Some lay explanations about gravitational lenses

The press has been very vocal about gravitational lenses lately. The discovery is worth the attention.

Gravitational waves are to gravitation what light or radio waves are to electro-magnetic forces. They are a very natural solution to the equation of Einstein that are the foundation of general relativity, the theoretical frame that describes gravitation.

The Einstein equation looks like

G_{μν }= 8ΠG T_{μν .}

The right hand side, T_{μν} , describes matter and energy location and velocities while the left hand side, G_{μν ,} is constructed from a prescription to measure distances. It is therefore natural to expect that if the matter oscillates in a proper way, like for example two bodies orbiting around one another, the prescription to measure the distances will also oscillate. These are gravitational waves. They modify the distances that we measure between objects, even if those objects don’t move.

One can visualise to some extend what this means by imagining two boats on a lake and by giving as a prescription to measure the distance between them that one measures the length of a spanned rope following the surface of the water between the two boats. Comes a wave between the two boats, the surface of the water is modified, the length of the rope changed, and the distance measured following the prescription modified, although neither boat has moved.

The difficulty in this game is that the effect is extraordinarily small. Typical effects are characterised by a number of the order of10^{-22 }. This is 0.00000000000000000000001. It is like 1 10 thousandth (1/10’000) of a second compared to the age of the Universe. This explains why it took so long to obtain this result and why the feat described February 11 by the LIGO team is so remarkable. The scientific paper describing the discovery is by a large team, it is to be found as *Abbott et al. Phys. Rev. Lett. 116, 061102.*

The discovery is a milestone in physics, it is also the first observation of an astronomical phenomena that cannot be observed in any other way. More on this later.