The wavefunction for a hypothetical quantum box of size Planck length (L),(adsbygoogle = window.adsbygoogle || []).push({}); when inverted through L, models the universe with this lower bound required by quantum gravitational constraints. The initial quantum box solutions are given by:

[tex]\phi_n=\sqrt(2/L)\\sin(n \pi x/L)[/tex]

However, having inverted the scale (so L-->1/L), the now "inverse quantum box" generates permitted states, all above L, i. e. those which obey this "ultraviolet" limit to quantum gravity:

[tex]\phi_n^-^1=\sqrt(L/2)\\sin(L/n \pi x)=\sqrt(1/2P)\\sin(1/Pn \pi x)[/tex].

This new wavefunction represents an envelope that modifies other wavefunctions when considering gravitational effects. It applies the correspondence principle, using the reciprocal Planck limit in terms of probability P=1/L, to find a particle outside the Planck region. The correspondence principle is, in effect, a manifest transformation of such forbidden quantum gravitational states (those <L) inverted through P.

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# Inverse wavefunction incorporates lower Planck gravitational bound

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