Lorentz Transformation
& Particle/Wave Duality
Length Contraction &
Relative Simultaneity
Length Contraction & Relative Simultaneity
John Field discusses the presumed length contraction and relative simultaneity effects of Special Relativity in his paper "A sign error in the Minkowski space-time plot and its consequences". In it he describes how these ideas have become embedded in the literature.
Firstly, he explains how these effects were introduced into Einstein's original 1905 paper. This was simply a matter of important constants that were omitted from Einstein's equations. Einstein had pointed out the need for these constants, but he failed to include them in his own work. This resulted in the apparent length contraction and relative simultaneity effects. Adding the constants to Einstein's equations causes both to disappear.
Field then shows how these same effects came to be included in graphical representations of the space-time relationships. This originated in a paper written by Minkowski in 1908. In a space-time diagram, derived by Minkowski, a world line OA' was rotated clockwise from OA, but should have been rotated anti-clockwise.
This had the effect of making it appear that the length of an object moving with respect to a given reference frame would contract when viewed at rest in that reference frame. Whereas, the corrected plot indicated that the length of the object remained the same.
The apparent relativity of simultaneity is a more subtle error. It arises from the interpretation of purely mathematical projection operations on the plot, that are unrelated to the basic physics of the problem. Field presents the original and corrected graphical representations.
John Field's paper "A sign error in the Minkowski space-time plot and its consequences" may be downloaded here.
