Could SR not be built from only one postulate?

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SUMMARY

The forum discussion centers on the possibility of combining the two postulates of Special Relativity (SR) as defined by Schutz: (1) the absolute velocity of an observer cannot be measured, and (2) the speed of light is constant at c for all unaccelerated observers. Participants argue that while combining these postulates into a single statement about the invariance of physical laws in inertial frames is conceptually appealing, it overlooks the necessity of Maxwell's equations in deriving the implications of SR. The discussion highlights that various formulations of SR exist, including those that drop the second postulate, but emphasizes the importance of maintaining a rigorous foundation for the theory.

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  • #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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