Spacetime states in Rovelli's book Quantum Gravity

[naima]

spacetime states in Rovelli's book "Quantum Gravity"

happy new year everybody,

I am reading "quantum gravity" of Rovelli.
He introduces functions f(x,t) defined on compact of space time that are zero outside.
They correspond to the time and space needed to a measurement.
page 168: they generalize conventional wave packets for which $$f(x,t) = f(x) \delta(t)$$ which are associated to instantaneous measurements.
There is no equation for them
He constructs the usual wave fonction $$\phi(x',t') = \int dx dt w(x',t',x,t) f(x,t)$$
Where w is the propagator. This wave function satisfies the Schrödinger equation.
We lose the information we had with f!
He says f and f' are equivalent iff they give the same $$\phi$$
Ok but why have we not to use the information in f?

 

[naima]

I found this: http://arxiv.org/abs/gr-qc/0111016"
It seems to be a new formalism building classical Quantum Mechanics upon "test functions" (the spacetime states)