why quantum gravity doesnot exist?

I am not an astrophysicist and not its student.All my knowledge about astronomy comes from you tube videos and discovery channel.From them i knew that to solve the mysteries of black hole both relativity and quantum theories should be combined as quantum gravity.But it does not exist.What is the problem in quantum gravity concept?

• Possibly better for Physics because there might be related questions there. But I will say that only a theory of quantum gravity does not exist. – HDE 226868 Oct 8 '14 at 14:59

I'm not sure what you mean by saying that quantum gravity "doesn't exist". But because this is the Astronomy SE, I will interpret your question as primarily asking why astronomy hasn't found evidence of quantum gravity. This is a reasonable question; after all, nineteenth-century astronomers have found evidence of funny business in the perihelion precession of Mercury, which in the twentieth century was understood as the relativistic corrections to the Newtonian orbits. Then astronomy one-upped that and found more evidence for general relativity.

So why not now? Because gravity is weak. Very weak. Weakness per se isn't a big problem theoretically; it makes it possible to calculate quantum gravity corrections when they aren't too large, which can be interpreted as a running Newton's constant: $$G(r) = G\left[1 - \frac{167}{30\pi}\frac{G\hbar}{r^2c^2} + \ldots\right]\text{.}$$ For example, for the Sun's gravitational field near the Sun's surface (mass $M_\odot\sim 2\times 10^{30}\,\mathrm{kg}$, radius $R_\odot\sim 7\times 10^8\,\mathrm{m}$), the relativistic corrections are of order $GM_\odot/rc^2\sim 10^{-6}$, a few parts per million, while the quantum gravity corrections are on the order of $G\hbar/r^2c^3\sim 10^{-88}$, which is so much smaller as to be completely hopeless.

Making the Sun a black hole would not improve things by much, since in that case $r = 2GM_\odot/c^2$ means while the relativistic corrections become appreciable, the quantum gravity corrections are on the order of $10^{-76}$. Note that larger black holes are actually worse, which is sensible because large-scale quantum gravity must agree with general relativity.

An interesting overview by Cliff P. Burgess can be found Living Rev. Relativity 7 (2004) 5, here.

Quantum gravity could be the reason protons overcome the coulomb force and bond at the nucleus of an atom (strong force). If you extrapolate the mass energy of the plank units that fill up the volume of the proton nucleus it could satisfy the Schwarzschild condition, which is indeed, relatively quite a bit of gravity.

• (Using 1 standard deviation of the 2012 measurement of the proton charge radius) – Dave Oct 31 '14 at 18:04
• Well, the reason protons stay together is the strong nuclear force. – HDE 226868 Oct 31 '14 at 18:14
• I'm saying the strong force can be explained by quantum gravity: sciencedomain.org/… – Dave Oct 31 '14 at 18:15
• Where does it say that in the PDF? I skimmed it, and I don't think that's the conclusion the author reached. – HDE 226868 Oct 31 '14 at 18:18
• I've heard the author explain the applications of his findings since then. Also note that this math uses the 2010 CODATA and in 2012 an even smaller charger radius was measured which led to several science magazines stating there is a problem in the standard model with the new more accurate size measurement of the proton being much smaller than the standard model's proton size. – Dave Oct 31 '14 at 18:38