The conservation laws of nonrelativistic and relativistic systems are reviewed and some simple illustrations are provided for the restrictive nature of the relativistic conservation law involving the center of energy compared to the nonrelativistic conservation law for the center of mass. Extension of the nonrelativistic interaction of particles through a potential to a system that is Lorentz-invariant through order is found to require new velocity- and acceleration-dependent forces that are suggestive of a field theory where the no-interaction theorem of Currie, Jordan, and Sudershan does not hold.
REFERENCES
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This belief is encouraged by mechanics texts that write one-particle “relativistic Lagrangians” with an arbitrary potential function rather than applying external forces to a relativistic particle. See, for example, Refs. 2 and 3.
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, which apparently corresponds to the currently preferred terminology. The word “mass” is now taken to be synonymous with what used to be termed “rest mass,” and many historical uses of the term “mass” are now considered less appropriate. This refinement in terminology requires that the mass of an object is a measure of its energy content only in its center-of-momentum frame. The term “center of mass,” taken to mean what we have termed “center of energy,” is no longer the appropriate terminology. This older terminology appears, for example, in the first edition ofE. F.
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The mistaken idea of Lorentz-invariant behavior as a description of nature involving only the use of relativistic mechanical momentum appears in the analysis of blackbody radiation by
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).© 2009 American Association of Physics Teachers.
2009
American Association of Physics Teachers
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