Gravitational potential energy

“ The effect can be deduced either from the relativity theory of gravitation or from the [Pg 122] quantum theory; for those who have some acquaintance with the quantum theory the following reasoning is probably the simplest. The stellar atom emits the same quantum of energy hν as a terrestrial atom, but this quantum has to use up some of its energy in order to escape from the attraction of the star; the energy of escape is equal to the mass hν/c2 multiplied by the gravitational potential Φ at the surface of the star. ”

“ Hence it appears that mass (inertia) and energy are essentially the same thing, or, at the most, two aspects of the same thing. It must be remembered that on this view the greater part of the mass of matter is due to concealed energy, which is not as yet releasable.
The question whether electrical energy not bound to electric charges has mass, is answered in the affirmative in the case of light. Light has mass. Presumably also gravitational energy has mass; or, if not, mass will be created when, as often happens, gravitational energy is converted into kinetic energy. ”

“ 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. ”

“ 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. ”

“ Owing, however, to the fundamental difference that was thought to exist between inertial mass, as representative of inertia, and gravitational mass, as representative of attraction, the electromagnetic field was never suspected of developing a gravitational field. Hence the difference between matter and energy remained fairly clear. Einstein’s theory, by identifying mass and energy and by showing that all forms of energy are capable of producing a gravitational field, tends to render the distinction less legitimate. ”

“ For, although the special theory of relativity makes allowance for an inertia of energy, it makes none for a gravitation of energy. Consequently, a body which absorbs energy in any way will register a gain of inertia but not of weight, thereby transgressing the principle of the equality of inertial and gravitational mass; for this purpose a theory of gravitational phenomena, a theory of gravitation, is required. ”

“ 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. ”

“ At the planet's surface, the total energy of an infinitesimally small portion of the gaseous mass is proportional to that mass. This amount of energy is, however, all that is available for transformation against gravitation in the ascent. But at the same time, the gravitative force on the particle, that force which resists its upward movement, is proportionately small corresponding to the small mass, so that the particle will in reality require to rise to the same altitude of 31 miles in order to completely transform its energy and attain absolute zero of temperature. ”

“ Now there is eternally in process a penetration of the stratum of matter by jets of the élan vital from the realm of pure spirit, each as it were striving to detach from the plane of matter some small portion, which is transformed in its passage through life and achieves entrance into the ultimate unknowable, when the process of redemption is, for this small particle, completed. Always, however, is exerted the gravitational pull of matter, and the energy that drove through, instead of pursuing a right line, tends to bend in a parabolic curve, like the trajectory of a cannon ball. ”

“ However, inertia and gravitation are in every respect and by all our experience, for the most varied materials and from the lightest to the heaviest, so closely connected with each other that we may seek without concern the origin of these two effects at the same place, namely in the latent energy of the chemical atoms. Assuming that gravity is directly proportional to the latent energy, then the mass depending on temperature is only very slightly larger than the ponderable mass which is quite independent of temperature. ”

“ The equation (51) teaches us how to introduce the energy-tensor (corresponding to the density of Poisson’s equation) in the field equations of gravitation. If we consider a complete system (for example the Solar-system) its total mass, as also its total gravitating action, will depend on the total energy of the system, ponderable as well as gravitational. This can be expressed, by putting in (51) , in place of energy-components tμσ of gravitation-field alone the sum of the energy-components of matter and gravitation, i.e. ”

“ Given a sufficient duration of retarding influence, gravity would eventually convert all energy into matter were it not for two factors: First, because of the antigravity influences of the energy controllers, and second, because organized matter tends to disintegrate under certain conditions found in very hot stars and under certain peculiar conditions in space near highly energized cold bodies of condensed matter. ”

“ 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. ”

“ Even at absolute zero, when all its vibratory or heat energy would be absent, it would be still an elastic whirling body pulling upon every other atom in the universe with gravitational energy, twisting other atoms into conformity with its own position with its magnetic energy; and, if such ether rings are like the rings which are made in air, will not stand still in one place even if no others act upon it, but will start at once by its own inherent energy to move in a right line at right angles to its own plane and in the direction of the whirl inside the ring. ”

