Laws of physics

“ Merely because in mathematics—in the case of , for example—the laws of Euclidean geometry were accepted from the start, whereas in physics preliminary information of this sort is denied us. And it is the same with all the magnitudes and constants of physics. It is impossible to predetermine by logical means the value of the invariant velocity, or of the gas constant, or of the size of the earth or of an electron. In every case, we must have recourse to physical measurements of one sort or another, for the constants of physics present no character of rational necessity. ”

“ The Future of Physics.—At times during the history of physics it has seemed as if the fundamental laws of 380this science had been so completely formulated that nothing remained to future generations beyond the routine of deducing to the full the consequences of these laws, and increasing the precision of the methods used to measure the constants appearing in them. ”

“ We have not a direct intuition of simultaneity, nor of the equality of two durations. If we think we have this intuition, this is an illusion. We replace it by the aid of certain rules which we apply almost always without taking count of them.
But what is the nature of these rules? No general rule, no rigorous rule; a multitude of little rules applicable to each particular case.
These rules are not imposed upon us and we might amuse ourselves in inventing others; but they could not be cast aside without greatly complicating the enunciation of the laws of physics, mechanics and astronomy.
We therefore choose these rules, not because they are true, but because they are the most convenient, and we may recapitulate them as follows: ”

“ We have these wide principles which sweep across the different laws, and if we take the derivation too seriously, and feel that one is only valid because another is valid, then we cannot understand the interconnections of the different branches of physics. Some day, when physics is complete and we know all the laws, we may be able to start with some axioms, and no doubt somebody will figure out a particular way of doing it so that everything else can be deduced. But while we do not know all the laws, we can use some to make guesses at theorems which extend beyond the proof. ”

“ In order to remedy this indeterminateness, it is usual to specify that the body on which the force is acting is one of unit mass; it is then called a test-body. Under these circumstances, we can explore a field of force by placing our test-body in successive regions of space and determining the magnitude and direction of the force which is acting on the body. When we have mapped out the magnitude and direction of the force for every point of space, we are in a position to state that we have determined the lay of the field of force.
In physics we are often concerned with fields of force. ”

“ If one consequently considers this fundamental assumption as disproved, then the attempt to establish the whole of physics (including electrodynamics and optics) upon the principle of relative motion, has to be denoted as failed for the time being. ”

“ A physical law does not say "A will be followed by B," but tells us what acceleration a particle will have under given circumstances, i.e. it tells us how the particle's motion is changing at each moment, not where the particle will be at some future moment. ”

“ The law of gravitation, as developed by Newton, bears sway in all those distant worlds. In them bodies attract each other with forces directly as their masses and inversely as the squares of their distances. There the laws of the emission, absorption, and transmission of light are the same as they are with us. There ignited hydrogen gives forth its three rays, the same rays that it gives forth to us. In the uttermost parts of the universe the law of definite combination, the numerical law, and the multiple law, stand good. ”

“ It is postulated that the energy and momentum of a beam of radiation are due to a mass moving with the velocity of light.
From this postulate alone it is shown that the mass of a body depends upon its energy content. It is therefore necessary to replace that axiom of Newtonian mechanics according to which the mass of a body is independent of its velocity, by one which makes the mass increase with the kinetic energy. ”

“ I should like to make it clear that the limitation of the scope of physics to pointer readings and the like is not a philosophical craze of my own but is essentially the current scientific doctrine. It is the outcome of a tendency discernible far back in the last century but only formulated comprehensively with the advent of the relativity theory. The vocabulary of the physicist comprises a number of words such as length, angle, velocity, force, potential, current, etc., which we call “physical quantities”. ”

“ It is not quite true to say that all the physical quantities are relative to frames of space. We can construct new physical quantities by multiplying, dividing, etc.; thus we multiply mass and velocity to give momentum, divide energy by time to give horse-power. We [Pg 23] can set ourselves the mathematical problem of constructing in this way quantities which shall be invariant, that is to say, shall have the same measure whatever frame of space may be used. One or two of these invariants turn out to be quantities already recognised in pre-relativity physics ”

“ 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. ”

“ We should have been compelled by logic to seek some law expressed in terms of “tensors,” and therefore independent of our choice of co-ordinates. [Pg 143] It is impossible without mathematics to explain the theory of tensors; the non-mathematician must be content to know that it is the technical method by which we eliminate the conventional element from our measurements and laws, and thus arrive at physical laws which are independent of the observer’s point of view. Of this method, Einstein’s law of gravitation is the most splendid example. ”

