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Quote from Rovelli's book, page 19:
"In classical general relativity...there is no preferred time variable...[but] we nevertheless have a notion of spacetime for each given solution. [By contrast] in quantum theory there are no trajectories. Thus, THERE IS NO PHYSICAL SPACETIME IN QUANTUM GRAVITY..."
http://www.cpt.univ-mrs.fr/~rovelli/book.pdf
This is the most interesting book of philosophy I can remember seeing in several decades
(also a book of natural philosophy, that is to say, physics)
The online draft of Rovelli's "Quantum Gravity" to be published by Cambridge U. Press
space IS the gravitational field----things move, rotate, accelerate with reference to the gravitational field
time has no physical existence---analogous to the fact that an electron has no real trajectory: the sum over possible trajectories gives the transition amplitude between here and there
time is a property of a classical solution of the GR field----a "trajectory" of geometrical states----but this is only a classical (non-quantum) approximations
there are only transition amplitudes between states of the 3D geometry----development along a classical trajectory does not correspond to physical reality
clocks (whether mechanical, electronic, astronomical) are real physical systems that we distinguish from other systems by convention---they evolve according to sum-over-paths transition amplitudes along with everything else---thus observed states of the world can include readings on various clocks but there is no physical time axis
"In classical general relativity...there is no preferred time variable...[but] we nevertheless have a notion of spacetime for each given solution. [By contrast] in quantum theory there are no trajectories. Thus, THERE IS NO PHYSICAL SPACETIME IN QUANTUM GRAVITY..."
http://www.cpt.univ-mrs.fr/~rovelli/book.pdf
This is the most interesting book of philosophy I can remember seeing in several decades
(also a book of natural philosophy, that is to say, physics)
The online draft of Rovelli's "Quantum Gravity" to be published by Cambridge U. Press
space IS the gravitational field----things move, rotate, accelerate with reference to the gravitational field
time has no physical existence---analogous to the fact that an electron has no real trajectory: the sum over possible trajectories gives the transition amplitude between here and there
time is a property of a classical solution of the GR field----a "trajectory" of geometrical states----but this is only a classical (non-quantum) approximations
there are only transition amplitudes between states of the 3D geometry----development along a classical trajectory does not correspond to physical reality
clocks (whether mechanical, electronic, astronomical) are real physical systems that we distinguish from other systems by convention---they evolve according to sum-over-paths transition amplitudes along with everything else---thus observed states of the world can include readings on various clocks but there is no physical time axis