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## Main Question or Discussion Point

Hello all,

I have been thinking about ways that classical mechanics can arise in the classical limit of QM, and I'm wondering how this might occur in quantum gravity. In particular: in the Feynman path integral technique, we start with what Feynman calls the "democracy of paths," according to which all paths, even non-classical ones, are attributed equal amplitude (equal absolute value, that is). In the classical limit, it is easily shown that the classical path of least action is "more probable" (speaking loosely) than all the rest, and in this way, Hamilton's action principle, and thus Newtonian mechanics, may be understood to be valid in the classical limit of QM. I state this a little more carefully in the thread:

https://www.physicsforums.com/showthread.php?t=112257

So here's what I'm wondering. Within any of the various quantum gravity programmes, is any attempt made to accomplish a similar derivation that yields, not (merely) Newtonian mechanics, but (more generally) GR? Here's what I'm envisioning: instead of a "democracy of paths," we have a "democracy of spacetimes" (DOS). Let me complete the analogy: in the FPI, we start with "all possible paths," which includes non-classical paths. In the "democracy of spacetimes," we start with "all possible spacetimes," which means we include spacetimes that do not obey Einstein's equation. In the FPI, we attribute an amplitude to each path, each with equivalent absolute value. In "DOS," we figure some way to assign probabilities -- I suppose there are various ways to do this. In the FPI, the classical paths turn out to be "more probable" than non classical paths. In DOS, we hope to show that classical spacetimes (ie, those that obey Einstein's equation) are "more probable" than non-classical spacetimes.

So I'm wondering: does LQG or any other theory of quantum gravity fit the above description?

David the Amateur Physicist

I have been thinking about ways that classical mechanics can arise in the classical limit of QM, and I'm wondering how this might occur in quantum gravity. In particular: in the Feynman path integral technique, we start with what Feynman calls the "democracy of paths," according to which all paths, even non-classical ones, are attributed equal amplitude (equal absolute value, that is). In the classical limit, it is easily shown that the classical path of least action is "more probable" (speaking loosely) than all the rest, and in this way, Hamilton's action principle, and thus Newtonian mechanics, may be understood to be valid in the classical limit of QM. I state this a little more carefully in the thread:

https://www.physicsforums.com/showthread.php?t=112257

So here's what I'm wondering. Within any of the various quantum gravity programmes, is any attempt made to accomplish a similar derivation that yields, not (merely) Newtonian mechanics, but (more generally) GR? Here's what I'm envisioning: instead of a "democracy of paths," we have a "democracy of spacetimes" (DOS). Let me complete the analogy: in the FPI, we start with "all possible paths," which includes non-classical paths. In the "democracy of spacetimes," we start with "all possible spacetimes," which means we include spacetimes that do not obey Einstein's equation. In the FPI, we attribute an amplitude to each path, each with equivalent absolute value. In "DOS," we figure some way to assign probabilities -- I suppose there are various ways to do this. In the FPI, the classical paths turn out to be "more probable" than non classical paths. In DOS, we hope to show that classical spacetimes (ie, those that obey Einstein's equation) are "more probable" than non-classical spacetimes.

So I'm wondering: does LQG or any other theory of quantum gravity fit the above description?

David the Amateur Physicist