Elementary particle

“ Hence, the main difficulty attending the possible amplification of objects less than about the 1100000 of an inch in diameter is a purely physical one, and depends upon the constitution of light itself.
The various phenomena of chemical physics teach us that matter is not homogeneous, but is made up of infinitesimal particles or atoms, the term atom meaning indivisible particle; and that the term molecule—meaning literally a little mass—refers to an aggregation of two or more atoms. ”

“ From the present state of theory it looks as if the electromagnetic field, as opposed to the gravitational field, rests upon an entirely new formal motif, as though nature might just as well have endowed the gravitational ether with fields of quite another type, for example, with fields of a scalar potential, instead of fields of the electromagnetic type.
Since according to our present conceptions the elementary particles of matter are also, in their essence, nothing else than condensations of the electromagnetic field, our present view of the universe presents two realities which are completely separated from each other conceptually, although connected causally, namely, gravitational ether and electromagnetic field, or — as they might also be called — space and matter. ”

“ We will illustrate this by two examples, in one of which the antecedent is the sum of many homogeneous, in the other of heterogeneous, parts. The weight of a body is made up of the weights of its minute particles; a truth which astronomers express in its most general terms when they say that bodies, at equal distances, gravitate to one another in proportion to their quantity of matter. All true propositions, therefore, which can be made concerning gravity, are derivative laws; the ultimate law into which they are all resolvable being, that every particle of matter attracts every other. ”

“ We have been seeking, in this chapter, to define matter so that there must be such a thing if the formulæ of physics are true. If we had made our definition such as to secure that a particle of matter should be what one thinks of as substantial, a hard, definite lump, we should not have been sure that any such thing exists. ”

“ A geometrician exactly knew the different energies acting in each case, with the properties of the particles moved, could demonstrate that after the causes given, each particle acted precisely as it ought to act, and that it could not have acted otherwise than it did. ”

“ 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. ”

“ When the distance between the attracting bodies becomes comparable with [22] their dimensions, so that they can no longer be regarded as practically at a point, the supposition is made that between every particle of the one and every particle of the other there is an action in the straight line joining the particles. The results which mathematical theory builds on this supposition are perfectly concordant with experience. ”

“ For if the bodies are divided into particles proportional to the wholes, and alike situated in them, it will be, as the attraction towards any particle of one of the bodies to the attraction towards the correspondent particle in the other body, so are the attractions towards the several particles of the first body, to the attractions towards the several correspondent particles of the other body; and, by composition, so is the attraction towards the first whole body to the attraction towards the second whole body. ”

“ For there is no kind of material, no body, and no thing that can be produced or conceived of, which is not made up of elementary particles; and nature does not admit of a truthful exploration in accordance with the doctrines of the physicists without an accurate demonstration of the primary causes of things, showing how and why they are as they are. ”

“ For such hard Particles being heaped up together, can scarce [Pg 390] touch one another in more than a few Points, and therefore must be separable by much less Force than is requisite to break a solid Particle, whose Parts touch in all the Space between them, without any Pores or Interstices to weaken their Cohesion. And how such very hard Particles which are only laid together and touch only in a few Points, can stick together, and that so firmly as they do, without the assistance of something which causes them to be attracted or press'd towards one another, is very difficult to conceive. ”

“ Summary.—Thus, then, on a review of the whole, we find all things are endowed with attractive power, and that there is no particle which is not directly or indirectly related, in manifold ways, to the other particles of the universe. There is, first, the universal attraction of gravitation, under which every particle is, by a fixed law, drawn to every other within the sphere of existence. There is, secondly, the attraction of cohesion or aggregation, which acts at short distances, and unites the otherwise loose atoms of bodies into coherent masses. ”

“ If a be the point in the drop, it is plain that the line from it through the centre is longer than a b or a c. Therefore a particle, a, will be attracted toward the centre rather than in the direction a b or a c, because there are more particles in the direction of the centre, and the more particles there are the stronger is the attraction. ”

“ Bodies may be dissected, substances may be analyzed, essentials may be abstracted in consideration.
The essentials are indissoluble in every particle. Where there is no unit there is no extension, no speed and no persistence. Where there is no speed there is no unit, no extension, no persistence. Where there is no persistence there is no unit, no extension and no speed. If any of the essentials of a particle of inanimate matter be taken away, the matter disappears. A particle is the essentials of which it is composed, and it has no other substrate. ”

“ Here the Reason flies at once to Imparticularity—to a particle—to one particle—a particle of one kind—of one character—of one nature—of one size—of one form—a particle, therefore, "without form and void"—a particle positively a particle at all points—a particle absolutely unique, individual, undivided, and not indivisible only because He who created it, by dint of his Will, can by an infinitely less energetic exercise of the same Will, as a matter of course, divide it. ”

“ As regards size, there is probably no sharp line of division between molecules and particles; the one gradually shades into the other. But the distinction that I would draw is this: the atom or the molecule, if free, is always part of a gas, the particle is never so. A particle is a bit of liquid or solid matter, formed by the Aggregation of atoms or molecules. ”

“ They are not elements, because each of them contains an infinite variety of particles, and each of these particles, again, is not elementary, because each contains an infinite variety of particles; which particles, again, are not elementary, because each contains an infinite variety of particles, and so on for ever. ”

