Field (physics)

“ It is essential to realize that all fields dealt with by physical science, the gravitational, electric, magnetic - however much they differ otherwise - have this one characteristic in common, that they have a centre where the field is at its highest intensity, diminishing as the distance from the centre increases. Motion in such a field naturally takes place from regions of lower to those of higher intensity - in other words, it follows the rising potential of the field. This accounts for the tendency of physical masses to arrive at the shortest possible distance between them. ”

“ The body (e.g. the earth) produces a field in its immediate neighbourhood directly; the intensity and direction of the field at points farther removed from the body are thence determined by the law which governs the properties in space of the gravitational fields themselves. ”

“ We may therefore receive, as a datum derived from a branch of science independent of that with which we have to deal, the existence of a pervading medium of small but real density, capable of being set in motion, and of transmitting motion from one part to another with great, but not infinite, velocity. ”

“ Clearly the artificial field of force is associated with curvature of track, and we can lay down the following rule:—
Whenever the observer's track through the four-dimensional world is curved he perceives an artificial field of force. ”

“ But remember, it is not a body that pulls another body, but a gravitational field that pulls another. The field is in space. A normal field is necessarily attached to the matter that it represents, or that represents it as you prefer, but this artificial field has no connection in the form of matter. It is a product of a machine, and exists only as a strain in space. To move it you must move all space, since it, like artificial matter, exists only where it is created in space. ”

“ Whenever a current is induced by the relative motion of a magnetic field and a conductor, the direction of the induced current is always such as to set up a magnetic field that opposes the motion. Lenz's Law follows from the principle of conservation of energy, that energy can be produced only from an expenditure of other energy. ”

“ Electrical Fields.—In our study of magnetism we learned that a magnet affects objects about it by its magnetic lines of force. In a similar way it is assumed that a charged body produces electrical effects upon its surroundings by electric lines of force. For example, the attraction that a charged body exerts upon light objects through short distances or the influence of a charge upon an electroscope several feet away, is said to be due to the electric field about the charged body. ”

“ If a point-mass of electric unit pole moves in an electro-magnetic field, then the force acting upon it is equivalent to the electric force existing at the position of the unit pole, which we obtain by the transformation of the field to a co-ordinate system which is at rest relative to the electric unit pole [New mode of expression] . ”

“ When the direction and magnitude of the force are the same throughout space and do not vary with time, the field of force is called uniform. Uniform fields of force are very difficult to obtain; the simplest illustration we can think of would be that given by a river flowing with constant speed along a rectilinear course. The force exerted by the current would of course remain the same in magnitude and in direction at all points in the river; and for this reason the field of force produced by the current would constitute a uniform field. ”

“ The attraction of the earth for other bodies on or near it is called gravity. The weight of a body is the measure of the earth's attraction for it; or it is the force of gravity acting upon it. Newton's third law of motion states that every action is accompanied by an equal and opposite reaction (Art. 80) . Hence, the attraction of the earth for a book or any other object is accompanied by an equal attraction of the book for the earth.
89. Weight.—In advanced physics it is proved that a sphere attracts as if it were concentrated at its center. ”

“ Do you not know that every mass of matter in motion carries with it an invisible gravitational field, every magnet an invisible magnetic field, and every living organism a mesmeric field? Even you have a perceptible mesmeric field. Feeble as it is, it is the strongest I have yet observed in a shortliver. ”

“ According to the field-concept, terrestrial manifestations of gravity are due to the earth's being the bearer of a gravitational field centred within the globe, and extending thence in all directions through space, across and beyond the earth's body. Every point in space, both inside and outside the earth, is characterized by a definite intensity of this field, the so-called gravitational potential. ”

“ The very fact that there is a limiting speed to light and particle motion introduces the concept that space has physical properties.
"In order to have an electromagnetic wave, one must have a medium in which an electric field or a magnetic field may exist. In order to have matter, which I believe to be a form of electromagnetic field in stasis, one must have special properties which make the existence of matter possible. In order to have inertia, one must also have spatial properties which make the existence of inertia possible. ”

“ With the introduction, in Chapter X, of the peripheral type of force-field which appertains to levity as the usual central one does to gravity, we are compelled to revise our conception of space. For in a space of a kind we are accustomed to conceive, that is, the three-dimensional, Euclidean space, the existence of such a field with its characteristic of increasing in strength in the outward direction is a paradox, contrary to mathematical logic. ”

“ The difference of potential between any two points is called an electromotive force. The lines of force are necessarily perpendicular to the surface. When the lines of force and the equipotential surfaces are straight, parallel, and equidistant, we have a uniform field. The intensity of the field is shown by the number of lines passing through unit area, and the rate of variation of potential by the number of equipotential surfaces cutting unit length of each line of force. ”

“ If these surfaces are so drawn that, when a unit pole passes from any one to the next in order, unity of work is done, then the work done in any motion of a magnetic pole will be measured by the strength of the pole multiplied by the number of surfaces which it has passed through in the positive direction. ”

