of UC Santa Cruz, former union boilermaker, ex-Marine, Vietnam vet, anti-war activist, dilettante in science with an earth-shaking theory on the nature of light (which no one will consider), philosopher in the tradition of Schelling, Hegel, Merleau-Ponty, Marx, and Fromm (sigh, no one listens to me on that either), author of a book on wine clubs (ahem), and cast-off programmer of ancient computer languages. I've recently had two physics articles published in an obscure but earnest Central European journal (European Scientific Journal http://www.eujournal.org/index.php/esj) but my main interests remain politics and philosophy.

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