Gravitational potential

“ The units already considered, namely foot-pounds or kilogrammetres, are gravitational units, depending on the force of gravity. This is the most obvious and natural method of measuring the potential energy of a raised weight, but it has the disadvantage of varying with the force of gravity at different places. The natural measure of the kinetic energy of a moving body is the product of its mass by half the square of its velocity, which gives a measure in kinetic or absolute units independent of the force of gravity. ”

“ The law of gravitation is not a law in the sense that it restricts the possible behaviour of the substratum of the world; it is merely the definition of a vacuum. We need not regard matter as a foreign entity causing a disturbance in the gravitational field ”

“ For smaller or hotter bodies, radiation repulsion overpowers mutual gravitation; and it increases with the fourth power of their absolute temperature. The gravitational attractive force between particles is exceedingly small; and that between two atoms or two electrons is negligibly small, even though they be within molecular distance of each other. ”

“ If so, the maintenance of the field of strain about an atom as it moves presents no greater difficulty than the maintenance of the field of light about a moving candle, or of the field of sound about a moving bell. The propagation of such ether strains as occur in light, electricity and magnetism is very greatly influenced by the material substances present in the strained medium. It is not probable that the gravitational strain differs from others in this respect, and we may reasonably hope to find some inductive phenomena in connection with gravitation. ”

“ So long as forces are confined to the thrusts and tensions of elementary mechanics, where there is supposed to be direct contact of material, there is good ground for this distinction; we can visualise the active hammering of the molecules on the body, causing it to change its motion. But when force is extended to include the gravitational field the distinction is not so clear.
For our part we deny the distinction in this last case. Gravitational force is not an active agent working against the passive tendency of inertia. Gravitation and inertia are one. ”

“ If now, as we find from experience, the acceleration is to be independent of the nature and the condition of the body and always the same for a given gravitational field, then the ratio of the gravitational to the inertial mass must likewise be the same for all bodies. ”

“ The special theory of relativity can, therefore, be regarded only as a stepping-stone to a more general principle, which orders gravitational phenomena satisfactorily into the principles of mechanics. ”

“ The force of gravity is not cut off or screened off by the interposition of other masses. A recent investigation by Professor Poynting, F.R.S., has shown that so far as all evidence goes all bodies, even the densest, are transparent with respect to gravitational forces. ”

“ Then the postulate of equivalence allows us to assert that exactly the same results would have ensued had the enclosure been at rest in a uniform gravitational field; so that regardless of whether or not uniform gravitational fields generated by matter can exist, we are led to the general conclusion that a gravitational field will bend the course of light waves and modify their velocity. ”

“ To be sure, the accelerated coordinate systems cannot be called upon as real causes for the field, an opinion that a jocular critic saw fit to attribute to me on one occasion. But all the stars that are in the universe, can be conceived as taking part in bringing forth the gravitational field; because during the accelerated phases of the coordinate system K' they are accelerated relative to the latter and thereby can induce a gravitational field, similar to how electric charges in accelerated motion can induce an electric field. ”

“ The gravitational atoms are directed not only toward the centers of the greater bodies, but toward each of their particles as well, since they move indiscriminately in all directions in space. The atoms, moreover, act effectively in those directions in which their antagonists are intercepted; that is to say, in all directions in which there are particles of matter. Therefore they tend to move the heavy masses which they encounter not toward the heavenly bodies in gross, but toward each of their particles in detail. ”

“ Among small bodies gravitational forces are slight, and are altogether exceeded by magnetic and electric or chemical forces. Indeed gravitational attraction between bodies of a certain smallness can be more than counterbalanced even by the pressure which their mutual radiation exerts—almost infinitesimal though that is;—so that as a matter of fact, small enough bodies of any warmth will repel each other unless they are in an enclosure of constant temperature, i.e. unless the radiation pressure upon them is uniform all round. ”

“ The solutions of all these difficulties depend either on the permeability of the heavy body or the subtlety and rapidity of the gravitational atoms - properties to none of which we are obliged to assign two opposing limits. ”

“ The centripetal agencies.
Gravity.—The most obvious of the concentrating forces is gravity, and in most questions relating to great segmental movements, it has been thought sufficient to consider gravity alone, but it is by no means certain that this does not lead to serious error. In studying the causes and effects of earth movements, it is necessary to consider both gravitational energy and gravitational force. Gravitational energy is greatest when the mass is most widely dispersed, and least when most concentrated. ”

“ Suppose now a second body is placed in the medium near the first as in the figure. It is evident that a shielding effect of each by the other is brought about. The complete symmetry of the system of impacts is disturbed and the equilibrium of each body is destroyed. By the unbalanced pressure on the remote side each will be urged towards the other, and we thus have the effect of gravitational attraction. To revert to our illustration from light, suppose that within the self luminous hollow sphere, two opaque bodies are situated. Each will cut off from the other a certain amount of light. ”

“ Approximate integration of the gravitational equations has in fact yielded the result that induction effects must occur when masses are in accelerated motion. This consideration makes it clear that a complete clarification of the questions you have raised can only be attained if one envisions for the geometric-mechanical constitution of the Universe a representation that complies with the theory. ”

“ Although it has become necessary to throw our formula into the melting-pot, that does not create any difficulty in measuring the interval. Without going into technical details, it may be pointed out that the innovations arise solely from the introduction of gravitational fields of force into our scheme. When there is no force, the tracks of all particles are straight lines as our previous geometry requires. In any small region we can choose an observer (falling freely) for whom the force vanishes, and accordingly the original formula holds good. ”

“ Many physicists believe that, since electrical forces operate independently of gravitational forces, interchanging the charges on protons and electrons would probably have no effect on the gravitational field. ”

“ Probably the mass necessary to demonstrate any action of the gravitational kind would be impractically large, unless the earth itself could be used. Now, by staking out mirrors at the corners of a field, it is arithmetically quite possible to arrange for a perceptible shift of the bands due to the rotation of the earth, if it carries ether round with it; but it does not seem possible to experimentally observe that shift, unless some method could be devised of making the observer and his apparatus independent of the rotation. ”