Vladimir Ignatowski

“ There are without doubt many processes that are allowed to propagate with superluminal velocity in relativity theory as well. For instance, in anomalous dispersing bodies the phase of light propagates with a velocity that can be faster than light. This is certainly not a contradiction against the relativity principle, because one cannot give a signal by a continuous periodic wave train. Recently Einstein has communicated to me another simple example in which there is superluminal velocity as well, but also in this case it's not about a "signal velocity". ”

“ Within such a body, every action is indeed propagating momentarily for a co-moving observer, and thus with superluminal velocity for a moving observer. It it were possible to show, that it contradicts the relativity principle by "telegraphing into the past" in this way, then the concept of the rigid body must surely be abandoned. ”

“ Imagine two rulers mutually inclined under a very acute angle, then move one of them with a velocity of 1cm/unit against the other one, then the intersection on the other one propagates with arbitrary large velocity. ”

“ Now it is clear that optics lost its special position with respect to the relativity principle by the previous derivation of the transformation equations. By that, the relativity principle itself gains more general importance, because it doesn't depend on a special physical phenomenon any more, but on the universal constant . ”

“ If one intersects the bent sheet previously constructed with such an oblique plane, then the intersection is evidently not straight, but has a bending that is moving to the right when one moves the intersecting plane towards above, that is, it is moving to the right with superluminal velocity. ”

“ At the end, I want to mention the velocities possible from the standpoint of the relativity principle.
Consider expression (24) for .
The contraction that we observe at a distance moving with system is depending on . Thus it has no meaning to assume that can become imaginary, i.e., must always be smaller than . But what is the meaning of ? means the velocity of the coordinate system , thus it cannot be larger than . In other words: none of the rest coordinate systems can move with superluminal velocity. ”

“ In order to illustrate the meaning of still further, we use an analogy from optics, namely the relation between image and object. From the pure optical standpoint, object and image are interchangeable. ”

“ Thus there is an arbitrary amount of synchronous clocks, from which it follows that this velocity is actually the velocity to catch up the time in the moving system. Thus the value is the limiting velocity, at which the numerator of the previous formula becomes zero, thus equal to , but not negative. A larger velocity is just not imaginable. ”

“ From (28) we see, that for us (the resting observer) the bending is moving the quicker, the slower is moving with respect to . If we now imagine that we play the role of the moving observer, then the propagation velocity of the bending will appear to us as infinitely large, because the observers elevate the rod at the same time according to their synchronous clocks. ”