Period (physics)

“ That we have not been accustomed to regard the world in this sense as a four-dimensional continuum is due to the fact that in physics, before the advent of the theory of relativity, time played a different and more independent rôle, as compared with the space coordinates. It is for this reason that we have been in the habit of treating time as an independent continuum. As a matter of fact, according to classical mechanics, time is absolute, i.e. it is independent of the position and the condition of motion of the system of co-ordinates. ”

“ Just as the period occupies a certain finite time, so the process occupies a certain finite space; and in the case of a light-wave travelling outward from a source of light, the finite space occupied by the process grows larger as it travels away from the source. For the purposes of stating the quantum principle, one period of a periodic process has to be treated as an indivisible whole. ”

“ All this discussion as to the nature of time and space has lifted above our horizon a great difficulty which affects the formulation of all the ultimate laws of physics—for example, the laws of the electromagnetic field, and the law of gravitation. ”

“ In the generalized theory of relativity, the doctrine of space and time, kinematics, is no longer one of the absolute foundations of general physics. The geometrical states of bodies page 10 and the rates of clocks depend in the first place on their gravitational fields, which again are produced by the material systems concerned. ”

“ It is only successful in the few cases where the general nature of a group appears without much trouble. The second method is to assume that the observations must run in series which are repeated after definite intervals of time. These intervals of time are in reality obtained from the general physical principle that if any force is periodic, that is, if its fluctuations are repeated after a definite period of time, then certain of its effects are also repeated after a definite period of time, which is the same as that of the force. ”

“ The principles of dynamics are equally applicable whether the periods of time which they contemplate shall be millions of years, as they often are in astronomy, or the millionth part of a second, as they often are in physics. ”

“ Every periodic process arranges itself so as to have [Pg 140] achieved a certain amount by the time one period is completed. This seems to show that nature has a kind of foresight, and also knows the integral calculus, without which it is impossible to know how fast to go at each instant so as to achieve a certain result in the end. ”

“ That [15] our measurements and whole science of Time depend absolutely on the operation throughout Nature of the Law of Periodicity, and (2) that the periodicities which affect and determine animal and vegetal life upon our Earth are the periodic movements of rotation and revolution of that Earth itself.
Now it is to the curvilinear motions of the heavenly bodies that we must ascribe our subjection to the periodic law. If these heavenly bodies moved for ever in straight lines, as they would do if unacted on by natural forces, the periodic rhythm of Nature would disappear. ”

“ Let us take an example which is salient enough; for, however arbitrary the conventional division of time may appear to a physicist's eyes, it is natural, when instituting a comparison between two epochs, to choose those which extend over a space of half a score of years, and are separated from each other by the gap of a century. ”

“ This couple will tend to increase the angular momentum of the system, and, acting cumulatively, will soon cause an appreciable change of period, disagreeing with observation if the speed is at all comparable with that of light. ”

“ The standard unit of time in all civilized countries is deduced from the time of rotation of the earth about its axis. The sidereal day, or the true period of rotation of the earth, can be ascertained with great exactness by the ordinary observations of astronomers ”

“ The motion of a uniform stretched string fixed at both ends is a periodic motion; that is to say, after a certain interval of time, called the fundamental period of the motion, the form of the string and the velocity of every part of it are the same as before, provided that the energy of the motion has not been sensibly dissipated during the period. ”

“ All the epoch-making work in physics and astronomy by such men as Galileo and Kepler, Newton and Laplace, Huyghens and Foucault, and the French academicians, bearing on the form of our globe, has been accomplished since his time. ”

“ The other part of the disturbing force remains nearly unchanged for a considerable period, and gives rise to changes in the elements which, though in general very small, remain for a long time without sensible alteration, and therefore continually accumulate, becoming considerable with the lapse of time: these are the secular inequalities. ”

“ It cannot be too strongly insisted that the terms distance, period of time, mass, energy, momentum, etc., cannot be used in a description of an atom with the same meanings that they have in our gross experience. ”

“ We must first guess at what the laws are approximately, then design an experiment so that, in accordance with this guess, the effect of motion on some phenomenon is much greater than the expected effect on the clock, then from measurements with uncorrected clock time find an approximate expression for the effect of motion on mass or length, with which we correct the clock, and so on ad infinitum. ”

“ It is interesting to realize that the modern development of science, in the relativity theory, has proved not only that time is not real, but a conception, but also has proved that the time of our conception does not flow uniformly at constant rate from past to future, but that the rate of the flow of time varies with the conditions; the rate of time flow of an event slows down with the motion relative to the event. ”

“ An atom is a clock, because the electrons go round the nucleus a certain number of times in a second; its properties as a clock are exhibited to us in its spectrum, which is due to light waves of various frequencies. The world is full of periodic occurrences, and fundamental mechanisms, such as atoms, show an extraordinary similarity in different parts of the universe. Any one of these periodic occurrences may be used for measuring time; the only advantage of humanly manufactured clocks is that they are specially easy to observe. ”

“ It means, in the first place, that the ultimate facts in physics must be events, rather than bodies in motion. A body is supposed to persist through a certain length of time, and its motion is only definite when we have fixed upon one way of dividing intervals between space and time. ”