“ Now, if we rest satisfied with this type of description of a field of force, we see that in the case of a uniform field, at any rate, there is no means of differentiating a region of the river or field that is upstream from one that is downstream. ”

“ I have shown in two recently published reports, [1] how one can arrive at field equations of gravitation, that are in agreement with the postulate of general relativity, i.e. which in their general form are covariant in respect to arbitrary substitutions of space-time variables. ”

“ Together with inertial forces, something comes into light which was until now be interpreted as the "geometrical structure": the "guidance field", as something real, as an acting power of shaking force in some cases. ”

“ The field of force about an atom is also capable of representation by a function of the space co-ordinates such that when the distance r from the atom is relatively great the equipotential surfaces are very nearly spheres. ”

“ Electricity ranks in eternal antagonism to magnetism.
33
SPHERE, HEAT, CHEMISTRY.
140. The line and surface are density, the representation of time and space; they have therefore like these originated out of nothing, namely, out of the point. The sphere is the expanded nothing. Nothing thus extended, or nothing posited, becomes a something, viz. line, surface, density, polarity. The line is a long nothing, the surface a hollow nothing, the sphere a dense nothing; in short, the something is a nothing which has received only predicates. All things are nothings with different forms. ”

“ The gravitational field surrounding the earth constitutes only one particular illustration. We may also consider the electric field surrounding an electron, or the magnetic field surrounding the poles of a magnet, or even combinations of these two fields, such as the electromagnetic fields produced by electric currents. ”

“ Now if the globes are not homogeneous, the space described by the denser globe must be augmented in the ratio of the density. For the motion, with an equal velocity, is greater in the ratio of the density, and the time (by this Prop.) is augmented in the ratio of motion directly, and the space described in the ratio of the time.
Cor. 5. And if the globes move in different mediums, the space, in a medium which, cæteris paribus, resists the most, must be diminished in the ratio of the greater resistance. ”

“ And therefore the globe meets with a resistance, which is to the force by which its whole motion may be either taken away or generated in the time in which it describes two thirds of its diameter moving uniformly forwards, as the density of the medium to the density of the globe. ”

“ Let two spheres of radius be connected together so that their centres kept at a distance , and let them be suspended in a uniform magnetic field, then, although each sphere by itself would have been in equilibrium at any part of the field, the disturbance of the field will produce forces tending to make the balls set in a particular direction. ”

“ The right-hand side expresses the interaction of the energy of the gravitational-field on matter. The field-equations of gravitation contain thus at the same time 4 conditions which are to be satisfied by all material phenomena. We get the equations of the material phenomena completely when the latter is characterised by four other differential equations independent of one another. ”

“ After tracing to the action of the surrounding medium both the magnetic and the electric attractions and repulsions, and finding them to depend on the inverse square of the distance, we are naturally led to inquire whether the attraction of gravitation, which follows the same law of the distance, is not also traceable to the action of a surrounding medium. ”

“ But even in elementary mechanics an important natural force appears, which does not seem to operate in this manner. Gravitation is not resolvable into a succession of molecular blows. A massive body, such as the earth, seems to be surrounded by a field of latent force, ready, if another body enters the field, to become active, and transmit motion. ”

“ In outer nature the all-embracing plane is as much the 'centre' of the earth's field of levity as the all-relating point is the centre of her field of gravity. All actions of dynamic entities, such as that of the ur-plant and its subordinate types, start from this plane. Seeds, eye-formations, etc., are nothing but individual all-relating points in respect of this plane. All that springs from such points does so because of the point's relation to the all-embracing plane. ”

“ So far we have considered the cancellation of a field of gravitation, but we may also consider the creation of a field of force in empty space far from matter. Thus, if a hollow chest be subjected to a variable acceleration through empty space, a variable field of force (inertial force) will be experienced by an observer in the chest’s interior. ”

“ Not only must it have an electric field; but that field must possess different potentials, possessing a higher potential the nearer the field gets to the sun, and a lower potential the farther away the field is. ”

“ As a result of this feature, whereas it is always possible to cancel a field of force entirely by changing the motion of our frame in a suitable way when the field contemplated exists in regions remote from matter, on the other hand, in the neighbourhood of matter, the field of force can be modified, and even cancelled in a small region, but never cancelled over any wide extension. ”

“ If we suppose any surface divided into elementary portions such that the surface-integral of each element is unity, and if solenoids are drawn through the field of force having these elements for their bases, then the surface-integral for any other surface will be re presented by the number of solenoids which it cuts. ”

“ Supposing what is above demonstrated, I say, that if the tangents of the angles of the sector of a circle, and of an hyperbola, be taken proportional to the velocities, the radius being of a fit magnitude, all the time of the ascent to the highest place will be as the sector of the circle, and all the time of descending from the highest place as the sector of the hyperbola. To the right line AC, which expresses the force of gravity, let AD be drawn perpendicular and equal. ”

“ Law of Gravitation.—Every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. ”

“ Recently I find now, that one is able to dispense with hypothesis concerning the energy tensor of matter, if one fills in the energy tensor of matter into the field equations in a somehow different way than it was done in my two earlier reports. ”