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orthonormal comments on What a reduction of "probability" probably looks like - Less Wrong
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It's worth noting that the conservation law for the L^2 norm is not a general condition, but a very special feature. We start talking about things as physically real when there's a conservation law involved (mass/energy, charge, momentum, etc). Other norms for the wavefunction don't have this property (except perhaps a few pathologically complex norms concocted for that purpose).
Good, I thought as much. Do you have links to papers about such exotic norms?
The existence of such exotic norms is just a guess. I do know for certain that other L^p norms and Sobolev norms aren't conserved over time (one can bound their rate of growth in some cases, but that's not nearly as special), but my relevant math books are in another city. I'll see if I can find a reference.