I read that LQG can (with the spinfoam formalism) give the Einstein equation when $h$ tends to zero. See the metrics created by an object in the sky. The equations of the geodesics contain a parameter (the mass) with positive sign. Another sign would make planets repel. Is there also in LQG a same parameter that discard repelling?
$\begingroup$
$\endgroup$
1
-
$\begingroup$ Related post by OP: physics.stackexchange.com/q/605922/2451 $\endgroup$– Qmechanic ♦Commented Jan 10, 2021 at 10:54
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
8
Asking this is like asking how the Standard Model explains why friction is exothermic. There’s a complex chain of approximations involved in both cases.
LQG (at least it’s spinfoam formulation) reduces to General Relativity in the classical limit. General Relativity reduces to Newton’s gravity in the non-relativistic weak field approximation. Newton’s gravity is an attractive force.
answered May 31, 2021 at 11:50
-
$\begingroup$ Where can I find a derivation of general relativity from spin foams? $\endgroup$ Commented May 31, 2021 at 13:38
-
$\begingroup$ @MitchellPorter Rovelli explains it in a lot of detail in his “Covariant LQG” textbook $\endgroup$ Commented May 31, 2021 at 13:39
-
$\begingroup$ Does it boil down to equation 8.109 in cpt.univ-mrs.fr/~rovelli/IntroductionLQG.pdf ? ... Is there actually an argument somewhere, that these configurations dominate the path integral? $\endgroup$ Commented May 31, 2021 at 14:49
-
$\begingroup$ @MitchellPorter your link doesn’t open for me unfortunately. The whole chapter 8 (called “classical limit”) is dedicated to this computation, it is an extensive computation that uses the stationary phase approximation to evaluate approximately the LQG spinfoam amplitude. The end result gives you the Regge action, which is equal to the Einstein-Hilbert action evaluated for a 4-simplex space time (this is because we chose to evaluate the amplitude on a 4-simplex space time to make the calculation simpler). The same calculation can be done for more complex space times. $\endgroup$ Commented May 31, 2021 at 16:06
-
$\begingroup$ @MitchellPorter ah I opened the link finally. Yeah, that's the mathematical form of the claim "GR is the classical limit of spinfoam LQG". There is actually an argument (actually, better – a computation) that this formula is correct. A special case for the 4-simplex space-time is described earlier in chapter 8 (see sections 8.1, 8.2, 8.3), then there are some words about generalizing this to arbitrary space-times (Muxin Han has obtained a lot of impressive results there essentially confirming 8.109 numerically, I'm not sure whether it was also derived analytically, but I'm sure it is possible) $\endgroup$ Commented May 31, 2021 at 16:25