- 39

- 2

- Summary
- A moving wagon fitted with printers at each end that simultaneously print dots on the rail makes the consequences of Lorentz transformations tangible. A lot of such wagons, forming a full circular train and a symmetrical rotating system, makes it clear that, within the scope of Lorentz transformations, the behaviour of a moving inertial system is incompatible with that of an infinitely small part of a rotating system, even though there are no differences between these systems to account for it.

In short:

Consider a train-wagon with rest-length L, having a printer on the front and the rear that can put a dot on the rail. Both printers have synchronised clocks. The wagon, being the moving frame MF, has a speed

Next, we put a lot of the former train-wagons together, to form a full circular train of

At

- there will be n dots on the rail,

- each dot will have the same distance to the next dot,

- the rear dot of wagon 1 will coincide with the front dot of wagon n, regardless of which wagon is numbered as number 1.

Hence, the distance between each pair of sequential dots will be L.

Now, for a close look to one unit of this rotating system. If

So, the contradiction at hand is that in SF the stretched wagon prints its dots at a distance L, while the contracted wagon prints its dots at the larger distance γL, even though they both print the dots simultaneously in their own frame. How can this be? Somewhere the behaviour of the rotating system, or at least a very small part of it, should smoothly meet that of Special Relativity Theory in straight forward motion.

Consider a train-wagon with rest-length L, having a printer on the front and the rear that can put a dot on the rail. Both printers have synchronised clocks. The wagon, being the moving frame MF, has a speed

*v*, and at*t0*both printers simultaneously put a dot on the rail.*Lsf*is the distance between these dots for an observer at rest along the rail, being the stationary frame SF. In accordance with Lorentz,*Lsf =*γL.Next, we put a lot of the former train-wagons together, to form a full circular train of

*n*wagons that are coupled by the printers, being the rotating system RS. The front printer of each wagon is the rear printer of the next wagon and therefore we have*n*printers. (To please Ehrenfest, the wagons are elastic enough to compensate for length contraction due to their velocity.)At

*t0*(in RS) every printer puts a dot on the rail. Given the unbroken rotational symmetry we must assume that, in SF,- there will be n dots on the rail,

- each dot will have the same distance to the next dot,

- the rear dot of wagon 1 will coincide with the front dot of wagon n, regardless of which wagon is numbered as number 1.

Hence, the distance between each pair of sequential dots will be L.

Now, for a close look to one unit of this rotating system. If

*n*is taken infinitely large, pushing the radius to the limit ∞, this RS-unit has virtually the same movement as our straightforward going single wagon. The only difference is that the RS-unit is, compared to the contracted single wagon, stretched by factor γ.So, the contradiction at hand is that in SF the stretched wagon prints its dots at a distance L, while the contracted wagon prints its dots at the larger distance γL, even though they both print the dots simultaneously in their own frame. How can this be? Somewhere the behaviour of the rotating system, or at least a very small part of it, should smoothly meet that of Special Relativity Theory in straight forward motion.

Last edited by a moderator: