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  • $\begingroup$ Evidence? How do you compute the energy of a charge distribution in a Voltage configuration? $\endgroup$
    – Cosmas Zachos
    Commented Oct 16, 2023 at 21:44
  • $\begingroup$ @CosmasZachos isn’t that only the case in the electrostatic case (discussed in my question). $\endgroup$
    – phonon
    Commented Oct 16, 2023 at 21:57
  • $\begingroup$ @CosmasZachos I’ve now updated the question significantly based on your suggestion. $\endgroup$
    – phonon
    Commented Oct 16, 2023 at 23:32
  • $\begingroup$ It's not clear to me what this question is asking: What is the definition of "voltage" here? It seems to me that Weinberg is simply calling $\frac{\partial H}{\partial \rho}$ "voltage" in analogy to electrostatics. In order to be able to have "evidence" for this being equal to "voltage" $V(x)$, you would have to have some independent definition of "voltage". $\endgroup$
    – ACuriousMind ♦
    Commented Oct 16, 2023 at 23:57
  • $\begingroup$ @ACuriousMind the voltage is something we should be able to measure in an experiment, which I’d argue is an independent definition. If you like, the question can be phrased in terms of evidence that $V$ is the experimental voltage. $\endgroup$
    – phonon
    Commented Oct 17, 2023 at 0:09