# Evidence for quantum gravity from gravitational waves

The rumor spreads that physicists will make their big gravitational wave announcement this thursday.

I am far from being an experimentalist, but I want to know if there is any chance that the mentioned observations will reveal any experimental evidence for quantum gravity.

Personally, I feel like this is merely impossible as gravitational waves should propagate in agreement with classical General Relativity. But I might very well not see pitfalls if there are any.

UPDATE: by "evidence for quantum gravity" I mean experimental results which don't agree with predictions of General Relativity or its classical generalizations. They might be coming from string theory or loop gravity or from a completely different approach which we haven't discovered yet. I want to understand what are the chances that new physics will show up during the upcoming gravitational wave observations.

Also, I expect gravitational waves to be in a highly coherent state, thus making the individual gravitons unobservable. Is this true?

• Can you please elaborate on what do you mean by evidence to "Quantum Gravity"? There are multiple candidate theories for Quantum gravity (such as loop quantum gravity, string theory etc.), what exactly are you pointing at? Evidence for what? Feb 10, 2016 at 14:34
• If anyone is interested in the actual tests of GR that were conducted using GW150914, they are in public LIGO report P1500213 -- dcc.ligo.org/cgi-bin/DocDB/… Feb 12, 2016 at 15:47

At this blog there are extensive discussions about an anouncement of gravitational waves tomorrow, Thursday the 11th.

by "evidence for quantum gravity" I mean experimental results which don't agree with predictions of General Relativity or its classical generalizations.

Let us clear up some frameworks here. General Relativity is a classical theory, not quantized, and its application is important where there are large gravitational masses , deforming the flat four dimensional space of special relativity, or where great accuracy is needed. It has been validated in astrophysical observations many times, and is even necessary for the GPS system to run accurately.

They might be coming from string theory or loop gravity or from a completely different approach which we haven't discovered yet.

String theory is a theory within the framework of quantum mechanics, and it allows for quantization of gravity. The General Relativity framework emerges naturally when the dimensions are right from the string theoretical framework.

I want to understand what are the chances that new physics will show up during the upcoming gravitational wave observations.

The probability is very small. The observations are within the classical General Relativity predictions . They will validate the existence of classical gravitational waves. Classical gravitational waves, know nothing about gravitons, like classical electromagnetic waves know nothing about photons.

In the link at the top, there is a link where possible new physics might be found with LIGO like detectors, but not with the existing observation, as far as I know.

Gravitons exist in the effective Quantum Field theories for gravity that are being used in cosmological models , as the Big Bang model. And in string theories, which can quantize gravity. LIGO is studying the classical gravitational wave.

Also, I expect gravitational waves to be in a highly coherent state, thus making the individual gravitons unobservable. Is this true?

I do not know what the coherence has to do with whether gravitational waves can be broken down into individual gravitons, in the way electromagnetic waves can be broken down into photons. LIGO is not designed for single graviton detection, as the coupling constant of a graviton is so small that it will be undetectable

There are gravitational wave observations that can test General Relativity (GR), looking for disagreement with classical predictions. There are some particular disagreements that are motivated by Loop Quantum Gravity and/or string theory, and there may also be generic deviations from classical GR that don't point to a particular theory.

Classical GR predicts gravitational waves (GW) propagate at the speed of light and have no dispersion. It also predicts no monopolar or dipolar radiation. Another way of saying this is that there is no scalar or vector gravitational radiation, only tensor gravitational radiation.

There are specific observations that could test these predictions for example Larson and Hiscock proposed using binary white dwarfs to test the speed of GWs. This puts effective bounds on the mass of a graviton (predicted massless). This observation requires low frequency GWs that LIGO cannot observe. A space based detector like eLISA would be required.

There are several alternative theories of gravity that are extensions of GR. For example Brans-Dicke gravity is a "scalar-tensor" theory. There are also "scalar-vector-tensor" theories. These would drastically modify the form of gravitational waves. So much so, that there are limits on these theories based on relatively weak-field binary pulsar observations.

