Equivalence principle

The equivalence principle goes back to considerations of Galileo Galilei (1636 /38). It states that heavy and sluggish mass of a particle are equivalent in the sense that all bodies fall regardless of their other characteristics such as chemical composition, size, shape and mass in vacuum in the absence of other forces in the same way. With the same initial location and with the same initial speed all body through the same case curve. As an extension of this weak equivalence principle, some authors describe (including Einstein himself ) the so-called strong equivalence principle of general relativity. This says that no gravitation fields are detectable in a freely falling reference system on small distance and time scales.

The equivalence of inertial mass and gravitational mass is formulated in Isaac Newton's Philosophiae Naturalis Principia Mathematica ( 1687 ), but remains unexplained in Newton's mechanics.

Equivalence of inertial and gravitational mass

As an inert mass, the mass is referred to Newton's second axiom:

Newton's first axiom expresses that particles are lazy: They persist in their state as long as no force on it works. The second axiom quantifies the inertia, the more inertial mass has a particle, the greater must be the power to it to speed up to a certain value. The inertial mass is additive: Putting a body composed of elements, then add their inertial masses, if one can neglect the binding energies of the constituents.

The gravitational mass is a measure of the gravitational attraction of two particles. In classical mechanics, the gravitational force is described by Newton's law of gravitation. A body of heavy mass attracts another body of gravitational mass in the distance with a force from the amount

Of. Just as the inertial mass of the heavy mass is additive: Putting a body composed of elements, then add their heavy masses, if one can neglect the binding energies.

Both mass types are a priori independent of each other, such as the inertial mass of a particle and its electric charge. But all previously conducted experiments confirm that the gravitational mass of a body corresponds to its inertial mass. Inertial and gravitational mass are equivalent. This experimental result is called the weak equivalence principle.

The weak equivalence principle is manifested in Galileo's case law that all bodies fall equally fast. In the Earth's gravity applies to a body of heavy mass approximately

As a law of gravity, with the acceleration of gravity. Neglecting frictional forces and the buoyancy, the result is the acceleration of the body by the second axiom

The equivalence principle leads now to

All bodies fall equally ( in vacuum) in the earth's gravitational field, regardless of their mass. If the weak equivalence principle is violated, then this law would be invalid. This can be verified experimentally.

Since the law of inertia and Newton's law of gravitation based on independent physical findings and axioms, in classical mechanics the weak equivalence principle remains unexplained.

Experimental verification

First attempts to inertial and gravitational mass already made ​​Isaac Newton (1689 ) and Friedrich Wilhelm Bessel (1832 ) in the form of pendulum experiments. Further investigations were in 1890 and 1909 by the Hungarian physicist Loránd Eötvös performed in the Eotvos experiment, named after him, which was repeated in 1964 by Roll, Krotkov & thickness in Princeton and in 1972 by Braginsky & Panov in Moscow in an improved form. Quantitatively, those measurements for equivalence of inertial and gravitational mass by the so-called Eötvös ratio

Described, represent where and are the measured accelerations of two different test body. While the classic pendulum experiments of Newton and Bessel reached an upper limit of the Torsionspendelversuche of Eötvös (1909 ) improved on this limit. Through experiments with laser reflectors, which had been erected in the Apollo missions to the Moon ( Lunar Laser Ranging ), Irwin Shapiro in 1976 could prove the validity of the equivalence principle with an accuracy of 10-12. Eric G. Adelberger et al. of the Eötwash group published in 1999 a work that confirms this principle with an accuracy of 10-13.

Sharper upper limits can be obtained by satellite-based experiments such as the STEP Mission (Satellite Test of the Equivalence Principle ), achieve Gravity Probe A or Microscope. Here, for example, the relative acceleration of the orbiting, freely falling test bodies measured with different chemical composition, which should lead to an expected accuracy of ( Microscope ) and ( STEP). Here, the formulation of the equivalence principle of general relativity theory (ART) is also more direct than in previous experiments, checked.

Equivalence principle in general relativity theory

Result of the weak equivalence principle is that an observer in a closed laboratory, without information from the outside, from the mechanical behavior of objects in the laboratory can not read whether he or weightlessness in free fall is located (See adjacent figure). This is equivalent to the statement that gravitational forces are equivalent to inertial forces. Therefore, gravitational forces can be eliminated by changing to an accelerated frame of reference.

This principle was generalized by Einstein in 1907:

An equivalent but mathematized and expressed with the terms of the general theory of relativity formulation of the strong equivalence principle is:

Quantitatively, this can be represented by Riemannian normal coordinates, which show that the deviations from the flat metric are proportional to the curvature tensor.

It should be noted, however, that this principle is only locally:

• Thus, a "down" (closer to the Gravizentrum ) object located is attracted more strongly than a more "up" befindliches. Is the free-falling space in the vertical direction is large enough, the observer will therefore find that objects that are above, from those who are further down, remove.
• Conversely, will differ with sufficient horizontal extent of the space, the direction of attraction to two horizontally away from each other noticeably objects, since they both are accelerated towards the center of gravity. Therefore, the free-falling observer will note that far apart preferred body move towards each other. An extensive body is thus experience a force that pulls apart it in one direction and compresses in the directions perpendicular thereto.

Since the electric field of charged body also has a large extent, there is a controversy about whether the principle of equivalence for such particles is true ..

The weak equivalence principle can not be explained by classical mechanics. In contrast, the ART explains the strong equivalence principle: test particles pass through, regardless of their composition or other characteristics the same case curve when initially match their location and speed. In the Newtonian sense, therefore, are sluggish and passive heavy masses, between which one can not distinguish in the ART, equivalent. The fact that all test particles through the same case curves arises in the ART from the fact that the Lagrangian of the ART does not change when changing the coordinates. The equivalence principle is explained by a symmetry.

The observation of a violation of the equivalence principle would, therefore, show that the ART would be of limited quality. With today's measurement accuracy you can not observe any deviations from the principle of equivalence.

In addition, the ART is considered an active principle of equivalence, namely that produce different matter or radiation have the same gravity, if only their energy - momentum tensor coincide.