I think this all makes sense to me, but I've never heard of this in lectures or in books, so I'll check if I'm getting this right.(adsbygoogle = window.adsbygoogle || []).push({});

In one dimension Galilean coordinate transformations are [tex]x'=x-ut[/tex] and [tex]t'=t[/tex]. Momentum transforms as [tex]p'=p-mu[/tex], and energy is [tex]E=p^2/(2m)[/tex]. With a quick calculation I get [tex]E't'-p'x'=Et-px-\frac{1}{2}mu^2t-mux[/tex]. So this means, that a wave plane solution [tex]\psi(t,x)=\exp(i(Et-px))[/tex] of the Shrodinger equation is not a solution in other inertial frames? In relativistic theory it goes better, as [tex]p_\mu x^\mu[/tex] is Lorentz invariant, and a solution of Klein-Gordon equation is always a solution also in other inertial frames.

So if I assume, that a wave function is real in the sense, that there truly is some complex number associated with each space time point, in non-relativistic theory I must assume an ether coordinate set? I think it somehow remarkable, that a Shrodinger equation is not Galilean invariant like the Klein-Gordon or Dirac equations are Lorentz invariant. :uhh:

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# Ether before relativity in quantum theory also

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