Could SR not be built from only one postulate?

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The discussion centers on the possibility of combining the two postulates of Special Relativity (SR) into a single postulate: that all laws of physics are the same in every inertial frame of reference. Participants debate whether this new formulation can adequately encompass the original postulates, particularly regarding the constancy of the speed of light and the implications of Maxwell's equations. Some argue that while combining the postulates is theoretically possible, it may overlook essential principles and lead to circular reasoning. The conversation highlights the complexity of SR, suggesting that understanding its foundations requires more than just a simplified approach. Ultimately, the consensus leans towards recognizing the necessity of multiple principles to fully capture the essence of SR.
  • #121
WannabeNewton said:
Charge density is the time-like component of the current 4-vector and charge is a Lorentz scalar. Charge is defined as the integral of the charge density over a space-like hypersurface. The proof that charge is a Lorentz scalar is actually quite simple, given the 4-divergence of the current 4-vector. It's basically just an application of Stokes' theorem.

Yes, you're right. I can't find my copy of Jackson, so I'm not sure what the alternative theory is that reduces to Coulomb's law in the nonrelativistic limit.
 
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  • #123
WannabeNewton said:
Charge density is the time-like component of the current 4-vector and charge is a Lorentz scalar. Charge is defined as the integral of the charge density over a space-like hypersurface. The proof that charge is a Lorentz scalar is actually quite simple, given the 4-divergence of the current 4-vector. It's basically just an application of Stokes' theorem.
The 4D divergence theorem
 

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