Time dilation and length contraction without relativity: The Bohr atom and the semi-classical hydrogen molecule ion

Allan Walstad

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arXiv · 1711.03995

Time dilation and length contraction without relativity: The Bohr atom and the semi-classical hydrogen molecule ion

Allan Walstad

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Abstract

Recently it was shown that classical "relativistic" particle dynamics was implicit in physics going back to Maxwell. The demonstration utilized a simple modification of a 1906 thought experiment by which Einstein established the mass equivalence of energy, independently of the relativity postulates. The modified thought experiment leads directly to correct expressions for the momentum and kinetic energy of a particle at high speed. In the present paper, one additional ingredient is added, namely, the Bohr quantization rule of the old quantum theory. It is found that a semi-classical model of a hydrogen atom and a hydrogen molecule ion exhibit, respectively, time dilation and length contraction.

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Allan Walstad. 2017-11-10. Time dilation and length contraction without relativity: The Bohr atom and the semi-classical hydrogen molecule ion. https://arxiv.org/abs/1711.03995

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