|:F|A2 d dcB|A2 F D2 E|F2 D A2 F|G2 E E2 F|
G2 e edc|BAG E2 F|G2 E BAG|F2 D D2:|
e|f2 d dAF|f2 d d2 e|fed cBA|G2 E E2 f|
g2 e ecA|g2 e e2 f|g>fe dcB|AB/A/G FGA|
f2 d d2 e|fd/d/d d2 e|fed cBA|G2 E E3|
gbg f/g/af|ege d2 A|cc/B/A GFE|F2 D- D2||
Here is a simple explanation
A quasiregular spacetime is a spacetime with a classical quasiregular singularity, the mildest form of true singularity. The definition of Horowitz and Marolf, for a quantum-mechanically singular spacetime is one in which the spatial-derivative operator in the Klein-Gordon equation for a massive scalar field is not essentially self-adjoint. In such a quantum-mechanically singular spacetime, the time evolution of a quantum test particle is not uniquely determined. Horowitz and Marolf showed that a two-dimensional spacetime with a classical conical singularity (i.e., a two-dimensional quasiregular singularity) is also quantum-mechanically singular. Here we show that an idealized cosmic string spacetime, a four-dimensional spacetime with conical singularity is, as expected, quantum-mechanically singular. We consider also an unusual Tod spacetime, which is geodesically complete but nevertheless classically singular, since it contains an incomplete curve of bounded acceleration. The Tod spacetime is therefore an even milder singular spacetime classically than a conical spacetime, because it is geodesically complete. We show that the Tod spacetime is nevertheless still quantum-mechanically singular, since the appropriate operator is not essentially self-adjoint.
Yeah, that’s what I was trying to say. Thanks old friend… 😏
The quantum singularity seems to be placed somewhere in Galicia - maybe at cabo fisterra, the end of the world?
~ or the beginning, or both in the one moment?
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