Inertial frame of reference

“ Of course, now that we have learned so much, thanks to the introduction of the inertial frame, there is nothing to prevent us from interpreting all our results and all our relationships backwards, as it were, in terms of a non-rotating earth. ”

“ The weakness of the principle of inertia lies in this, that it involves an argument in a circle: a mass moves without acceleration if it is sufficiently far from other bodies; we know that it is sufficiently far from other bodies only by the fact that it moves without acceleration. Are there, in general, any inertial systems for very extended portions of the space-time continuum, or, indeed, for the whole universe? ”

“ Such a freely moving cavity radiation, separated form outer space by thin rigid reflective walls, provides a good example of a rigid body, whose laws of motion completely differ from those of ordinary mechanics. Although it differs, considered superficially, in no way from other rigid bodies and also possesses a certain inertial mass and obeys the law of inertia, its mass changes significantly with temperature and it also depends in a certain specifiable way from the magnitude of the velocity as well as from the direction of the moving force in respect to the velocity. ”

“ In this book the tradition of Faraday and Maxwell still rules our outlook; and for us matter and electricity are but incidental points of complexity, the activity of nature being primarily in the so-called empty spaces between.
The vague universal frame to which rotation is referred is called the inertial frame. It is definite in the flat space-time far away from all matter. In the undulating country corresponding to the stellar universe it is not a precise conception ”

“ But since it is, as shown earlier, impossible to separate the energy of the kinetic motion of a body from its internal state, it follows immediately that a constant with the properties of inertial mass may not exist. The reason for this lies again in the internal energy of thermal radiation which contributes to the inertia of a body in a small but determinable way, i.e., by a term which depends on the radiation density or temperature. If, however, we want to define mass rather by momentum than by kinetic energy, namely as the ratio of momentum by velocity, we obtain no different result. ”

“ This meant that either there was a unique inertial system enabling us to define absolute motion and rest in nature, or that we would have to build up a theory of relativity, not on the inertial law and inertial systems, but on some new foundation which would definitely ensure that the form of all physical laws would be preserved in passing from one system of reference to another. ”

“ The basic principle of inertial navigation is the measurement of the accelerations acting on a craft, other than those not associated with its orientation or motion with respect to the earth, and the double integration of these accelerations along known directions to obtain the displacement from the start point. Due to increasing position errors with time, an inertial system must be reset from time to time using another navigation system. ”

“ We assume, then, that the various distributions of the inertial forces manifesting themselves in our various frames must be attributed to the conditions of rest and of motion of these frames, not with respect to the remainder of the universe, which would be as good as annihilated, but with respect to those limited portions of the ether or of space in which the frames are situated. ”

“ The energy of these oscillations, which can be very substantial, would (as long as the atoms remain unchanged) emerge in no other way than through inertia, by which it opposes to a translational acceleration of the oscillating system, and by the gravitational effect which is apparently in close connection to it. However, the views based on the kinetic theory of gases, which assume the inertial mass as something primarily given and the chemical atoms as rigid bodies or as simple material points, are insufficient for a further development of those ideas ”

“ The new principle of relativity and the equations of electrodynamics led, rather, to the fundamentally new discovery that inertial mass is a property of every kind of energy, and that a point-mass, in emitting or absorbing energy, decreases or increases, respectively, in inertial mass, as is shown in Note 5 for a simple case. ”

“ But then, on the electrical theory of matter, even inertia is not the thoroughly constant property we once thought it. It is a function of velocity for one thing, and when speeds become excessive the inertia of matter rises perceptibly in value. ”

“ When the calculations are extended to charges moving with high velocities, it is found that the electrical inertia is not strictly constant but depends on the speed; in all cases the variation is summed up in the statement that the inertia is simply proportional to the total energy of the electromagnetic field. We can say if we like that the mass of a charged particle at rest belongs to its electrostatic energy; when the charge is set in motion, kinetic energy is added, and this kinetic energy also has mass. ”

“ On the electronic hypothesis, the source of all inertia is the inertia of the ether, and until we are able to dissect this last quality into anything simpler than the time-element involved in the production of an ether strain or displacement, we must accept it as an ultimate fact, not more elucidated because we speak of it as the inductance of the electron. ”

“ The development of electrodynamics and the phenomena of radiation generally showed, however, that the laws of radiation in one inertial system did not preserve their form when referred to another inertial system: and ' were no longer equivalent for the description of phenomena such as that of light passing through a moving medium. ”

“ While the inertia and momentum of a weight dropped in from the "outside" surface would carry it far past the magnetic center, yet, before reaching the "inside" surface of the earth it would gradually diminish in speed, after passing the halfway point, finally pause and immediately fall back toward the "outside" surface, and continue thus to oscillate, like the swinging of a pendulum with the power removed, until it would finally rest at the magnetic center, or at that particular point exactly one-half the distance between the "outside" surface and the "inside" surface of the earth. ”

