Length contraction of a train

[Sentosa]

There's a section in my astronomy book on relativity. The image shows a train traveling at a slow speed and a second image of the train approaching the speed of light. The text says the second train is length contracted, but only in the horizontal direction. In the vertical direction the train is not length contracted. If this is the case, then how can the wheels continue to rotate? Take a look at the image; they're obviously not circular.

 

[A.T.]

http://www.spacetimetravel.org/tompkins/node7.html
http://www.spacetimetravel.org/rad/rad.html

 

[PeroK]

There's a section in my astronomy book on relativity. The image shows a train traveling at a slow speed and a second image of the train approaching the speed of light. The text says the second train is length contracted, but only in the horizontal direction. In the vertical direction the train is not length contracted. If this is the case, then how can the wheels continue to rotate? Take a look at the image; they're obviously not circular.

There are two important points in answer to your question.

First, all motion is relative. So, in fact, there is no such thing as something moving near the speed of light. Only moving near the speed of light relative to something else.

If you imagine those particles at CERN that have been accelerated to near the speed of light. In their reference we are all moving at near the speed of light, so we are all length contracted, as are all our trains.

Length contraction is, therefore, not absolute but relative.

Second, it follows from the above, that length contraction does not involve any inherent deformation in an object. The train has no idea that it is length contracted in another reference frame, so functions mechanically normally.

 

[jbriggs444]

Second, it follows from the above, that length contraction does not involve any inherent deformation in an object. The train has no idea that it is length contracted in another reference frame, so functions mechanically normally.

Note however that a train moving at near light speed relative to us on a track that is at rest relative to us will have its wheels spinning at a ferocious rate. The wheels are neither at rest with respect to the train nor at rest with respect to us. Indeed, there is no inertial frame in which the wheels are at rest. Their shape in the drawing is an artists conception, not something that should be taken seriously.

The notion of rigid rotation is one that works at low speed but which has difficulties at relativistic speeds.

 

[PeroK]

@jbriggs444
It's a good point. A train traveling at near light speed relative to the track is effectively a mechanical impossibility.