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I am studying gauge transformations, and my professor asked me:

"Can the potentials obtained by the Lorenz gauge be considered physical quantities?"

I assumed that "physical quantity" is something that can be measured.

I tried to answer with: "suppose by contradiction that A and A' generate observable quantities, we would then have two different measures and this violates ... " Well, as I did not know how to end, I asked some friends, and all I got was "... violates the axiom that physics should be the same for all observers" That sounded weird to me, I would find it odd if that was the reason. For me, in assuming such contradiction, I would expect that by assuming such a statement I would arrive at a violation of some conservation law.. Is there an argument involving conservation laws? The only thing that makes us believe that something has the same measure for two observers is an axiom?

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    $\begingroup$ It very much depends on what exactly you mean by "physical quantity". An object that appears in a physical model/law? Then very much yes. But, sometimes, "physical quantity" is basically a synonym for gauge invariant, and so the answer is tautologically no. So what do you mean by "physical quantity"? $\endgroup$ – AccidentalFourierTransform Jul 14 at 1:31
  • $\begingroup$ I think that my professor talked about something that you can measure in lab. $\endgroup$ – Daniel Byron Jul 14 at 1:40
  • $\begingroup$ You choose a gauge to make the problem simple. It's arbitrary - and if you're solving equations you have to make a choice. It's not physical. Fields aren't physical. But it is possible to choose a gauge which results in results which aren't physical. $\endgroup$ – Cinaed Simson Jul 14 at 3:28
  • $\begingroup$ I meant to say fields aren't observables. $\endgroup$ – Cinaed Simson Jul 14 at 8:24

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