“ We may define a periodic phenomenon as one which, with the uniform change of the variable, returns448 time after time to the same value. If we strike a pendulum it presently returns to the point from which we disturbed it, and while time, the variable, progresses uniformly, it goes on making excursions and returning, until stopped by the dissipation of its energy. If one body in space approaches by gravity towards another, they will revolve round each other in elliptic orbits, and return for an indefinite number of times to the same relative positions. ”

“ In addition to the existence of space-time and its invariant intervals, the really novel views which the theory forces upon us consist in the relativity of such primary concepts as length, duration, simultaneity, mass, force, etc., to which temperature should also be added. We also obtain new views on causal connections, and a better understanding of the principle of action and of the principles of conservation. Matter becomes fused with energy and disappears as a substance, and conservation is not rigorous. Furthermore, matter possibly creates space-time, and all motion may be relative. ”

“ It moves steadily along the time-dimension, from the past toward the future, only because the electrons that compose it are constantly moving along the space-dimensions, are constantly revolving around their nucleus, at the same unvarying speed. If you stopped that revolving of electrons, the ball of metal would become static, timeless, would cease to move along the time-dimension. ”

“ All mechanical laws exhibit acceleration as a function of configuration, not of configuration and time jointly; and this principle of the irrelevance of the time may be extended to all scientific laws. In fact we might interpret the "uniformity of nature" as meaning just this, that no scientific law involves the time as an argument, unless, of course, it is given in an integrated form, in which case lapse of time, though not absolute time, may appear in our formulas. ”

“ There could be no time without motion, and no motion without space, and no space without number. The first or simplest manifestation of time is the division of motion into parts by events. This gives us the simplest concept of time known to science, and whenever in science time is considered, some motion is divided into parts by events. Thus the motion of the earth about the sun is divided into annual parts by events, and the motion of the earth on its axis is divided into daily parts by events. ”

“ The power of attraction which, according to the theory of gravity, each body possesses, is in proportion to the quantity of matter contained in that body. But the periodic time in which one body, at a given distance, revolves round another that attracts it, is shorter in proportion as this power is greater, and consequently as the quantity of matter in the attracting body. If the densities of Jupiter and Saturn were the same with that of the Earth, the periodic times of their several Satellites would be shorter than by observation they are found to be. ”

“ For instance, if in mechanics and astronomy we had selected at random some arbitrary definition of time, if we had defined as congruent the intervals separating the rising and setting of the sun at all seasons of the year, say for the latitude of New York, our understanding of mechanical phenomena would have been beset with grave difficulties. As measured by these new temporal standards, free bodies would no longer move with constant speeds, but would be subjected to periodic accelerations for which it would appear impossible to ascribe any definite cause, and so on. ”

“ Hence the interval is at once identified with something familiar to experience, namely the thing that a scale and a clock measure. However advantageous that may be for the sake of bringing the theory into touch with experiment at the outset, we can scarcely hope to build up a theory of the nature of things if we take a scale and clock as the simplest unanalysable concepts. The result of this logical inversion is that by the time the equation is encountered, both sides of the equation are well-defined quantities. ”

“ The unit of time adopted in all physical researches is one second of mean solar time.
In astronomy a year is sometimes used as a unit of time. A more universal unit of time might be found by taking the periodic time of vibration of the particular kind of light whose wave length is the unit of length. ”

“ Density multiplied by volume in space gives us mass or, what appears to be the same thing, energy. But from our space-time point of view, a far more important thing is density multiplied by a four-dimensional volume of space and time; this is action. The multiplication by three dimensions gives mass or energy; and the fourth multiplication gives mass or energy multiplied by time. Action is thus mass multiplied by time, or energy multiplied by time, and is more fundamental than either.
Action is the curvature of the world. ”

“ Since we realise that the definitions of time-congruence we ultimately adopt are governed by our desire to obtain the maximum of simplicity in the co-ordination of some particular group of phenomena, considerable divergences in our definitions might be expected when we considered in turn phenomena of a different nature. Why, indeed, should a determination arrived at in terms of the vibrations of atoms agree in any way with the astronomical definition issuing from the earth’s rotation? ”

“ We need four measurements to fix a position, and four measurements fix the position of an event in space-time, not merely of a body in space. Three measurements are not enough to fix any position. That is the essence of what is meant by the substitution of space-time for space and time. ”

“ In the second place, we must repeat the comment already made in discussing time, namely, that there is still a very wide gap between the theory and its physical application, in that we have no way of identifying our physical clocks and our physical measures of time with the thing called time in the formulas. ”

“ This Aristotelic definition of physical time is more than two thousand years old, yet it clearly represents the idea of time which has been used in classic science, especially in the mechanics of Galileo and Newton, until quite recent years. ”

“ When the time between the two events is exactly equal to the time taken by light to travel from one to the other, the interval is zero; the two events are then situated on parts of one light ray, unless no light happens to be passing that way.
When we come to the general theory of relativity, we shall have to generalize the notion of interval. The more deeply we penetrate into the structure of the world, the more important this concept becomes; we are tempted to say that it is the reality of which distances and periods of time are confused representations. ”