Max von Laue

“ All of those who show no current (and thus also no momentum) in a valid system (the rest system [17] ) . To those belong: heat [18] , chemical energy, elastic energy, inner energy of atoms, and maybe also new and unknown energy forms. Electromagnetic energy has to be excluded in general, since it can also flow in the rest system . If this doesn't occur in a special case, then one can include it in as well; tensor then encloses also Maxwell's stresses besides the elastic ones, and vector also the electromagnetic momentum besides the mechanical momentum. ”

“ If both kinds of forces are transformed in the same way to other reference frames, then this resultant remains zero in all systems, and there is no reason for a rotation. Although it's unquestionable that this answer hits the truth, it isn't entirely satisfactory in so far as it is connected to molecular theory, with which this problem has nothing to do per se.
Already with respect to Newton's mechanics it has often been point out, [9] that it is more logical to place the dynamics of continua in front of that of the mass point. ”

“ A complete static system is also the capacitor of the Trouton-Noble experiment with its field. The total system requires (at uniform velocity) a torque as little as a mass point. The torque, exerted by the electromagnetic forces upon the capacitor itself, it exactly that one, which is required by this elastically stressed body according to § 4. Neither the electromagnetic momentum of the field, nor the mechanical momentum of the body, have in this case the direction of velocity, but the total momentum consisting of both of them has surely that direction, as it follows from (22) . ”

“ Transformation of momentum, energy and stresses. The transformation formulas for momentum, energy density and the stresses in the passage from one valid reference system to another system , is definitely determined by deriving them from the components of the world tensor . ”

“ A four-vector – the six-vector is not needed in the following – has the direction sense of a directed distance; i.e. its four components are transformed with a Lorentz transformation like the corresponding coordinates. By a world tensor, however, we understand the totality of 16 components , which are transformed as the squares and products of . Between them, there are always six symmetry relations . Analogous to the fact that (with respect to tensor in three dimensions) the divergence becomes a space vector, here the divergence is a four-vector with components ”

“ An unsymmetrical tensor is, for example, the tensor product of two vectors and . Its components are
We call a valid space-time-system according to the relativity principle; several of that kind are distinguished by us by appended indices . The passage from to (Lorentz transformation) is represented by us – in accordance with Minkowski [12] – as an imaginary rotation of the four-dimensional axis-cross , where ; that is, by the scheme:
There, the coefficients satisfy the known reality- and orthogonality conditions. ”

“ In this field, the momentum density (related to its rest system) is everywhere zero and its energy is rigidly connected at its place. In every other reference system , the total energy (including the electromagnetic energy when it is present) shares the motion. Consequently we can understand in formulas (8a) under the total energy, under the total momentum, and under the sum of elastic stresses and Maxwell stresses. ”

“ If we integrate equations (8) over the volume
of a body, in which the velocity is spatially constant, then we find for its energy
and its momentum
the relations
There, is the rest energy, like is a symmetrical tensor.
When a body is accelerated in a adiabatic-isopiestic way (i.e. with constant and ) , namely in longitudinal direction, then by (8a) the momentum increase is generally not at all in the common direction of velocity and acceleration. Its transverse component is rather equal to
and not at all vanishes in the limiting case . ”

“ Transformation of force; energy- and momentum theorem. From the investigations of Minkowski, Sommerfeld and Abraham [14] we can see, that the ponderomotive force related to unit volume (force density) of electrodynamics, can be supplemented to a four-vector , when one adds as fourth component to the three spatial components etc., where is the velocity of the point of contact of , thus denotes the work per volume- and time unit. ”

“ That Born felt compelled to assume spherical symmetry, lies in the fact that he didn't consider the mechanical momentum of the electron, which can only be assumed as zero at certain assumptions concerning the form and charge distribution, for example when one assumes spherical symmetry ”

“ It seems to me that there is a hint in the two mentioned problems, that the advantages of the mentioned way before the opposite one (to derive the dynamics of continua from that of the mass point) , are even much greater in the theory of relativity as in the old theory. Therefore, in the following we want to investigate the concept of elastic stresses in its connection with momentum and energy. [10]
Introductory remarks. In the classic theory of elasticity, the stresses form a tensor of symmetric , i.e. ”