Lorentz and Other Invariances

James Hill
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James Hill: University of South Australia

Chapter Chapter 7 in Mathematics of Particle-Wave Mechanical Systems, 2022, pp 183-204 from Springer

Abstract: Abstract In special relativity the criterion of Lorentz invariance is there to establish the veracity or otherwise of any proposal, or in other words, a good proposition in special relativity must satisfy the criterion of Lorentz invariance, and this is a nontrivial constraint. In this chapter we examine the Lorentz invariances of the basic equations themselves and the associated Lorentz invariances implicit in the previously derived exact wave-like solution. We have previously stated that a Lorentz invariant quantity is one that assumes an identical form under a Lorentz transformation, and we establish here that the general force equations ( 3.4 ) are fully Lorentz invariant. However, this does not imply that all aspects of the solutions of ( 3.4 ) are Lorentz invariant, and there will be solutions that are not fully Lorentz invariant, and the exact wave-like solution provides an example.

Date: 2022
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DOI: 10.1007/978-3-031-19793-2_7

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