**The Principle of Equivalence**

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.

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

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.

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.

** Summation **

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:

Gravitation is established as a deformation of spacetime in the presence of mass, its effects being the product of the concentration of spacetime toward centers of mass, or "vertices." As such, gravitation cannot be a force, it cannot therefore be mediated by a particle, and it cannot radiate as mass-energy. The assimilation of gravitation by quantum theory and its derivatives as a field of force, and the positing of a gravitational quantum of action where none is apparent, theoretically necessary, or conceptually coherent are entirely without justification.3

These are admittedly unsettling propositions, but in consolation, their acceptance would make one of the principal objectives 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 acceptance might also signal the need to rely more upon conceptualization, and not so heavily on mathematical formalisms in the development of physical hypotheses.

**Endnotes**

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