“ By that, the mass defined by inertia would only be constant at small velocities, and would increase with increasing velocity. Since inertia as well as gravitation emerging from the body, is proportional to the number of quanta composing the body, it follows, that the mass defined by inertia must be proportional to the one specified by gravitation. If a body with mass , is attracted by a body of mass up to a distance of , then the electromagnetic energy store of gravitation is diminished by the amount , where denotes the gravitational constant. ”

“ It is only when there is numerical equality between the inert and gravitational mass that the acceleration is independent of the nature of the body. Let now be an inertial system. Masses which are sufficiently far from each other and from other bodies are then, with respect to , free from acceleration. We shall also refer these masses to a system of co-ordinates , uniformly accelerated with respect to . Relatively to all the masses have equal and parallel accelerations; with respect to they behave just as if a gravitational field were present and were unaccelerated. ”

“ Inertia says a body will move once started, but it doesn't say why or how. How does that particle once started gain the knowledge to continue without some direct control over its spatial framework? That it will continue, we know. That in the presence of a gravitic field or a magnetic field or other attractive force at right angles to its motion, we can create an acceleration which will maintain it in an exactly circular path called an orbit. ”

“ However, the question of an electrodynamic explanation of inertia remains open; but instead there arises, on the other hand, the advantage that it's not necessary to ascribe to the electron neither a spherical form nor even any other form in order to arrive at a certain dependence of inertia on speed. ”

“ The self-induction therefore opposes every variation of the intensity of the current, just as in mechanics the inertia of a body opposes every variation of its velocity.
Self-induction is a veritable inertia. Everything happens as if the current could not establish itself without putting in motion the surrounding ether and as if the inertia of this ether tended, in consequence, to keep constant the intensity of this current. ”

“ The fact that it would rise in value by a calculable amount, and that the rise would be perceptible when the speed of motion approached in value to within, say, a tenth of the velocity of light, was predicted mathematically;1 and now, strange to say, it has recently become possible to observe and actually measure the increase of inertia experimentally, and thus to confirm the electrical theory not only as qualitatively or approximately true, but as completely and quantitatively accurate. ”

“ Another consideration is that the magnetic field itself, when moved in space, suffers no frictional resistance. There is no magnetic energy wasted through ether inertia. These phenomena show that whether the ether exhibits the quality called inertia depends upon the kind of motion it has. ”

“ We have seen how the rotating parts of the engine can be balanced, but we have not considered the reciprocating parts. To understand this question of balancing we must talk about “inertia forces.” All bodies possess inertia, that is, they resent changes in their state of rest or motion. If a body is moving uniformly it tends to keep on doing so, whereas if it is at rest it tends to remain so. To start the body off from rest, or to stop the body and bring it to rest, requires a force to be exerted, and this force may be called the inertia force. ”

“ Because the principle of inertia is certainly nearly true. When the engine experiences a sudden and sharp check, or an acceleration, the fly-wheel serves to keep it steady. Driven by the speed it has acquired, and driving the engine in its turn, it tends to preserve its velocity, and it prevents or modifies accidental checks or accelerations. The principle is therefore based upon experience, especially on the experiments of Galileo, who verified it by rolling balls down planes inclined at different angles. ”

“ Supposing an original state of rest, about to pass into motion in obedience to the disturbing forces, the currents commencing at the centre will follow the lines of most rapidly-decreasing density; seeing that the inertia will be least in those lines. That is to say, there will be a current from the centre towards each pole, along the axis of rotation; and the space thus continually left vacant will be filled by the collapse of matter coming in at right angles to the axis. ”

“ Everybody knows that the characteristic feature of matter is what we call inertia. If matter is at rest, a force is needed to set it in motion. If it is in motion, it needs a force to stop it. It needs one to accelerate the movement and one to alter the direction. This resistance which matter offers to the forces which tend to modify its condition of rest or movement is what we call inertia. But different bodies may offer a different degree of resistance to these forces. If a force is applied to an object, it will give it a certain acceleration. ”

“ Such an inertial system is determined by the straight lines which connect three point-masses infinitely distant from one another (and thus unable to exert a mutual influence upon one another) and which are not subject to any other forces. This definition makes it evident why no [Pg 89] inertial system will be discoverable in nature, and why, consequently, the law of inertia will never be able to be formulated so as to satisfy the physicist. References:—
C. Neumann. "Ueber die Prinzipien der Galilei-Newtonschen Theorie," Leipzig, 1870. ”

“ The inertia of matter, which represents the second independent definition of matter besides gravitation, can be derived without further hypotheses from the concept of electromagnetic inertia, which is already employed many times.
We think of the electric elementary quantum as an electrified point. The forces and polarizations emanating from such a moving point, were derived by Heaviside. ”