# Why test the equivalence principle?

Let us first remember what is the equivalence principle.

The equivalence principle expresses a property which is at the basis of Einstein’s general relativity: the equivalence between acceleration and a gravitational field. More precisely, observations made in a system in acceleration (e.g. a rocket) are indistinguishable from those made in a gravitational field (e.g. on Earth). This allows to understand better the notion of mass, which is actually describing two apparently independent concepts:

• the mass of a material object characterizes how it couples to a gravitational field; for example a more massive object is submitted to a greater attraction to the Earth, a greater weight. This mass is called the gravitational mass.
• the mass of a material object characterizes its inertia, that is its resistance to changes of motion. This mass is called the inertial mass. Since acceleration corresponds to a change of velocity, hence a change in motion, it is this mass that appears in the famous law of motion: force = mass x acceleration.

The equivalence principle tells us that gravitational mass and inertial mass are identical. This is why it is at first so difficult to disentangle the notion of weight (related with the gravitational mass) from the notion of inertia (related with the notion of inertial mass).

This principle has some important consequences. Take for example a kilogram of gold and one of platinum. They resist to changes of motion in the same way: they have the same inertial mass. Hence they have the same gravitational mass and identical motions in a gravitational field; they are attracted in the same way by the Earth. This has been checked on ground to a precision of one part in 10 000 000 000 000 (in other words 10-13).

But theorists are not fully happy with the theory of Einstein. They would like to unify general relativity with the quantum theory which describes non gravitational forces. They thus have to change, even though in a subtle way, the description of the gravitational attraction. But by doing so, they often lose the precise identification between gravitational and inertial mass.

For example, let us consider string theory where the basic objects are no longer point particles but microscopic one-dimensional objects (the strings!): our good old particles are considered as grains of energy which correspond to modes of oscillation of these fundamental strings. We are used to (violin) strings emitting (sound) waves, but remember that, in the microscopic world, waves and particles are united in a single concept (the two sides of the same coin if you prefer). This is why different types of oscillations of the fundamental microscopic strings lead to different types of particles, with different energies E, hence different masses m (E=mc2).

Now in such a theory, the gravitational force between two particles/waves is understood as an oscillation, or a series of oscillations of the underlying string. It is thus not at all obvious that the gravitational force between say two protons is identical to the gravitational force between two neutrons, or between a proton and a neutron. Thus, if two material objects have the same inertial mass but different number of protons and neutrons, they may be falling differently in the gravitational field of the Earth. They would thus have different gravitational masses. This leads to a violation of the equivalence principle.

This is exactly what the Microscope mission aims at testing, gaining two orders of magnitude over the existing experiments on Earth (10-15).

### 5 Comments

• Barbara Harrison

interesting

• Mike Demitre

We are getting closer to a unified theory!

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