Mass (physics)

“ Thus is suggested finally the law of gravitation in its most general form: every particle of matter attracts every other particle with a force proportional to the mass of each, and inversely proportional to the square of the distance between them. ”

“ We have thus two kinds of mass, neither of which quite fulfils the old ideal. The mass as measured by an observer who is in motion relative to the body in question is a relative quantity, and has no physical significance as a property of the body. The “proper mass” is a genuine property of the body, not dependent upon the observer; but it, also, is not strictly constant. As we shall see shortly, the notion of mass becomes absorbed into the notion of energy; it represents, so to speak, the energy which the body expends internally, as opposed to that which it displays to the outer world. ”

“ But we prefer to conclude with a mathematical demonstration drawn from the weight of matter. The weight of a mass of matter depends on the number of material terms to which the action of gravity is applied, and it increases exactly in the same ratio as the number of the elementary terms contained in the mass. This being the case, let us assume that there is somewhere an atom of continuous matter. The action of gravity will find in it an infinite multitude of points of application; for it is of the nature of continuum to supply matter for an endless division. ”

“ Consequently gravitation is proportional to the volume, while the pressure of light is proportional to the surface of the body acted upon. Now the mass, or volume, of any body varies as the cube of its diameter, and the surface only as the square. If, then, we have two bodies, one of which has twice the diameter of the other, the mass of the second will be eight times less than that of the first, but the surface will be only four times less. If the second has only one-third the diameter of the first, then its mass will be twenty-seven times less, but its surface only nine times less. ”

“ So it was natural to assume that the mass of the body at rest was due to its contained or bound energy, which would be released were the body to disintegrate into nothingness. The formula connecting this energy of constitution of the body with its mass was obtained from the mathematical expression of the mass, and it was found that in C.G.S. units the contained energy was equal to the mass multiplied by the square of the velocity of light. ”

“ This shows that the quantity of matter existing in those bodies implies “a constant of mass” independent of the intensity of gravitation, and that the ratio of the two masses is the ratio of two “absolute” quantities—that is, of two numbers of primitive material units.
It is not true, therefore, that the weight is not “the presentation of an absolute substantive entity,” as the author pretends. Weight implies mass and gravitation, and presents the one as subject to the other. Now, the mass is an “absolute substantive entity,” as we have shown. ”

“ The law of masses may be extended to as great masses as those for which observation proves it (for example the mass of Jupiter) , by making the diameters of the bars of the supposed cage atoms constituting heavy bodies, small enough. ”

“ Now we choose mass as a unit of measure of the quantity of material; and we are justified in doing so, because experiments have shown that material, confined in a closed space, does not appreciably alter its mass. The mass is proportional to the weight, generally measured as [Pg 234] the force exerted at some definite latitude on the earth’s surface, tending to pull the body towards the centre of the earth. ”

“ Since the force which pulls the stone towards the earth is one kilogram, and since in any system of units the product of mass and acceleration represents force, the mass of our stone is the 9.81th part of unit mass. ”

“ For the purpose of general illustration the reader is asked to conceive a mass of heterogeneous matter, concentrated round a given point in space, forming a single body. This mass is assumed to be assembled and to obtain its coherent form in virtue of that universal and inherent property of matter, namely, gravitative or central attraction. ”

“ For any given observer, the measured mass of the whole physical universe is constant. [8] The proper mass of all the bodies in the world is not necessarily the same at one time as at another, so that in this respect the measured mass has an advantage. The conservation of measured mass is the same thing as the conservation of energy. This may seem surprising, since at first sight mass and energy are very different things. But it has turned out that energy is the same thing as measured mass. ”

“ Familiar cases can readily be found of the perception of the mass of bodies, independently of their tendency to fall towards the earth. The mass of any portion of matter is found to be permanent under chemical and other changes, and this fact adds to its importance as a physical quantity. The study of the structure of atoms has suggested a connexion of mass with electrical phenomena which implies its dependence on motion ”

“ On the table before me lies a solid lump of steel, but in the light of up-to-date science I know that the atoms of that seemingly inert mass are vibrating with the most intense energy, continually dashing hither and thither, impinging upon and rebounding from one another, or circling round like miniature solar systems, with a ceaseless rapidity whose complex activity is enough to bewilder the imagination. The mass, as a mass, may lie inert upon the table ”