“ The conception of force is, so to speak, eliminated from the conditions of the problem, which is reduced to one of pure kinematics. At the outset, the position of each body, considered as a material particle, is defined by reference to a system of co-ordinate axes, and not by any verbal description. Differential equations which express the changes of the co-ordinates are then constructed. The process of discovering the laws of motion of the particle then consists in the integration of these equations. ”

“ If, on the other hand, the nature of gravity were essentially not electrodynamic, it would be possible for some deviation from the accepted laws of dynamics, owing to a motion of translation through space, to be revealed by direct astronomical observations. ”

“ We know that matter is built up of electrically charged particles, but we do not know the laws which govern the constitution of these particles. In treating mechanical problems, we are therefore obliged to make use of an inexact description of matter, which corresponds to that of classical mechanics. ”

“ The laws of electrodynamics require that such a force be generated, and yet no force can be observed; so we must assume that the mysterious compensations that conceal our motion through the ether are of so perfectly general a nature that they affect mechanics as well as electromagnetics and optics. ”

“ Chemistry here comes to the aid of mechanics, and we may say boldly that that matter, which is identical with ours, is subject, like it, to the laws of gravitation. Certainly, when Newton decomposed a beam of white light, and laid the first basis of the theory of the spectrum, he had not the slightest suspicion that his law of gravitation would, at a later period, find in it wings to carry it into regions where all measurement ceases and all calculation is powerless. ”

“ In its exact equality and its perfect independence of all circumstances, except mass and distance, the force of gravity stands apart from all the other forces and phenomena of nature, and has not yet been brought into any relation with them except through the general principle of the conservation of energy. Magnetic attraction, as remarked by Newton, follows very different laws, depending upon the chemical quality and molecular structure of each particular substance. ”

“ Yet the law of the parabolic motion would be resolvable into the very same simple laws into which that of the elliptical motion is resolved, namely, the law of the permanence of rectilineal motion, and the law of gravitation. ”

“ Consider the electrons as material points and ask how their mass should vary as function of the velocity not to contravene the principle of relativity. Or, still better, ask what should be their acceleration under the influence of an electric or magnetic field, that this principle be not violated and that we come back to the ordinary laws when we suppose the velocity very slight. We shall find that the variations of this mass, or of these accelerations, must be as if the electron underwent the Lorentz deformation. ”

“ 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 . ”

“ But supposing that from a peculiarity in the constitution nuclei are formed, we know very well how, by the power of gravitation, the process of an aggregation of the neighbouring matter to these nuclei should proceed until masses more or less solid should be detached from the rest. It is a well-known law in physics, that when fluid matter collects towards, or meets in a centre, it establishes a rotatory motion. ”

“ 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. ”

“ When certain series of phenomena have been classified together as obviously occurring under the domination of the same or similar causes, we speak of having determined a law of nature. For example, the fact that any body in motion tends to go on at the same rate of speed in a direct line forever, expresses such a law. The fact that the gravitation pull is directly as the mass and inversely as the square of the distance of the bodies it involves, expresses another such law. ”

“ Also the physical laws, which are differential equations defining as functions of and certain constants, are in general altered by a change of the system of reference. Physical science has, however, been so built up that there are certain transformations which leave the form of the equations unaltered. In the classical, or Newtonian, mechanics these are all orthogonal transformations of the three coordinates combined with an arbitrary uniform velocity of these axes and an arbitrary change of the units of length and time. ”

“ 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 limiting ratio of the momentum of a body to its velocity, when it is brought to rest, will be called its mass when at rest. The unit of mass is the gram.
The kinetic energy (E') of a body will be measured by the distance through which it will move before being brought to rest by a constant opposing force of one dyne, acting in the line or the body's motion. The unit of energy will be the erg.
These definitions, although somewhat unusual in form, are perfectly consistent with the ordinary definitions of Newtonian mechanics. ”

“ Section 21 - In What Respects are the Foundations of Classical Mechanics and of the Special Theory of Relativity Unsatisfactory? We have already stated several times that classical mechanics starts out from the following law: Material particles sufficiently far removed from other material particles continue to move uniformly in a straight line or continue in a state of rest. We have also repeatedly emphasised that this fundamental law can only be valid for bodies of reference which possess certain unique states of motion, and which are in uniform translational motion relative to each other. ”

“ If one arrives by a different choice at different results, then all laws wouldn't be invariable with respect to the same transformation, thus the relativity principle would be wrong. Evidently, such laws related to physical processes in empty space, are the most simple ones. Since in the other ones, the velocity of matter relative to the references system is included in its mathematical formulation, and must be co-transformed by a transformation; in vacuum, however, were we know nothing about moving things, this complication vanishes. ”