Translation (physics)

“ For other physical quantities such as electric and magnetic forces, it is necessary to follow a less direct method; we will seek, perhaps with a little groping, the formulas of transformation suitable to ensure the invariance of the electromagnetic equations. ”

“ The mathematician assumes that just as his equations were the necessary mathematical consequences of his original equations , so also must the physical translation of constitute a physical phenomenon , which follows as a necessary consequence of the existence of the physical phenomenon . ”

“ It consists, broadly speaking, in showing that, although the particles, points, and instants with which physics operates are not themselves given in experience, and are very likely not actually existing things, yet, out of the materials provided in sensation, it is possible to make logical constructions having the mathematical properties which physics assigns to particles, points, and instants. If this can be done, then all the propositions of physics can be translated, by a sort of dictionary, into propositions about the kinds of objects which are given in sensation. ”

“ After working through whole strings of equations, in which the symbols stand for things whose intrinsic nature can never be known to us, he arrives at last at a result which can be interpreted in terms of our own perceptions, and utilized to bring about desired effects in our own lives. What we know about matter, abstract and schematic as it is, is enough, in principle, to tell us the rules according to which it produces perceptions and feelings in ourselves; and it is upon these rules that the practical uses of physics depend. ”

“ But attention may be more usefully directed to the extravagantly gratuitous guess involved in hypothesis 3. As a minor point, it is not even carefully worded; for entities which cannot be expressed in terms of matter and motion are common enough without going outside the domain of physics. Light, for instance, and Electricity, have not yet proved amenable, and do not appear likely to be amenable, to purely dynamical theory. ”

“ Modern physics, as a science, is an immense system of indices in the form of names and numbers whereby we are enabled to work with Nature as with a machine. [464] As such, it may have an exactly-definable end. But as a piece of history, all made up of destinies and incidents in the lives of the men who have worked in it and in the course of research itself, physics is, in point of object, methods and results alike an expression and actualization of a Culture, an organic and evolving element in the essence of that Culture, and every one of its results is a symbol. ”

“ 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”. ”

“ The special relativity theory is therefore the application of the following proposition to any natural process: "Every law of nature which holds good with respect to a coordinate system K must also hold good for any other system K' provided page 9 that K and K' are in uniform movement of translation." ”

“ They are the same for the man in the express train as for the man standing on the station platform. The Principle of Relativity requires us to think that this is not so, but that, contrary to all our settled notions, the actual space and time vary—really undergo an alteration, a contraction or expansion—with each different system of movement of translation to which the observer is bound. Events that for an observer belonging to one system of movement happen in the same place, for another observer in a different system of movement happen in different places. ”

“ In particular, all translations of equal amplitude are conjugate, as also are all rotations of equal amplitude. Any two translations are permutable with each other, and give when combined another translation. The totality of translations constitutes, therefore, a subgroup of the general group of motions; and this subgroup is a self-conjugate subgroup, since a translation is always conjugate to a translation.
All the points of space constitute a set of objects which are interchanged among themselves by all operations of the group of motions. So also do all the lines of space and all the planes. ”

“ They concern the adaptation of the principles of mathematical physics to the form of the relativity principle which is here maintained. Einstein’s method of using the theory of tensors is adopted, but the application is worked out on different lines and from different assumptions. ”

“ It is perfectly natural that the principle of excluded perpetual motion should have been first developed in the simple domain of pure mechanics. Towards the transference of that principle into the domain of general physics the idea contributed much that all physical phenomena are mechanical phenomena. ”

“ My object is to shew how it comes about that we have inherited a mathematical scheme which in its final form embraces subjects physically so different as Heat-Conduction, Hydrodynamics, Elasticity, Magnetism, Electricity, and Light, and can be made to include any one of these by assigning proper names to the symbols. ”

“ The triumph of exact science in the foregoing problem consisted in establishing a numerical connection between the pointer reading of the weighing-machine in one experiment on the elephant and the pointer reading of the watch in another experiment. And when we examine critically other problems of physics we find that this is typical. The whole subject-matter of exact science consists of pointer readings and similar indications. ”

“ Must the independence of physical laws with regard to a system of coordinates be limited to systems of coordinates in uniform movement of translation with regard to one another? What has nature to do with the coordinate systems that we propose and with their motions? Although it may be necessary for our descriptions of nature to employ systems of coordinates that we have selected arbitrarily, the choice should not be limited in any way so far as their state of motion is concerned. (General theory of relativity.) ”

“ The introduction of the substitutions (10) , (12) or (13) always gives, if δ is given by the constraints along a given surface as an arbitrary function of time, the transition from the effect of a stationary source to the effect when it is in translational motion. If, for example, we have on a very small sphere of radius R, then the propagated dilation is given by:
} The substitution (10) gives the influence of a translation of a "sounding" sphere parallel to the X-axis. ”

