The length of a longitudinally moving rod
Einstein used the Lorentz-equations to transform the instantaneous position-coordinates at the moving-tail and moving-nose of a rod (within an inertial reference-frame (IRF) relative to which the rod is moving with a speed v) into the inertial reference-frame within which the rod is permanently stationary. He concluded from this transformation that such a rod contracts when it is moving past at a speed v. But, according to Galileo's principle of inertia, the natural state of a matter-entity, when it experiences no forces, is to remain stationary within its own inertial reference-frame. Motion of such an entity with mass is caused by a relativistic coordinate transformation of its position-coordinates from the inertial reference-frame within which this entity is permanently stationary into the inertial reference-frame within which the entity is observed to be moving with the speed v. When judged in terms of Galileo's concept of inertia, Einstein's transformation of moving coordinates into permanently stationary coordinates has no physics-meaning. Here, the change in length of a rod (passing at speed v) is derived by Lorentz-transforming the permanently stationary position-coordinates at the beginning and end of the rod, from the inertial reference-frame within which the rod is permanently stationary into the inertial reference-frame relative to which the rod is moving with speed v. In contrast to Einstein's derivation, an increase in the length of the moving rod is obtained: It is found that this length-increase bestows on any matter-entity a de Broglie wavelength.
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Document Type: Research Article
Publication date: 30 December 2013
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