# Einstein and the relativity

The Newtonian universe, as imperfect as it could be, allowed a lot of progress in astronomy. It remained unchanged during more than two centuries, till the beginning of the XXth, when Einstein proposed the theory of relativity, as an answer to the dead end reached by physics.

## The special relativity

The speed of light is finite : the first one to realize this fact was Oleaus Römer in 1675, when he studied the satellites of Jupiter and their eclipses.

The undulatory characteristic of light was put in evidence in the XVIIIth century, and in 1817, Fresnel proved that it was a transverse undulatory vibration. If there is a vibration, he thought that a support was needed : it will be the aether, infinitely stiff, but offering no resistance to the movements of celestial bodies.
In 1887, Michelson and Morley showed, in a famous experience, that, if this aether was real, then the Earth had no speed with regard to it.

The successive failures of classical mechanics, and its obvious incompatibility with electromagnetism brought Einstein to the theory of special relativity , which leans on two fundamental principles :

• the laws of the physics are always the same in any inertial frame, regardless of position or velocity.
• the speed of light in vacuum is absolute and universal.

Physically, the first principle means that there is no absolute spacetime, no absolute frame of reference with respect to which position and velocity are defined. Only relative positions and velocities between objects are meaningful.

As a result of the second principle, the galilean law of addition of speeds becomes false. If a people is moving at the speed of 1 meter/second on the wagon, and if this wagon rolls at 10 m/s relatively to a fix observer, hence this observer sees the people moving at the speed of 11 m/s : it is the classical law of addition of speeds, which is only an approximation for the low speeds of the relativistic law.

In classical mechanics, if v is the speed of a moving object in a system of reference, which is moving at the speed V, hence the speed of the object expressed in a motionless system of reference becomes v' = v+V.
In special relativity, the law of addition of speeds becomes
v' = (v+V)/(1+vV/c²)

Of course, these two expressions are equivalent, if the speeds are low relatively to the speed of light.

As a consequence, the measures of time, length and energy are relative, i.e. specific for each observer.

Within the framework of specail relativity, the metric of the space-time expresses as a function of coordinates x, y, z and t like ds²=c²dt²-dx²-dy²-dz²
This metric defines a flat space-time, called a Minkowski space-time, similar to the absolute Newtonian space-time, where the metric is ds²=dx²+dy²+dz².

Hence, the distance between every couple of points located on a light cone is zero (ds=0), and the only reachable points are those which are inside the cone, because the interval ds² between two points must always be positive.

If you want an easy way to display the relativistic effects, I suggest you to visit this page where you can play with an applet. It will show you the time dilatation and length contraction at relativistic speeds.

## The general relativity

Ten years after special relativity, Einstein generalizes his principle of equivalence to all the systems of reference, whatever motion they have. Einstein puts then the principle of equivalence : acceleration and gravitation are indiscernible. It means that you can't find an experiment which could allow to decide whether your system of reference is accelerating - a rocket which takes off for exemple - or is situated in the gravity field of a mass - on the surface of Earth or any other star.

Unlike the absolute Newtonian space, this one is bound to its contents. It is not pre-existent and its geometry will come from the presence of masses. Hence, these masses will modify the behaviour of bodies and light.

The rigid Newtonian universe is so replaced by a four-dimensional Riemann space-time, which is bended by the presence of masses. Gravitation is replaced by geometric properties of space-time : a massive body bends the space-time around it.
In order to take these effects into account, we must give up the three dimensions universe of Newton and replace it with a four dimensions space-time continuum. When Newton saw a force between two bodies, Einstein only sees a bending of space-time, and a star rotating around another one can be imagined as "rolling" around the curvature created by this one.

What are the main consequences of this theory for astrophysics?

• we have already seen the first one : light rays are deviated by a massive body. They follow the trajectories corresponding to the shortest pathes ( geodesics).
• In the neighborhood of a massive body, time passes slowlier. One of the consequences is the gravitational redshift, a shifting towards low frequencies of light emitted from the surface of a massive body.
• when light rays pass near a massive body, they are delayed because they have a longer way to travel (Shapiro effect).

All these effects have been experimentaly measured.
Another experimental test, the first one that has been led, concerns the advance of the perihelion of Mercury. This planet has a very eccentric orbit, hence great variations of speed. General relativity is the only theory able to explain why its perihelion regularly advances of 43 seconds each century, once shielded the influence of other planets.