“ The principle of the conservation of force would lead us to assume that when A and B attract each other less because of increasing distance, then some other exertion of power, either within or without them, is proportionately growing up. And again that when their distance is diminished, as from 10 to 1, the power of attraction, now increased a hundred-fold, has been produced out of some other form of power which has been equivalently reduced." [9] Were gravity merely a dynamic energy, generated in time and space by an anterior and exterior force, the inference would undoubtedly be correct. ”

“ Moreover the increase of kinetic electric energy of an electron arising from its motion with velocity v depends on , on the coefficient of inertia of the aether, and on the dimensions of its nucleus, where cis the velocity of radiation: the increase of its gravitational energy would presumably in like manner depend on , where c' is the velocity of propagation of gravitation and is enormously greater than c. On neither ground does it appear likely that mass is to any considerable degree an attribute of gravitation. ”

“ It is probable that some day we may be able to understand how the force of gravity appears to act instantaneously at a distance, and how all the transformable forces, gravity, light, heat, electricity, and molecular or atomic forces, are but different manifestations of one common energy. But in the meantime we know this for certain, that the law of gravity is not a local or special phenomenon, but prevails universally from the fixed stars to the atoms, from the infinitely great to the infinitely small. ”

“ According to the general theory of relativity, a clock will go faster the higher the gravitational potential of the location where it is located, and during partial process 3 U2 happens to be located at a higher gravitational potential than U1." U2 is in fact not at a higher gravitational potential than U1 during partial process 3, since partial process 3 occurs after the gravitational field has switched, accelerating bodies toward the positive x-direction. ”

“ As a fact of daily observation, motion is a variable function, and like heat, color, form, or density, is not conserved.
When a stone is thrown upward therefore, it loses tension, because this Ms been found empirically to be the inflexible law of distance-ratio for the gravitative force, and for no other human reason. It gains in potential energy by the ascent because there has been a corresponding expenditure of kinetic energy in effecting the ascent ”

“ 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 ”

“ Gravity presence and action is what prevents the appearance of the theoretical absolute zero, for interstellar space does not have the temperature of absolute zero. Throughout all organized space there are gravity-responding energy currents, power circuits, and ultimatonic activities, as well as organizing electronic energies. ”

“ It is impossible to imagine an infinite attribute belonging to a finite entity. [4] It is therefore in space that the energy that contributes the power of gravitation exists, and the element of matter merely gives to it a centripetal direction. This, as a consequent of the law of gravitation, seems noteworthy from it probably being applicable to molecular forces generally. It favors the idea that the function of the material element is to give directions to a living force that pervades space. ”

“ One of these forces is the bond of gravitative attraction between planet and primary which is never severed, and when complete separation of the two masses finally occurs, the incessant combination of this force with the tangential force of disruption acting on the planet will compel it into a fixed orbit, which it will pursue around the central axis. When all material links have thus been severed, the two bodies will then be absolutely separate masses in space. ”

“ In contrast to electric and magnetic fields, the gravitational field exhibits a most remarkable property, which is of fundamental importance for what follows. Bodies which are moving under the sole influence of a gravitational field receive an acceleration, which does not in the least depend either on the material or on the physical state of the body. For instance, a piece of lead and a piece of wood fall in exactly the same manner in a gravitational field (in vacuo) , when they start off from rest or with the same initial velocity. ”

“ Local or linear gravity becomes fully operative with the appearance of the atomic organization of matter. Preatomic matter becomes slightly gravity responsive when activated by X ray and other similar energies, but no measurable linear-gravity pull is exerted on free, unattached, and uncharged electronic-energy particles or on unassociated ultimatons. ”

“ In the new order of transformations which come into play in virtue of the rotatory motion of a planetary mass in the field of its primary, we shall find other incepting influences in action entirely different in nature from the gravitation influence, but, nevertheless, arising from the same primary mass in a similar way. Now the application of energy to the planet, causing it to rotate in the lines or under the influence of these incepting fields of the primary, brings into existence on the planet an entirely new order of phenomena. ”

“ 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. By a suitable choice of units we can thus make this ratio equal to unity. We then have the following law: The gravitational mass of a body is equal to its inertial mass. ”

“ He could not really believe in an inherent central force of attraction residing in a material atom, by which it could draw towards itself another such atom situated at a distance, or that it could affect other matter in any way than by the impact of intervening atoms; and he predicted that some day the cause of universal gravitation would be discovered. ”