# The experimental status of general relativity

It is now folklore that general relativity is well tested and that there are no experiments that disagree with the predictions. This goes back to the early days, Einstein calculated the perihelion of Mercury   accurately in 1915  and Eddington in 1919 proved that the bending of light around the Sun is in agreement with general relativity.

Since then there has been many different experiments aimed at testing different aspects of the theory. These include detailed analysis of the time delays of messages to spacecraft all the way to studies of binary pulsars.

What I was not aware of is just how accurate general relativity is.

The Eötvös Experiment

One of the founding pillars of general relativity is the weak equivalence principle. It basically says that the passive gravitational mass is the same as the active inertial mass. This idea is much older then general relativity and Newton was the first to do experiments testing this.

Eötvös used a two equal masses of different composition on a torsion balance to test this principle. More details can be found here. The Eötvös parameter is defined as

$$\eta = 2 \frac{|a_{1}-a_{2}|}{|a_{1}+ a_{2}|}$$,

which is the fractional ration of the accelerations of the two masses. If gravity couples differently to the different materials then this should show up as a non-zero value of this parameter.

Eötvös was able to get this parameter down to $$10^{-9}$$, so clearly very small.

The Eöt-Wash group at Washington using modern techniques have brought this value to $$\eta \approx 10^{-13}$$.

Local Lorentz Invariance

General relativity also requires that locally we have Lorentz invariance. The breaking of Lorentz invariance would imply some universally preferred rest frame. One way to test this is to look at the speed of light. So let us define

$$\sigma = c^{-2} -1$$.

Units have been picked here so that the “usual speed of light” is one. So in general relativity $$\sigma =0$$ locally.

Examine very carefully the energy levels of atoms and how this changes due to our orientation in the Universe one can test Lorentz invariance of the electromagnetic sector.

Such test give $$\delta \approx 10^{-22}$$.

There has been a bit of interest in examining the potential for Lorentz violating in extensions of the standard model. These tend to have motivation from quantum gravity where it is expected that local Lorentz invariance will be broken.

Other tests

Other tests, both direct and indirect have been preformed and all give good agreement with general relativity. This includes:

This is both reassuring and frustrating for theoretical physics. The lack of experimental direction on what replaces general relativity at the quantum level has, in my opinion, not helped the quest for quantum gravity. But that is another story.

For more details of the experimental tests of general relativity see [1,2].

References

I won’t give references to the original material, see the following for details:

[1] Clifford M. Will. The Confrontation between General Relativity
and Experiment. Living Rev. Relativity, 9, (2006), 3.

[2] S G Turyshev. Experimental tests of general relativity: recent progress and future directions. Phys.-Usp. 52 1, 2009.