Terrell Rotation

Terrell rotation.

Is it possible to see Length Contraction
Question 2: Is it possible to to measure Length Contraction

Background question 1 and 2

Accordingly to Litterarture there is a difference between To See and To Measure Length Contraction.
For Details See: James Terrell, "Invisibility of the Lorentz Contraction," Physical Review , Volume 116, Number 4, November 15, 1959, pp. 1041-1045.
For a simulation of Terrell Rotation SeeProgram 4

Description of Terrell Rotation.

Consider a train, with length l0, which moves from left to right with a speed v.
Consider a second train, with same length l0, which also moves from left to right with a speed v, on a parallel track, parallel to the first train. From the point of view of observer O the second train moves behind the first train.

What does observer O see ?

When the two trains are left from O, O sees the whole side of the first train, the side in the beginning of the second train and the front of both trains. Depending of how far left, the distance between the two trains and length l0, the more O will see of the second train.
When the two trains are in front of O, O will only see the first train.
When the two trains are right from O, O sees the first train, the side at the end of the second train and the end of both trains.

In fact, when you consider the combined shape of the two trains as a square, this whole square appears to rotate when this square moves from left to right. However there is no rotation involved: it is a visible illusion.
If you do the train simulation and the side of the first train is yellow and the side of the second train is brown than you clearly will "see" this rotation; however it is an illusion.

When you perform this simulation at high speed, than what O sees slightly changes.

When O sees the first train in front of him, then the actual position of the first train is more to the right. O sees the first train retarded or delayed.
The real position of the second train is identical as the real position of the first. However O sees the second, being further away, from a more earlier moment position, ie more towards the left. That means O sees more from the brown side at the end of the second train.
This means the second train seems to be rotated more than before. This extra angle is the Terrell Rotation angle Theta.

The next question to answer is will observer O see Length Contraction.
IMO if you compare, what you should see at high speed, including Terrell Rotation, when no length contraction is involved (ie length l0) with when length contraction is considered (ie lenght l) than you actual should see a difference.

Measuring Length Contraction

In order to measure Length Contraction you need a grid of clocks at equal distances. All the clocks should be synchronised in the frame of Observer O. As such you can measure the length of the train simultaneous in the frame of the Observer.
All this is true in principle but can not be performed in practice.

First because it is impossible to set up such a grid in space.
Secondly because if you want to test it on (accurate) Earth, the effects are very small, that the distances between the clocks have to be in the mm range. This is complet impractical. See Example and try v/c = 0.003

Reflection

The book "Spacetime Physics: introduction to special relativity" by E.F. Taylor and J.A. Wheeler also discusses the concept of (terrell) rotation. Paragraph 3-17 is called: "Contraction or Rotation ?". I agree with the question mark.

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Created: 24 September 2002

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