Lorentz contraction

“ But I show, in agreement with Lorentz, that it is incapable to accord with the impossibility of an experiment showing the absolute motion. As I have said, this is because is the only case for which all the Lorentz transformations form a group.
But with the hypothesis of Lorentz, the agreement between the formulas does not occur all alone; we obtain at the same time a possible explanation for the contraction of the electron, assuming that the electron, deformable and compressible, is subjected to a constant external pressure whose work is proportional to volume changes. ”

“ Then, while preserving the Lorentz contraction and the formulæ in which it is expressed, Einstein says that this contraction, while it really exists, is only an appearance, a sort of optical illusion, due to the fact that the light which shows us objects does not travel instantaneously, but with a finite velocity. ”

“ Until now, we only have spoken about the restricted relativity theory. The general theory denies the existence of coordinate systems, which have by themselves the preferred state of an inertial system. The attempt by Lange should be without result, if all bodies, except the test bodies, are taken away. Just because those large masses of the fixed stars are on the whole at rest in the astronomical coordinate system, it has something in advantage before the others. Nevertheless, this only inessentially changes the view on Lorentz contraction previously presented. ”

“ These are also the values of the electric and magnetic forces produced at points outside, by Lorentz's electron, or by any charged system in which, when at rest, the charge is distributed with spherical symmetry and which, when in motion, suffers the Lorentz-FitzGerald contraction. is the force exerted by the moving charge upon a unit charge which is at rest at the point If the unit charge at is in motion with the velocity then the force exerted upon it, which we may call () , is where represents the vector product. ”

“ As to the experiments of TROUTON and NOBLE, their negative result becomes at once clear, if we admit the hypotheses of §8. It may be inferred from these and from our last assumption (§ 10) that the only effect of the translation must have been a contraction of the whole system of electrons and other particles constituting the charged condenser and the beam and thread of the torsion-balance. Such a contraction does not give rise to a sensible change of direction. ”

“ A body that has an "independent" volume, i.e. independent of external influences, does not exist in all of nature, and even less in relativity theory. At least I think, that the attempt to make the abstraction of the rigid body (which is so important for ordinary mechanics) also useful for the theory of relativity, does not promise any real success [2] .
The task, to determine the deformation of a somehow accelerated body is therefore essentially a problem of elasticity, in relativity theory and in ordinary mechanics. ”

“ The difference against electrodynamics, which achieves the same independently from the relativity principle, is not a principal one though, but solely lies in the current state of physical research. We simply have much more complete and precise knowledge in the theory of electricity, than in mechanics. ”

“ That this conclusion wasn't drawn before the relativity theory, was only due to the fact that this reference system was previously materialized as "aether". But relativity theory has banished the idea of a corporeal aether.
Now we come back to the body, which at first rests in system , but afterwards it obtains a motion against . Its shape is the result of the equilibrium existing between the forces acting from atom to atom (this word is used in the widest sense, thus with the inclusion of electrons or similar things) . If we set the body in motion with invariable shape, i.e. ”

“ As long nothing is known about these influences, as long nothing can be said about the contraction of the volume. Most directly, this can be seen at slightly compressible bodies, as in gases, but it applies equally well to solid bodies. ”

“ Born limits the definition of rigidity to a single electron. Against this we surely cannot object from the outset, but whether it brings us physically further than the general principles of relativity theory, might well escape each test for the time being. ”

“ What is unsatisfactory for some in this way of conclusion, is the fact that it only gives a reason for its recognition, but not a cause; it doesn't follow the causal relation of reality. Before we attempt to fill this gap, we still want to emphasize that such a deviation of the line of reasoning from the causal interconnection is nothing unusual in physics. On the contrary, its value for science (especially as regards the most general natural laws) rests on the fact, that it relieves us from the effort, to follow the often less vivid causal-connections of nature in all details. ”

“ Now we ask what would we be able to see if the measure were not bound solidly to the earth, if it, let us suppose, moved down or up with the place where it is located and where we are ourselves. If in this case the speed were constant, then, and this is in accord with the special theory of relativity, there would be no motion observed at all; we should again find an acceleration of 981 for a falling body. It would be different if the measure moved with changeable velocity. ”

“ Indeed, why should we, since we assumed that the aether is not in motion, ever speak about a force acting on that medium? The most simple would by, to assume that on a volume element of the aether, considered as a whole, never acts a force, or even refuse to apply the concept of force on such an element that of course never moves from its place. Of course this view violates the equality of action and reaction —, since we have reason to say that the aether exerts forces on ponderable matter ”

“ Indeed, if the actions exerted by positive and negative ions depended on vector-quantities of the same kind, in such a way that all phenomena in the neighbourhood of a pair of ions with opposite charges were determined by the resulting vector, then electric actions could only be absent, if this resulting vector were 0, but, if such were the case, no other actions could exist; a gravitation, i.e. a force in the absence of an electric field, would be impossible. ”

“ If we limit the light to a flicker of the slightest duration, so that only a little bit, C, of a ray of light arises, or if we fix our attention upon a single vibration of light, C, while we on the other hand give to the projectile, B, a speed equal to that of light, then we can conclude that B and C in their continued motion can always remain next to each other. Now if we watch all this, not from the movable compartment, but from a place on the earth, then we shall note the usual falling movement of object A, which shows us that we have to deal with a sphere of gravitation. ”

“ Thus strengthened in the faith that his theory already has inspired, we may assume with him that there is not a single physical or chemical phenomenon — which does not feel, although very probably in an unnoticeable degree, the influence of gravitation, and that, on the other side, the attraction exercised by a body is limited in the first place by the quantity of matter it contains and also, to some degree, by motion and by the physical and chemical condition in which it moves. ”

“ 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. ”

“ Let on the other hand:
we see that the Lorentz transformation will cause to make δx, δy, δz and δ1x, δ1y, δ1z, δ1t undergo the same linear substitutions as with x, y, z, t.
We regard
as the coordinates of three points P, P', P" in a 4-dimensional space. We see that the Lorentz transformation is a rotation of that space around the origin, regarded as fixed. ”

“ As in empty space, so too in the interior of material bodies, the ether, and not matter viewed atomistically, was exclusively the seat of electromagnetic fields. According to Lorentz the elementary particles of matter alone are capable of carrying out movements; their electromagnetic activity is entirely confined to the carrying of electric charges. Thus Lorentz succeeded in reducing all electromagnetic happenings to Maxwell’s equations for free space. ”

“ Consequently, if, neglecting the effects of molecular motion, we suppose each particle of a solid body to be in equilibrium under the action of the attractions and repulsions exerted be its neighbours, and if we take for granted that there is but one configuration of equilibrium, we may draw the conclusion that the system Σ' , if the velocity w is imparted to it, will of itself change into the system Σ. In other terms, the translation will produce the deformation . ”

“ The conservation of energy. § 13. To justify our hypotheses, it is necessary to show its agreement with the energy law. We consider an arbitrary system of ponderable bodies that contain ions, around which only the aether exists up to an infinite distance, and around it we put an arbitrarily closed surface . During an element of time , the work that affects ponderable matter and which stems from , is
where it is to be noted, that no work is done by the forces (which are derived from ) , because they are always perpendicular to the direction of motion. ”

“ The considered body (e.g. a steel magnet) shall contain only conduction electrons and such ones (when the body is at rest) which produce , yet not ; it shall have the shape of an infinitely extended even plate, bounded by two planes : the middle plane is made by us to the -plane (Fig. 6) . When it is at rest, a constant magnetization may exist in the -direction, while . If the body acquires the velocity in the -direction, then an observer not participating at the motion, is observing the electric polarization ”

“ In other terms, whatever be the nature of the particles composing a ponderable body, so long as they do not move relatively to each other, we shall have between the forces acting in a system (Σ' ) without, and the same system (Σ) with a translation, the relation specified in (21) , if, as regards the relative position of the particles, Σ' is got from Σ by the deformation (kl, l, l) , or Σ from Σ' by the deformation . ”

“ It is true that the inquiry was transferred to the field of physics, following Cavendish's success in demonstrating the common attraction between bodies with which laboratory work can be done, but it always was evident that natural philosophy had no grip on the universal power of attraction. While in electric effects an influence exercised by the matter placed between bodies was speedily observed — the starting-point of a new and fertile doctrine of electricity — in the case of gravitation not a trace of an influence exercised by intermediate matter could ever be discovered. ”

“ Modern physicists were willing to suppose that light might be subject to gravitation — i.e., that a ray of light passing near a great mass like the sun might be deflected to the extent to which a particle moving with the same velocity would be deflected according to the orthodox theory of gravitation. But Einstein's theory required that the light should be deflected just twice as much as this. ”

“ Here, we don't discuss the subtle, related question concerning the localization of the energy. We can restrict ourselves with the fact, that the entire energy located in an arbitrary space — the "electric" portion calculated by formula (12) — always varies, as if the energy would travel according to the way determined by (13) .
Tensions in the aether. § 15. The forces determined by our formula (V) , not only require the motion of ions in ponderable bodies, but also in some circumstances can unify themselves to an action, that tends to set the body into motion. ”

“ Einstein supposes that space is Euclidean where it is sufficiently remote from matter, but that the presence of matter causes it to become slightly non-Euclidean — the more matter there is in the neighborhood, the more space will depart from Euclid. By the help of this hypothesis, together with his previous theory of relativity, he deduces gravitation — very approximately, but not exactly, according to the Newtonian law of the inverse square. ”

“ Strictly speaking, not a single experiment in which a charged body or a current conductor moves, can be handled carefully, if the state of motion of the aether is not considered at the same time. In any phenomenon of electricity, the question arises whether an influence of the earth's motion is to be expected; and regarding the consequences of the latter for optical phenomena, we have to demand from the electro-magnetic theory of light that it can account for the already established facts. ”

“ Now, Planck and Einstein have already announced, that all ponderomotive forces must be transformed by the Lorentz transformation in the same way, as in electrodynamics. Thus it must be possible in all areas of physics, to combine the force density with its power to a four-force. ”

“ If the ponderable matter is moving, then — since it carries the charge along with it — at a certain point of space there always exists another , and soon it is (when we are dealing with mutually separated ions) different from zero here and there. Yet the condition of the aether has constantly to obey equation (I) .
§ 6. The change of , that happens with time at a certain point of space, constitutes an electric current (Maxwell's displacement current) that can be represented by . We assume that it exists also in the interior of charged matter. ”