Max von Laue

Name: On the Discussion Concerning Rigid Bodies in the Theory of Relativity
Author: Max von Laue

On the Discussion Concerning Rigid Bodies in the Theory of Relativity

Summary

“On the Discussion Concerning Rigid Bodies in the Theory of Relativity”, is a work by Max von Laue. It explores elements such as disturbance, ruler and relativity.

Quotes from On the Discussion Concerning Rigid Bodies in the Theory of Relativity (Max von Laue)

Max von Laue, On the Discussion Concerning Rigid Bodies in the Theory of Relativity

“ Now, in Newton's mechanics there is of course another definition of rigidity, which fits even better to the physical state of facts; there, one considers the rigid body as the limiting case of a deformable body with a very great elasticity coefficient. This passage to the limit can in any case also be executed in the theory of relativity, although it wouldn't lead to the rigid body, but to a body deformable as less as possible, which possibly has especially simple properties as well. ”

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Source: Wikisource

Max von Laue, On the Discussion Concerning Rigid Bodies in the Theory of Relativity

“ All three proposals have the (quite justified) idea in common, that a rigid body, contrary to the infinitely many degrees of freedom of the deformable ones, has only a finite number of them (there, the body is of course imagined as a continuum) . We now want to show, that the relativity principle excludes this possibility due to dynamical causes, so that any attempt in that direction is hopeless from the outset. ”

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Source: Wikisource

Max von Laue, On the Discussion Concerning Rigid Bodies in the Theory of Relativity

“ The motion of the body at instant then has surely degrees of freedom. Because a part of it which is not yet belonging to any of these intersections, is still at rest in , while in the parts represented by the intersections, a motion dominates that is independent from the other disturbances, and which naturally has at least one degree of freedom. The number of disturbance points, however, can be arbitrarily increased; thus the number of kinematic degrees of freedom of a body has no upper limit. ”

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Source: Wikisource

Max von Laue, On the Discussion Concerning Rigid Bodies in the Theory of Relativity

“ However, to prevent misinterpretations, it shall be clearly noticed, that – under certain circumstances – a body of course can move without change of shape related to the employed co-moving system; this is indeed proven by the uniformly accelerated (hyperbolic) motion. Also in classical hydrodynamics, a particle of a fluid can occasionally be in motion as if it were rigid. ”

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Source: Wikisource

Max von Laue, On the Discussion Concerning Rigid Bodies in the Theory of Relativity

“ The second ruler, which should be momentarily brought into motion by an impulse emanating from , doesn't remain straight but bulges in . The velocity, with which the disturbance emanating in is communicated to the other points of the ruler, is itself at most equal to that of light; the distant parts at first remain at rest, and only after a certain time they are also affected by the disturbance. ”

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Source: Wikisource

Max von Laue, On the Discussion Concerning Rigid Bodies in the Theory of Relativity

“ Here, a far reaching analogy to the case of the propagation of light already used by Sommerfeld (l. c.) exists. Purely periodic and thus temporally infinite wave trains cannot serve as a signal for the occurrence of an event. Accordingly, it is no contradiction against relativity theory, that under some circumstances (in dispersing bodies and for anomalous spectrum areas) the phase velocity of periodic sinus waves is greater than . ”

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Source: Wikisource

Max von Laue, On the Discussion Concerning Rigid Bodies in the Theory of Relativity

“ There, we always use one and the same reference system. A ruler is at rest here, while another one (forming an angle with the first) moves with velocity perpendicular to its direction. The intersection point of both rulers then travels over the first with velocity , and also when has moderate values (ca. 1 cm/sec) one can achieve that becomes greater than the speed of light by the choice of sufficiently small values for . ”

Max von Laue

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