Strain Gauge

A long rectangular bar of metal sits at rest in my reference frame. The strain gauge attached to its middle reads zero. Now I run in the direction parallel to the length of the bar at an enormous constant speed V at nearly light speed. I measure the bar length to determine that Lorentz-Fitzgerald contraction has occurred that is, that the bar measures shorter than before. What should the strain gauge show?

Answer

The strain gauge continues to show a zero value. What I interpret as a length contraction when I run past is really the measurement of the length component along my direction of motion of the metal bar that appears to be rotated. The atoms do not move closer to one another, so the strain gauge remains at zero.

The apparent rotation is called the Terrell effect: if a snapshot is taken of a moving object, the object does not appear contracted, but rather rotated. A snapshot is understood to be a two dimensional, non-stereoscopic photograph. The stereoscopic appearance of a three-dimensional object is more complicated because shearing and other distortions can be present. In fact, there is no such thing as a rigid object in relativity!