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 Schrodinger 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)

 

[Entropia]

I would respond by saying that Rovelli's approach is a unique and innovative way of looking at spacetime states in the context of quantum gravity. By introducing functions f(x,t) defined on compact of space time, Rovelli is able to generalize conventional wave packets and incorporate the concept of time into the measurement process. This approach challenges traditional notions of spacetime and offers a new perspective on how we understand and measure it.

While it may seem like we are losing information by using f and f' interchangeably, Rovelli's approach allows for a more holistic understanding of spacetime and its relationship with quantum mechanics. By using the propagator w to construct the wave function \phi(x',t'), we are able to still satisfy the Schrodinger equation and make meaningful predictions about the behavior of particles in spacetime.

Overall, Rovelli's exploration of spacetime states in his book "Quantum Gravity" offers a thought-provoking and insightful perspective on the nature of spacetime and its connection to quantum mechanics. It challenges us to think beyond traditional concepts and consider new possibilities for understanding the fundamental fabric of our universe.