“ In this way both the unit of force and the unit of mass are made to depend on the value of the force of gravity, which varies from place to place, so that statements involving these quantities are not complete without a knowledge of the force of gravity in the places where these statements were found to be true. ”

“ Atoms are absolute physical constants, or constants of mass; and I have shown that there are, and can be, no absolute constants of mass. And it is evident now, I trust, that there are similarly no constant central forces belonging to, or inherent in, constants of mass as such. Both the constants of mass and the constant forces assumed to belong to them are simply parts of the scaffolding of the intellect, when it seeks to subject the phenomena of the material world to exact mathematical determination. ”

“ Considered in the most general way, we may define matter as a complex of gravitational, kinetic and chemical energies, which are found to cling together in the same space. Of these energies the capacity factors, namely, weight, mass and elements, are conservative as described, while the intensity factors, potential, velocity and affinity, may change in wide limits. To explain why we find these energies constantly combined one with another, we only have to think of a mass without gravity or a ponderable body without mass. ”

“ A distance we can measure in any length unit, but what about the unit for the "active mass"? We have seen that it is not a mass at all in the common acceptance of this term, and it can therefore not be expressed in any unit suitable for ponderable masses. We are thus compelled to settle the magnitude of the unit by the same formula which defines the force. The conception of unit active mass may then be derived from the following condition: If two equal masses one centimetre apart act upon each other with unit force, then each of them is a unit of active mass. ”

“ Such a mass, if exposed to constant temperature and pressure, would be in neutral equilibrium. A point in the developable surfaces represents a mass of which the matter is divided between two coexisting phases, which are represented by the extremities of the line in the figure passing through that point. A point in the primitive surface represents of course a homogeneous mass. ”

“ A variation of the direction of these fields relative to the line of motion of the electron would probably afford a means of making the necessary measurements for the experimental proof of the relations requisite for use in the preceding discussion.
§ 7. Mass and Energy. If, as is frequently done, we employ for the definition of the kinetic energy E the relation (compare §1)
it is clear that for the mass m we should take the longitudinal mass . ”

“ Calculation shows that the force required is the same as would be needed if the mass were somewhat greater than it is in reality. In other words, if we determine the mass in the usual way from the phenomena, we get the true mass increased by an amount which we can call the apparent, or electromagnetic, mass. The two together form the effective mass which determines the phenomena. ”

“ To these ideas Newton added the very important and difficult conception of mass.
If we are comparing two different bodies of the same material but of different sizes, we are accustomed to think of the larger one as heavier than the other. In the same way we readily think of a ball of lead as being heavier than a ball of wood of the same size. ”

“ A part of the total energy which belongs to the matter in the vicinity of the separating surface, relates to pairs of particles which are on different sides of the surface, and such energy is not in the nature of things referable to either mass by itself. Yet, to avoid the necessity of taking separate account of such energy, it will often be convenient to include it in the energies which we refer to the separate masses. When there is no break in the homogeneity at the surface, it is natural to treat the energy as distributed with a uniform density. ”

“ Can this law be verified by experiment? For that it would be necessary to [Pg 98] measure the three magnitudes which figure in the enunciation: acceleration, force and mass.
I assume that acceleration can be measured, for I pass over the difficulty arising from the measurement of time. But how measure force, or mass? We do not even know what they are.
What is mass? According to Newton, it is the product of the volume by the density. According to Thomson and Tait, it would be better to say that density is the quotient of the mass by the volume. What is force? ”

“ Since energy is the same thing as measured mass, we may also take action to be measured mass multiplied by time. In classical mechanics, the “density” of matter in any region is the mass divided by the volume; that is to say, if you know the density in a small region, you discover the total amount of matter by multiplying the density by the volume of the small region. In relativity mechanics, we always want to substitute space-time for space ”

“ If quantity of matter is to be identified with its mass, the second phenomenon does not happen. It could easily be conceived of as happening, but it is provided against by a special law of nature—the conservation of mass. ”