“ And in doing so the science upon which we must depend is physics. Modern physics, however, is very abstract, and by no means easy to explain in simple language. I shall do my best, but the reader must not blame me too severely if, here and there, he finds some slight difficulty or obscurity. ”

“ In the study of heat, sound, and light we may strive merely to understand the nature of the external stimuli that come to us through touch, hearing and sight; but in mechanics, where we examine critically the simplest ideas of motion and inertia, we acquire the method of analysis which when applied to the mysteries of molecular physics and electricity carries us along avenues that lead to the most profound secrets of nature. Utilitarian aspects dwindle in our perspective as we face the problem of the structure, origin, and evolution of matter—as we question the independence of space and time. ”

“ This point of view is that from which Geometry separates itself from Mathematics in general, Descriptive Geometry from Geometry in general, still more from which Kosmical Physics, Hydraulics, Aerostatics, branch away from Natural Philosophy,—in other words, the point of view from which special sciences are seen to separate themselves from the more general sciences to which they are subordinate. ”

“ If, in a body or a system of bodies, without a translation, a system of vibrations be given, in which the displacements of the ions and the components of and are certain functions of the coordinates and the time, then, if a translation be given to the system, there can exist vibrations, in which the displacements and the components of and are the same functions of the coordinates and the local time. ”

“ We do not forget that we are dealing with the shell of a hollow sphere, not with a ring, or section of a cylinder, and we can conceive that there would be, from the first, partial motions of translation in multitudes of directions, radial, angular, transverse, etc. ”

“ The development of physics on the speculative side has led, then, to the idea, gradually become more definite and fixed, of a universal medium, the existence of which is a matter of inference. To this medium properties have been assigned which are such as to enable us to form an intelligible, consistent conception of the mechanism by means of which phenomena, the mechanics of which is not capable of direct observation, may be logically considered to be produced. ”

“ On the ground of it we shall commit no error if, in determining the paths and of two rays that start from a point , and are made to interfere at a point , we take no account of the motion of the apparatus. The change in the difference of phase produced by the translation will be given by the difference between the values which the integral
takes for the lines and so determined. ”

“ This ideal has often played an effective part in popular lectures, but in the workshop of the serious inquirer it has discharged scarcely the least function. What has really been achieved in mechanical physics is either the elucidation of physical processes by more [Pg 160] familiar mechanical analogies, (for example, the theories of light and of electricity,) or the exact quantitative ascertainment of the connexion of mechanical processes with other physical processes, for example, the results of thermodynamics. ”

“ 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. ”

“ Such examples may seem trivial, but they contain the essence of the most refined and transcendental theorizing. The reason why physics grows more deductive the more the fundamental properties it assumes are of a mathematical sort, such as molecular mass or wave-length, is that the immediate consequences of these notions are so few that we can survey them all at once, and promptly pick out those which concern us. ”

“ Dialectic and physics, thus united at their basis, meet again in their results. In mechanical science, which is the best part of physics, mathematics, which is the best part of dialectic, plays a predominant rôle; it furnishes the whole method of understanding wherever there is any real understanding at all. ”

“ Let us consider in any given medium any electromagnetic field. For any volume element of the medium, the law holds that is invariant in the passage from the one to the other observer. It follows from this that is invariant; i. e., the kinetic potential of a unit volume or the “space density of kinetic potential” is invariant. ”

“ Whenever the laws of nature are reduced to a mathematical form we may expect to meet with singular cases, and, as all the physical sciences will meet in the mathematical principles of mechanics, there is no part of nature where we may not encounter them. In mechanical science the motion of rotation may be considered an exception to the motion of translation. It is a general law that any number of parallel forces, whether acting in the same or opposite directions, will have a resultant which may be substituted for them with like effect. ”

“ If a material point be at rest in this system, then its position in this system can be found out by a measuring rod, and can be expressed by the methods of Euclidean Geometry, or in Cartesian co-ordinates.
If we wish to describe the motion of a material point, the values of its coordinates must be expressed as functions of time. It is always to be borne in mind that such a mathematical definition has a physical sense, only when we have a clear notion of what is meant by time. ”

“ The branch of the older physics—distinguished, according to the bodily senses concerned in each, as acoustics, optics and heat—have melted into a dynamic of matter and a dynamic of the æther, and these again can no longer keep their frontiers mathematically clear. The last discussions of epistemology are now uniting with those of higher analysis and theoretical physics to occupy an almost inaccessible domain, the domain to which, for example, the theory of Relativity belongs or ought to belong. ”

“ If the formula derived is correct, then Π, as a function of frequency of the excited light represented in Cartesian coordinates, must be a straight line, whose inclination is independent from the nature of the substance investigated. ”

“ The special sciences are all, to one degree or another, concerned with identifying patterns that hold only in sub-sets of the domain studied by physics. This is not to say that the special sciences all reduce to physics or that they’re all somehow parasitic on the patterns identified by fundamental physics. ”