The Local Nature of the Correspondence Principle
The Correspondence Principle requires that the Lorentz transformation reduce to the Galilean transformation at low velocities. But Gedanken experiments over large distances reveal that the Correspondence Principle cannot hold everywhere, because the time part of the Lorentz transformation involves a term ?x , and x can always be chosen large enough to compensate for small ?. The behavior of the Lorentz transformation at large distances from the origin is decidedly non-Galilean, even at low velocities.
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