GWs also encode information about the trajectories of the particles producing them. There is plenty of active research looking for how to detect generic deviations from GR in the motion of GW producing particles, for example LIGO's TIGER project and the Parameterized Post-Einsteinian framework. These methods would require a very, very loud GW signal or many GW detections to work effectively, making these sorts of tests longterm goals of GW astronomy.

Currently there are no observed deviations from classical GR. Any observed deviation would need to be addressed in the next generation of gravitational theory. While these methods don't specifically test Quantum Gravity, they may motivate advances in theory.

Formula for the metric tensor of the Schwarzschild solution $$g_{00}=-1+r_g/r:g_{rr}=\frac{1}{1-r_g/r},g_{\theta \theta}=r^2,g_{\phi \phi}=r^2sin^2\theta$$ Formula for the changing part of the pseudo-tensor energy density for the non-relativistic Schwarzschild solution $$\Delta t_{00}=\frac{11}{2r_1^2}+\frac{15}{8}(\frac{dln(1-r_{g1}/r_1)}{dr_1})^2 +\frac{15}{8} cot^2(\theta)/(1-r_{g1}/r_1)$$ Where $$r_k^2=r_{g_k}^2+d^2+x^2,k=1,2$$, x - middle distance between black holes With a radius greater than the gravitational minimum energy density is achieved under the condition $$\theta=\pi/2$$. Energy density is equal to $$\Delta t_{00}^{\pi}=\frac{11}{2r_1^2}+\frac{11}{2r_2^2}+ \frac{15}{8} [(\frac{r_{g1}/r_1)}{r_1-r_{g1}})^2+(\frac{r_{g2}/r_2)}{r_2-r_{g2}})^2]$$ Half the distance between black holes is $$x=V_0(t_0-t_1-t),t \in [0,t_0-t_1]$$, $$t_0$$ - signal duration, $$t_1$$- signal duration after crossing the gravitational radius After crossing the gravitational radius, the minimum energy corresponds to the angle $$\theta=\pi \sqrt{\frac{\sqrt{r_{g1}^2+d^2}-\sqrt{r_{g2}^2+d^2}}{\sqrt{r_{g1}^2+d^2}+\sqrt{r_{g2}^2+d^2}}}$$ the emitted signal corresponds to the energy difference $$\Delta t_{00}^0=\frac{15}{8} [1/(1-\sqrt{r_{g1}^2+d^2}/r)- 1/(1-\sqrt{r_{g2}^2+d^2}/r)]= \frac{15}{8}\frac{\sqrt{r_{g1}^2+d^2}-\sqrt{r_{g2}^2+d^2}}{[r-(\sqrt{r_{g1}^2+d^2}+\sqrt{r_{g2}^2+d^2})/2]^2}/sin^2(\theta)$$ This formula, when the masses of black holes coincide, should give a finite non-zero radiation energy. For different masses of black holes, the passage to the limit is not needed. Moreover, the limit passage is realized according to the rule of L'Hôpital provided $$r_{g1} \to r_{g2}$$$$\Delta t_{00}^0= \frac{15}{8\pi^2} \frac{\sqrt{r_{g1}^2+d^2}+\sqrt{r_{g2}^2+d^2}}{[r-(\sqrt{r_{g1}^2+d^2}+\sqrt{r_{g2}^2+d^2})/2]^2}$$ $$r=V_0(t_0-t_1-t);t \in [t_0-t_1,t_0],r<(r_{g1}+r_{g2})/2$$ The radiated mass is determined from the equality $$\Delta t_{00}^0=\frac{11}{2r^2}+\frac{15}{8}(\frac{dln(1-r_{g}/r)}{dr})^2, r_g=2G\Delta m/c^2$$ The calculated energy density is proportional to the signal envelope, from where the gravitational radii can be determined to within a factor using the least squares method. This factor is determined from the condition $$\omega_{\pi}=\frac{c}{r_{g1}}+\frac{c}{r_{g2}}$$ before the intersection the gravitational radius and equals after the intersection $$\omega_{0}=\frac{2c}{r_{g1}+r_{g2}}$$ of the gravitational radius where $$\omega_{\pi},\omega_{0}$$ is the frequency of the received signal before the intersection of the gravitational radius and after the intersection of the gravitational radius