# The Principle of the Relativity of the Gravitational Potential

• Gustav Mie
Chapter
Part of the Boston Studies in the Philosophy of Science book series (BSPS, volume 250)

1. Gravity has long eluded theoretical investigation, and, apart from the meager knowledge gained by experience, the main reason is that the gravitational field exhibits the peculiarity that the field itself is amplified when it performs external work. It is therefore difficult to design the theory so that it does not conflict with the energy principle. Admittedly the magnetic field of two current-carrying conductors shows the same peculiarity. However, in that case one readily recognizes in the apparatus that provides the current the source of energy both for the energy increase of the magnetic field and for the energy carried off as work. For the gravitational field such an external energy source is absent, and therefore one formerly used to assume in gravitational theories that the energy of the field is negative, so that upon amplification of the field a positive energy is released and is manifested as work gained. Every theory of gravitation that is built upon the scheme of Maxwell's equations must make the assumption of a negative energy. But this assumption is untenable, because a field whose energy is negative cannot be in stable equilibrium, but is always unstable. Namely, whereas an electrostatic field, for example, exhibits that distribution of lines of force for which the energy has the smallest possible value, a field that is similarly constituted but with negative energy has of course precisely the largest possible value at equilibrium. It is therefore to be expected that when the equilibrium is slightly perturbed, the field will continually release energy to the exterior | while simultaneously moving further and further away from its equilibrium state. So in this way one does not attain a satisfactory theory of gravity.

A simple, feasible way leading out of this difficulty was first indicated by M. Abraham.1 This way consists of including in the state variables, upon which the amount of energy per cubic centimeter depends, the potential of the field, formerly taken to be only a “mathematical construct”, rather than only the field strength of the gravitational field, formerly considered exclusively. Now, when two gravitating masses approach each other, there is on the one hand an increase in the energy of the field, counted as positive exactly like that of an electric field of similar appearance, but at the same time there is a change, a decrease to be exact, in the internal energy of the approaching material bodies, because in them the potential of the gravitational field becomes different. So the two gravitating masses release a part of their internal energy as a consequence of the change in their gravitational potentials, and thus provide the source for the work gained due to the attraction as well rather than only the increase in energy of the gravitational field. Thus, in the case of the gravitational field, matter under the influence of a changed potential performs the same task as the current source in the case of the magnetic field between current-carrying conductors mentioned above.

## Keywords

Gravitational Field Gravitational Potential Lorentz Transformation Inertial Mass Material Body
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