# Maybe there is no grand unified theory?

by Warp
Tags: grand, theory, unified
 P: 289 Einstein's equation $R_{\mu \nu} - {1 \over 2} g_{\mu \nu} R = T_{\mu \nu}$ tells us how geometry is coupled to matter. Since matter is in a quantum superposition, isnt geometry as well?
 P: 718 Whom is your question directed to, julian? That is in fact one the points of tension between QM and GR. The curvature tensor is purely classical and we don't have a well-defined notion for a 'superposition of curvature'. However, QM says it should be coupled to something that is in a superposition. Hence, one of the incompatibilities between QM and GR is the question of what the gravitational field looks like for a particle small enough to have quantum effects dominate.
P: 1,498
 Quote by julian Einstein's equation $R_{\mu \nu} - {1 \over 2} g_{\mu \nu} R = T_{\mu \nu}$ tells us how geometry is coupled to matter. Since matter is in a quantum superposition, isnt geometry as well?
This is the motivation behind so-called semi-classical treatments of gravitational phenomena, in which the stress-energy tensor is replaced by its quantum expectation value, $\langle T_{\mu \nu} \rangle$, but the geometric side of the Einstein Equations remain classical. This approach, while only approximating the full quantum theory of gravitation, is quite powerful. Hawking used it to discover that black holes radiate, and it is central to the derivation of the temperature anisotropies in the CMB.
 P: 289 The origin question was can GR and QM be independent theories...and I'm saying they are incompatible.
P: 289
 Quote by bapowell This is the motivation behind so-called semi-classical treatments of gravitational phenomena, in which the stress-energy tensor is replaced by its quantum expectation value, $\langle T_{\mu \nu} \rangle$, but the geometric side of the Einstein Equations remain classical. This approach, while only approximating the full quantum theory of gravitation, is quite powerful. Hawking used it to discover that black holes radiate, and it is central to the derivation of the temperature anisotropies in the CMB.
Really the right hand side is an operator. Attempts are made to replace the right hand side by an expectation value but an iterative procedure must be implemented to define the expectation values. It has been shown that the iteration does not converge in general, whence we must quantise the gravitational field...see p.g. 5-6 of Thiemann's book.
P: 1,498
 Quote by julian Attempts are made to replace the right hand side by an expectation value but an iterative procedure must be implemented to calculate expectation values. It has been shown that the iteration does not coverge, whence we must quantise the gravitational field...see p.g. 5-6 of Thiemann's book.
Of course. Hence how I said that this approach approximates the full quantum theory of gravititation (but I'm unclear on the non-convergence issue. I'm not an expert on stress-tensor renormalization by any means, but I was under the impression that there were finite representations of $\langle T_{\mu \nu}\rangle$. In other words, aren't those dangerous UV modes Thiemann mentions integrated out?). Saying that GR and QM are incompatible isn't new -- this was recognized long ago, and forms the basis of the OP's question. It seems you already know the answer to the question you asked.
 P: 289 People talk about singularities and how GR and QM must merge in certain circumstances. But if you take QM to apply at all levels (which I do!) then they are always incompatible.
 P: 289 Hello Bapowell The iteration is unstable in general. It was Robert Wald and Flanagan [gr-qc/960252] who showed this. "In other words, aren't those dangerous UV modes Thiemann mentions integrated out?" I'm not sure how to answer it, I'm not an expert either. But what I do know is that Thiemann shows in his book that a canonical quantization of GR (with full backreaction of matter on the quantum gravitational field) is finite.
 Sci Advisor P: 1,498 Thanks for the reference julian. I'll have a look.
 P: 289 Hi bapowell I think people take they view that quantum mechanics stops at some length scale, beyond which matter is classical, and then put it into Einstein's equations. I'm of the opinion that there is no artificial boundary between classical and quantum...
PF Gold
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 Quote by julian Hi bapowell I think people take they view that quantum mechanics stops at some length scale, beyond which matter is classical, and then put it into Einstein's equations. I'm of the opinion that there is no artificial boundary between classical and quantum...
That may be (and I agree), but as a practical matter, there is enormous range of validity to the limits of measurement for Newtonian mechanics, Maxwell's equations, and GR. As a practical matter, one must try to understand the boundaries of when classical theories are good enough, unless you want to waste endless effort calculating trivial results.
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 Quote by julian The origin question was can GR and QM be independent theories...and I'm saying they are incompatible.
Here is a discussion of GR as a quantum theory.

