Abstract
THE relativistic soundness of the quantum theoretical formula has been questioned by Synge1. In an interesting note, he derives instead the formula where m′ is the relativistic mass of the system (atom) in its initial state S′ in the initial rest frame (the centre of mass frame) and m is the lower energy state S of the system (mc2 being the proper energy in this state). The energies E′ and E are measured in the initial and final rest frame of the system. We do not in any way disagree with Synge, but wish to give a slightly different formulation of this question which, in a sense, preserves (1) by giving it an interpretation fully consistent with equation (2). This requires all the energies in equation (1) to be measured in the same frame.
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References
Synge, J. L., Nature, 228, 271 (1970).
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LANDSBERG, P., HINDMARSH, J. Energy Levels and Lorentz Invariance. Nature 229, 332–333 (1971). https://doi.org/10.1038/229332a0
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DOI: https://doi.org/10.1038/229332a0
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