In the middle of studying for my matrix mechanics/atomic orbial/diatomic bonding final and something has been itching at my buttcrack for a while. Above Z=20 or so the lower orbitals (that dont actually exist so I've come to find out) have to be calculated with relativistic QM because the classical picture of their orbital speed becomes so great that the electron would have to be traveling faster than c (again, electrons may as well not even exist as far as I'm actually concerned, but cut me slack since its only been 6mo or so since I first started studying QM). My question is, what sort of time dilation are we talking about for those inner electrons? Does it have any quantifiable effect? Is there gravitational time dilation at those scales? Given the Pauli exclusion principle, do we actually have to worry about relativistic effects on electrons trapped that deeply in the atom and if so what are the relativistic effects on real world calculations? I should be able to understand any QM speak up to Dirac Notation which I have only grazed over (not required until graduate level courses). I realize this is a question best fitted for my professor but between now and the end of the semester I need to spend my time around him picking his brain for my final. Thanks.