Invariance of Transverse Lengths
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Exercise:
Transverse lengths i.e. lengths perpicular to the motion of an object are not affected by relativistic effects unlike longitudinal lengths which are contracted. vspacemm Ase that transverse lengths are shortened when an object moves with respect to an observer. Show that this leads to a contradiction e.g. for a train driving on rails.
Solution:
We ase that when the train is at rest with respect to the rails the wheels on an axle and the rails have the same distance. When the train is in motion we can describe the situation for two different observers: Observer A is at rest with respect to the rails. In this reference frame the axles of the moving train would be shortened while the rails would have their proper distance. Observer B is at rest with respect to the train. In this reference frame the rails would be closer together while the axles would have their proper length. center includegraphicswidth.cm#image_path:transverslengths-# center In conclusion for A the wheels would be on the inside of the rails while for B they would be on the outside of the rails. This would allow to distinguish between the two inertial reference frames e.g. by placing a switch on the inside of the rails which would only be activated in reference frame A which contradicts the relativity postulates.
Transverse lengths i.e. lengths perpicular to the motion of an object are not affected by relativistic effects unlike longitudinal lengths which are contracted. vspacemm Ase that transverse lengths are shortened when an object moves with respect to an observer. Show that this leads to a contradiction e.g. for a train driving on rails.
Solution:
We ase that when the train is at rest with respect to the rails the wheels on an axle and the rails have the same distance. When the train is in motion we can describe the situation for two different observers: Observer A is at rest with respect to the rails. In this reference frame the axles of the moving train would be shortened while the rails would have their proper distance. Observer B is at rest with respect to the train. In this reference frame the rails would be closer together while the axles would have their proper length. center includegraphicswidth.cm#image_path:transverslengths-# center In conclusion for A the wheels would be on the inside of the rails while for B they would be on the outside of the rails. This would allow to distinguish between the two inertial reference frames e.g. by placing a switch on the inside of the rails which would only be activated in reference frame A which contradicts the relativity postulates.