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Lorentz and Other Invariances

In: Mathematics of Particle-Wave Mechanical Systems

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  • James Hill

    (University of South Australia)

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.

Suggested Citation

  • James Hill, 2022. "Lorentz and Other Invariances," Springer Books, in: Mathematics of Particle-Wave Mechanical Systems, chapter 0, pages 183-204, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-19793-2_7
    DOI: 10.1007/978-3-031-19793-2_7
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