Gilbert Newton Lewis

“ From the fundamental conservation laws we know that when a body is set in motion and thus gains mass and energy, these must come from the environment. So also when a moving body is brought to rest, it must give up mass as well as energy to the environment. The mass thus acquired by the environment is independent of the particular form which the energy may assume, and we are thus forced to the important conclusion that when a system acquires energy in any form it acquires mass in proportion, the ratio of the energy to the mass being equal to the square of the velocity of light. ”

“ To anyone unfamiliar with the prevailing theories of light, knowing only that light moves with a certain velocity and that in a beam of light momentum and energy are being carried with this same velocity, the natural assumption would be that in such a beam something possessing mass moves with the velocity of light and therefore has momentum and energy. ”

“ Whether our conclusions can be retained when we consider processes in which the relative motion is being established, in other words, processes in which acceleration takes place, it is not our present purpose to determine. ”

“ If we assume an aether pervading space, and assume that this æther possesses no mass except when it moves with the velocity of light, it is obvious that an æther drift could in no way affect a beam of radiation nor could it be detected by any mechanical means. ”

“ An observer in a given system allows such a force to act upon unit mass as to give it an acceleration of one , and calls this force the dyne. If now we assume that the system is in motion, with a velocity v, in a direction perpendicular to the line of application of the force, we conclude that the acceleration is really less than unity, since in a moving system the second is longer in the ratio , and the centimeter in this transverse direction is the same as at rest. On the other hand, the mass is increased owing to the motion of the system by the factor . ”

“ Hence it is obvious that if in any other way than by radiation the body gains or loses energy it must still gain or lose mass in just the above proportion. In other words, any change in a body's content of energy is accompanied by a definite change in its mass, regardless of the nature of the process which the energy change accompanies. ”

“ From the standpoint of the principle of relativity, one of the most interesting quantities in mechanics is the so-called kinetic energy, which is the increase in energy attributed to a body when it is set in motion with respect to an arbitrarily chosen point of rest. ”

“ The question whether a method is conceivable by which absolute motion in space may be distinguished from relative motion must be answered definitely in the affirmative by one who accepts the above equations of non-Newtonian mechanics. A body is absolutely at rest when any motion imparted to it increases its mass, or when a certain force will give it the same acceleration in any direction. ”

“ The point of view first advanced by Einstein, which we have here adopted, is radically different. Absolute motion has no significance. Imagine an electron and a number of observers moving in different directions with respect to it. To each observer, naïvely considering himself to be at rest, the electron will appear shortened in a different direction and by a different amount; but the physical condition of the electron obviously does not depend upon the state of mind of the observers. ”

“ Thus a ton weight given the velocity of the fastest cannon-ball would, according to this equation, gain in mass by less than one millionth of a gram. It is obvious that, except in those unusual cases in which we deal with velocities comparable with that of light, our non-Newtonian equations are identical with those of ordinary mechanics far within the limits of error of the most delicate experiments. ”

“ The consequences which one of us has obtained from a simple assumption as to the mass of a beam of light, and the fundamental conservation laws of mass, energy, and momentum, Einstein has derived from the principle of relativity and the electromagnetic theory. ”

“ An observer on system a places two carefully compared clocks, unit distance apart, in the line of motion, and has the time on each clock read when a given point on the other system passes it. An observer on system b performs a similar experiment. The difference between the readings of the two clocks in one system must be the same as the difference in the other system, for by the principle of relativity the relative velocity v of the systems must appear the same to an observer in either. ”

“ The view here proposed, which appears at first sight a reversion to the old corpuscular theory of light, must seem to many incompatible with the electromagnetic theory. If it were really so I should not have ventured to advance it, for the ideas announced by Maxwell constitute what may no longer be regarded as a theory, but rather a body of experimental fact. The new theory is offered, not in any sense to replace, but to supplement the accepted theories of light. ”

“ If our ideas possess a certain degree of artificiality, this is also true of others which have long since been adopted into mechanics. The apparent change in rate of a moving clock, and the apparent change in length and mass of a moving body, are completely analogous to that apparent change in energy of a body in motion, which we have long been accustomed to call its kinetic energy. ”

“ We have shown how observers stationed on systems in motion relative to one another have been able to preserve their fundamental principles of mechanics only by adopting certain novel conclusions. These conclusions are self-consistent; in the one case where they have been tested they are in accord with experiment; and they enable us to save all the fundamental physical concepts which have been found useful in the past. We have, however, considered primarily only systems which are initially in uniform relative motion. ”

“ The plausibility of our fundamental assumption which led directly to equation (15) has been greatly increased by the agreement, between this equation and Kaufmann's results, and also perhaps by the similarity between this equation and those deduced from electromagnetic theory. But the simplest as well as the strongest evidence of the correctness of our point of view comes from a consideration of the non-Newtonian equation for kinetic energy. ”

“ It is true that metaphysicians hold that in the strictest sense absolute motion is not only unknowable but unthinkable, but we may say at least that the above method permits theoretically the detection of absolute translational motion in the same sense that a study of centrifugal forces enables us to detect absolute rotational motion. ”

“ When Lorentz first advanced the idea that an electron, or in fact any moving body, is shortened in the line of its motion, he pictured a real distortion of the body in consequence of a real motion through a stationary ether, and his theory has aroused considerable discussion as to the nature of the forces which would be necessary to produce such a deformation. ”

“ The first assumes that the electron is and remains a rigid sphere, the second assumes an electron which is spherical when at rest but which in motion contracts in the direction of its translation and expands laterally so as to keep a constant volume. ”

“ We thus see that a meter-stick, which, when held perpendicular to its line of motion, has the same length as a meter-stick at rest, will be shortened when turned parallel to the line of motion in the ratio , and indeed any moving body must be shortened in the direction of its motion in the same ratio. ”

“ Therefore, accepting this principle, we shall accept the consequences to which it leads, however extraordinary they may be, provided that they are not inconsistent with one another nor with known experimental facts. ”

“ B, however, is equally justified in considering his system at rest and A's in motion, and by identical reasoning has come to the conclusion that A's clock is not keeping time. Thus to each observer it seems that the other's clock is running too slowly. ”