Equivalence principle - Definition and Overview

Einstein's principle of equivalence states that the (local) effects of a gravitational field are identical in all respects to the effect of uniform acceleration. It is a central principle in the theory of general relativity.

This version subsumes and explains the more limited version, which is the equivalence of gravitational and inertial mass. The following measurements attempted to detect a difference between gravitational and inertial mass:

This principle, enunciated by Albert Einstein, 1907 as the equivalence of gravitational and inertial mass, is a central tenet of his theory of general relativity.

Some immediate consequences of this are

• that light rays will appear bent in a gravitational field. The Einstein field equation predicts, for example, that a light ray will deflect toward the sun by 1.75 arc-seconds.
• and that time will move slower in a gravitational well.

Reinterpretation of Gravity

In newtonian dynamics motion has the property: 'An object in motion will move in a straight line. A force will make it deviate from straight line motion. In relativistic dynamics motion has the property: 'An object in motion will move along the geodesic. A force will make it deviate from moving along the geodesic'.

In relativistic dynamics, the geodesic is somewhat analogous to the shortest distance between two points. It can be shown that the geodesic is a mathematical optimum, it is the trajectory with the least possible time dilation.

The shape of the geodesic is determined by two factors: the space-time curvature of the volume of space the moving object is in, and the relative velocity of the object with respect to the gravitating mass that is curving space-time. Example: if two cannons are fired, one at an angle of 30 degrees to the horizon, and the other at 60 degrees to the horizon, then the two cannonballs will travel along different geodesics because their velocities have a dissimilar angle with respect to the direction of the space-time curvature they are interacting with. Another example: different velocities in similar space-time curvature gives different geodesics.

Near a gravitating mass, like planet Earth, the curvature of space-time is spherically symmetrical. If you are free falling in a straight line straight towards the center of mass, you are moving along the geodesic. In this particular case the geodesic is a straight line, in this case the curvature of space-time manifests itself in the fact that with respect to the center of the Earth you are accelerating.

In the Euclidian space of newtonian dynamics, there is only one type of acceleration. Relativistic dynamics features two fundamentally distinct types of acceleration. There is the type of acceleration that is associated with a force that is causing an object to deviate from moving along the geodesic, and there is space-time curvature related acceleration. The non-Euclidian properties of the geometry of relativistic dynamics are highly counter-intuitive. With respect to your local volume of space-time, if there is no force, you are not accelerating. However, with respect to volumes of space-time with dissimilar space-time curvature than the volume you are in, you are accelerating. In summary, the principle of equivalence entails the following assumptions:

Being in free fall in a volume of curved space-time is profoundly similar to floating in zero-curvature space-time. Locally, curved space-time is fundamentally indistinguishable from zero-curvature space-time.

• If the surface of a gravitating body is pushing against you, keeping you from moving along the geodesic, that is: causing you to deviate from moving along the geodesic, then that surface is accelerating you in your local volume of space-time.
• If you are in a space-ship and you engage your thrusters, then this force will make you deviate from moving along the geodesic.
• If you are in a pilot training centrifuge, or rollercoaster ride, or in any situation making curves, a force is necessary to make you deviate from moving along the geodesic.

Note: Einstein used the principle of equivalence to guide his explorations in search for General Relativity. But Einstein did not view the principle of equivalence in the way it is described in this section of the article, this description draws heavily on the benefit of hindsight. The discription in this section of the article presents a modernized principle of equivalance, not a historical one.

See also

• Mach's principle

References

• Steven Weinberg Gravitation and Cosmology ISBN 0-471-92567-5, pp. 188-190 (for bending of light in a gravitational field), 342-348 (for time dilation during gravitational collapse).

External links

• 16 November 2004, physicsweb: Equivalence principle passes atomic test (http://physicsweb.org/articles/news/8/11/8/1) Quote: "...Physicists in Germany have used an atomic interferometer to perform the most accurate ever test of the equivalence principle at the level of atoms..."
• Webarchive backup (without pictures ((incl. formulas)): Lecture 6: The Principle of Equivalence (1): In Which We See Gravity Doing Things To Time (http://web.archive.org/web/20040223110146/www.pa.uky.edu/~cvj/as500_lec6/as500_lec6.html), original broken address (http://www.pa.uky.edu/~cvj/as500_lec6/as500_lec6.html)