#### atyy

Science Advisor

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In order not have (1) and (2) be identical, so that (1) can be consistent with Lorentzian and Galilean inertial frames, would it work to specify the "laws of physics having the same form" as being derivable from a Lagrangian that is covariant under space and time translations, and in which the spatial metric has the form diag(1,1,1) and derivatives of the metric do not appear?Logically, we have the same situation as in Einstein's 1905 formulation, which is that the second postulate is really a special case of the first. (Maxwell's equations are laws of physics.) The minimal set of laws of physics to which you could apply this type of axiomatization would be Maxwell's equations themselves, in which case the content of axioms 1 and 2 becomes identical. In this case, the axioms are certainly self-consistent, as well as consistent with all the experiments that established Maxwell's equations, since Maxwell's equations can be expressed in a form that is invariant under a change of coordinates, including a change to an accelerating frame: http://en.wikipedia.org/wiki/Covariant_formulation_of_classical_electromagnetism In this example, however, the postulates are needlessly weak, because they don't need the restriction to frames of reference in constant rectilinear motion relative to one another.