http://arxiv.org/abs/1209.3511
 P: 505 So a Grand Unified Theory is one that includes all the Standard Model without including gravity, and a Theory of Everything one that also includes gravity. I don't think that I want to split hairs over this issue.
P: 1,498
 Quote by lpetrich So a Grand Unified Theory is one that includes all the Standard Model without including gravity, and a Theory of Everything one that also includes gravity.
Traditionally, yes, that's the correct distinction. GUTs are meant to unify the strong, weak, and electromagnetic forces only.
 P: 505 As to Standard-Model particles, there are some interesting regularities in their gauge interactions. I'll concern myself with the unbroken SM here, since that is what we must account for. Quantum numbers: (QCD multiplicity, weak-isospin multiplicity, weak hypercharge) The gauge particles are all in the adjoint representations of their gauge-symmetry groups, so that does not really tell us very much. QCD: gluon: (8,1,0) WIS: W: (1,3,0) WHC: B: (1,1,0) The Higgs particle is a single doublet: (1,2,-1/2) The left-handed and right-handed elementary fermions: Quark: (3,2,1/6) - (3*,2,-1/6) Up: (3*,1,-2/3) - (3,1,2/3) Down: (3*,1,1/3) - (3,1,-1/3) Lepton: (1,2,-1/2) - (1,2,1/2) Neutrino: (1,1,0) - (1,1,0) Electron: (1,1,1) - (1,1,-1) If you are starting to suspect some patterns, you are not alone. In fact, there is an interrelationship that I rediscovered; I don't know who originally discovered it. Weak isospin works like 3D angular momentum, with overall quantum number WIS and multiplicity 2*WIS + 1. There is a "spin parity" that is conserved in rep products. Integer spins have parity 0, half-odd spins parity 1, and they add modulo 2. QCD has a similar quantum number, "triality". It's more complicated to calculate, so I'll give its values for the reps mentioned here: 1 (scalar) -- 0 8 (adjoint) -- 0 3 (fundamental) -- 1 3* (fund. conjugate) -- 2 Trialities add modulo 3. With QCD triality and WIS parity: Quark: (1,1,1/6) - (2,1,-1/6) Up: (2,0,-2/3) - (1,0,2/3) Down: (2,0,1/3) - (1,0,-1/3) Lepton: (0,1,-1/2) - (0,1,1/2) Neutrino: (0,0,0) - (0,0,0) Electron: (0,0,1) - (0,0,-1) Now to the weak hypercharge. After some experimenting, one finds a simple formula: WHC = (integer) + (1/2)*(WIS parity) - (1/3)*(QCD triality) One can use (WIS) instead of (1/2)*(WIS parity), and it will work just as well. One can get this formula from some GUT's, like Georgi-Glashow.
 P: 275 OP, the reason it should be related is very simple. EFE simply tells how the geometry must be curved by the influence of mass/stress/energy. It doesn't show how the mass is connected to geometry... which occurs in very small scale. So without knowing how mass is connected to geometry. It's just like believing in Magic like telling children about TV getting images and not explaining how.. but only that pushing channel and volume buttons can change the images (like EFE).
 P: 505 It isn't as magical as it might seem when one considers the Lagrangian: L = R/(16*pi*GN) + L(nongravitational) The first term is the Einstein-Hilbert term. Doing a variation by the metric gives Einstein's field equation G = 8*pi*GN*T. That aside, there isn't much that suggests a connection between gravity and everything else that's known, no readily-apparent pattern that the graviton fits into alongside some other elementary particles.

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