(adsbygoogle = window.adsbygoogle || []).push({}); Does the "Equivalence principle" holds in QM.

If we know that in QM under an "small" height so [tex] z<< R_{earth} [/tex] (radius of the earth) so the QM equation is (SE):

[tex] -D^{2}\Phi (z) +2m^{2}gz\Phi (z) =2mE_{n} \Phi (n) [/tex]

SO the wave function is just a "Airy function" and [tex] | \Phi (z) |^{2} [/tex] is an "intensity" near a caustic (then does it means that the problem of "gravity" is somehow related to optics ??)

- from the ODE above , we can guess that in QM "galileo was wrong", sice a Hamer and a feather won't fall at the same speed (If Bohmian mechanics is right you get the same answer due to the "Bohmian potential" )

- Then, was Einstein Wrong?, in the sense that inertial and gravitational mass are not the same ? Ehrenfrest's theorem produces:

[tex] \frac{<F_g >}{<a_g>}= \frac{<F_i>}{<a_i>} [/tex]

but only as a "mean value" in the practice perhaps in an experiment you could get different inertial and gravitational masses due to QM effect, then how does it affect to GR?.

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# Does the Equivalence principle holds in QM.

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