There are two principles of equivalence: the “weak” principle and that of Einstein.

The weak principle of equivalence

This “principle” is an experimental report, ever contradicted and with the quite practical consequences, raised with the row of unexplained principle because.

The weak Principe of equivalence says that the inertial mass and the gravific mass are equal whatever the body (it makes some acts of their proportionality, but from that one deduces that with a good choice of measuring units, one obtains their equality).

The consequence of this principle is that all the bodies subjected to the same field of Gravitation fall simultaneously when they are released simultaneously.

This report of the simultaneity of the falls was made as of Galileo. Isaac Newton by his universal Loi of the gravitation showed that was equivalent to the equality between inertial mass and gravific mass, and tried out this equality, by the means of the gravitation, using the comparison of the frequencies of beams made up of different materials.

Thereafter, of multiple experimenters tested this equality, reducing always more the possible difference between these two masses.

The principle of equivalence of Albert Einstein

The principle of equivalence of Albert Einstein is one of the basic principles at the base of the theory of the General relativity.
Einstein presents it like a interpretation principle of equivalence called weak since, i.e. the principle of equivalence of Albert Einstein gives a significance to the weak principle of equivalence .

On the basis of the assumption that there is strict equality between the heavy mass (at the origin of gravitational attraction between the bodies) and inertial mass (at the origin of resistance to the actuation of a body), it affirms that the effects (local) of a gravitational field are identical to the effects of a Accélération of the reference frame of the observer.

With this extension of the principle of relativity to include the gravitation there, locally and in the form of accelerated reference frames, Einstein takes the first step to go from the restricted Relativité to the General relativity.

The elevator of Einstein

To popularize its idea, Einstein used the image of an elevator in the astral vacuum, upwards drawn with a constant acceleration by a géant.

• If the walls are transparent, a physicist placed outside would observe that held objects then simultaneously released by a person placed inside, would be propelled at the same speed in the same direction that the elevator, would preserve their common speed because of the Principe of inertia, while being caught up with simultaneously by the ground of the elevator (of which speed increases with constant acceleration, by assumption).

• If the walls are opaque, a physicist locked up inside would see that all the objects that it releases simultaneously in the elevator fall simultaneously, whatever their masses. The physicist knowing the law of the Gravitation, and without anything to know of outside, can conclude that its elevator is motionless in a constant field of gravitation, as on the surface of the ground or of another planet.

It is to be stressed that the reasoning of the physicist locked up holds only insofar as it admits the law of gravitation, in particular the equality between the inertial mass and the gravific mass which only can justify the simultaneity of the fall of body of different masses by the force of gravitation.

It is as important to notice as if the elevator is too large, the physicist locked up can start to try out his environment to see whether this gravitation is similar to that on ground: modification with altitude, etc And in this case, it will find differences.

Of course, if the reference frame is accelerated in a different way, variable, the force observed by the physicist which is subjected there will be identifiable with a gravitation because all the objects will be subjected there same manner, but a variable gravitation: locked up in its box, it will be able to suppose to undergo the gravitation of one or more capricious planets.

By this experiment by the thought, Einstein shows that the local effects of the gravitation and a reference frame accelerated for the observer are not physically distinguishable: there is local equivalence.

Freefall and Reference frame galiléen (inertial)

A typical location for an elevator is to be in freefall in a field of gravitation, and the vacuum.

• If the walls are transparent, an external observer sees all the objects which are there, falling at the same speed, under the terms of the weak principle of equivalence, and at the same speed as the lift car.
• If the walls are opaque, an observer inside sees all the objects which surround it released of any gravitation, in weightlessness, subjected to the only law of inertia or other external forces which can be exerted on them (such electromagnetism, of pushed of the physicist or the shocks between them). The reference frame of the lift car is thus an inertial reference frame (galiléen), room and of limited time in general.

This particular case, as valid in traditional physics as in relativistic physics (insofar as the gravitation is included there), makes it possible to define reference frames galiléens auquels nobody had not thought before Einstein, and obliges to consider that all the inertial reference frames are not in translations at constant speed the ones compared to the others. It also makes it possible to generalize the valid tensorial equalities in restricted Relativité (where all the reference frames are inertial) in tensorial equalities of the General relativity.

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