“ The effect of Differentiation on a Particle is very remarkable, the first Differential being frequently of a greater value than the original Particle, and the second of less enlightenment.
For example, let L='Leader,' S='Saturday,' and then L.S.='Leader in the Saturday,' (a particle of no assignable value) . Differentiating once, we get L.S.D., a function of great value. Similarly it will be found that, by taking the second Differential of an enlightened Particle, (i.e. raising it to the Degree D.D.,) the enlightenment becomes rapidly less. ”

“ And thus, whether we contemplate the infinitely small or the infinitely grand, in every case comes back upon us the wide induction, that the action of matter in atom, in molecule, or in mass, is ever at a distance! Of actual contact there is probably no instance afforded in nature, excepting in the intimate substance of the ultimate atom. ”

“ Research in quantum mechanics, to take one example on which my background allows me to speak at least semi-intelligently, might incorporate work from particle physicists doing empirical work with cloud chambers, high-energy particle physicists doing other empirical work with particle accelerators, and still other particle physicists investigating the mathematics behind spontaneous symmetry breaking. ”

“ He might say to himself, ‘I do not want to exaggerate the temperature, so I will see if I can manage without going beyond 10,000,000°.’ That sets a limit to the activity to be ascribed to each particle; therefore when the mathematician reaches a great depth in the sun and accordingly has a heavy weight of upper material to sustain, his only resource is to use large numbers of particles to give the required total impulse. He will then find that he has used up all his particles too fast, and has nothing left to fill up the centre. ”

“ It is obvious, that if elementary matter consists of indestructible and indivisible particles, each of which constantly preserves the same weight relatively to all the others, compounds formed by the aggregation of two, three, four, or more such particles must exemplify the rule of combination in definite proportions deduced from observation. ”

“ That which is accomplished by convention in arithmetic, is accomplished by incorporation in nature. In this manner by combination the quantitative property of number in the particle becomes the classific property or kind in the molecule, and as there is a hierarchy of molecules and every one considered as a unit may become a particle in a higher order, we are compelled to consider it in this double and relative capacity, as one of many and as many in one. A molecule in its internal aspect appears as many ”

“ Whenever an -particle is expelled the group in the periodic system to which the resultant product belongs is two units less than that to which the parent body belongs.
2. Whenever a -particle is expelled, the group of the resultant body is unit greater than that of the parent. ”

“ These changes can be expressed most simply by the introduction of a vector quantity to represent the displacement of any particle.
When the body is deformed by the action of any forces its particles pass from the positions which they occupied before the action of the forces into new positions. If are the co-ordinates of the position of a particle in the first state, its co-ordinates in the second state may be denoted by The quantities, are the “components of displacement.” When these quantities are small, the strain is connected with them by the equations
12. ”

“ The identity of the radiant particle with the component of the atom is inferable. It possesses the requisite properties of mass and resilience, and sufficient linear motion. Whether it should also have attraction imputed to it as inherent depends on whether that property in the molecule, where alone it is observed, is derived from the particle. If not, the latter needs only mass to conserve its deflections and its course under the first law of motion, and resilience to secure its compensatory readjustment in equilibrium. ”

“ But, according to the Newtonian law, two elements, when their distance has become infinitely small, act on one another with an intensity infinitely great. Therefore, if the Newtonian law hold good even to the very centre of the element, the [pg 011] elementary power possesses infinite intensity. ”

“ Therefore if in bE, which is perpendicular to the circular base of the cylinder NAO, and equal to the radius AC, we take bH equal to ; then bH will be to bE as the effect of the particle upon the globe to the effect of the particle upon the cylinder. And therefore the solid which is formed by all the right lines bH will be to the solid formed by all the right lines bE as the effect of all the particles upon the globe to the effect of all the particles upon the cylinder. ”

“ One class has no special particle in the passive, the active particle being um; in the others the special particle has generally initial p in the passive, which becomes m in the imperative-infinitive and future active, and n in the preterite and present active, as pag, mag, nag, etc. ”

“ But if their quantities of matter are unequal, then, at an average of all the chances, each will intercept a number of particles proportional to its quantity of matter, and so the forces with which the bodies are impelled toward one another, will be as the quantity of matter directly, and the square of the distance inversely. ”

“ Doubtless the centers of force vary in their distance one from another, but that which is truly the matter of one atom touches the matter of its neighbors. Hence matter will be continuous throughout, and in considering a mass of it, we have not to suppose a distinction between its atoms and any intervening space. ”

“ It must not be forgotten that in science we must always be patient with the question “Why?” We can never get to the bottom of things. On account of the nature of the problem, answers cannot be given to the questions why the smallest material particles (for the time being hydrogen nuclei and electrons) —the elementary physical individuals—exist, or why the fundamental laws for their mutual relationships—the most elementary relationships existing between them—are of this or that nature ”

“ It will be observed that, if the substance to which for instance, relates is an actual component of each of the homogeneous masses, we shall have If it is an actual component of the first only of these masses, we shall have If it is also a possible component of the second homogeneous mass, we shall also have If this substance occurs only at the surface of discontinuity, the value of the potential will not be determined by any equation, but cannot be greater than the potential for the same substance in either of the homogeneous masses in which it may be a possible component. ”