Modifying Lorentz Transformations for Invariant Length

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SUMMARY

The discussion focuses on the challenge of modifying Lorentz transformations in special relativity (SR) to incorporate an invariant length, specifically the Planck length. The original poster expresses difficulty in integrating this 3D invariant length into the 4D framework of SR. The conversation references the concept of doubly special relativity as a potential avenue for exploration. No definitive solutions were provided, indicating a need for further research in this area.

PREREQUISITES
  • Understanding of Lorentz transformations in special relativity
  • Familiarity with the concept of invariant length
  • Knowledge of Planck length and its significance in physics
  • Basic principles of doubly special relativity
NEXT STEPS
  • Research the mathematical framework of doubly special relativity
  • Explore modifications to Lorentz transformations for invariant lengths
  • Study the implications of Planck length in theoretical physics
  • Investigate existing literature on invariant length theories
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The discussion is beneficial for theoretical physicists, researchers in relativistic physics, and students exploring advanced concepts in special relativity and invariant lengths.

unchained1978
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I've been reading up on the idea of an invariant length (planck length possibly) and have tried my hand at modifying the lorentz transformations of SR such that they accommodate an invariant length. Unfortunately I haven't been able to find a way to do it. Does anyone know how one would go about this?

The Planck length is a 3D length as far as I understand, so I don't see it fit to incorporate this invariance into the line element of SR, which is a 4D length. Any help would be appreciated.
 
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