I Building Quantum GR out of quantum rulers and quantum clocks

cuallito
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Hi, has anyone tried to build "quantum GR", using the expectation value of |Psi(x)> as a "quantum ruler" and |Psi(t)> as a "quantum clock" to build up the idea of a "quantum metric"?
 
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What is |Psi(t)>? How do you calculate it? Can you show an example?
 
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