# Definitions for FOUR-ACCELERATIONfour-ac·cel·er·a·tion

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1. four-accelerationnoun

A four-vector that describes the change in a particle's four-velocity over time

### WikipediaRate this definition:0.0 / 0 votes

1. Four-acceleration

In the theory of relativity, four-acceleration is a four-vector (vector in four-dimensional spacetime) that is analogous to classical acceleration (a three-dimensional vector, see three-acceleration in special relativity). Four-acceleration has applications in areas such as the annihilation of antiprotons, resonance of strange particles and radiation of an accelerated charge.

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1. Four-acceleration

In special relativity, four-acceleration is a four-vector and is defined as the change in four-velocity over the particle's proper time: where and and is the Lorentz factor for the speed . A dot above a variable indicates a derivative with respect to the coordinate time in a given reference frame, not the proper time . In an instantaneously co-moving inertial reference frame, and, i.e. in such a reference frame Geometrically, four-acceleration is a curvature vector of a world line. Therefore, the magnitude of the four-acceleration is equal to the proper acceleration that a moving particle "feels" moving along a world line. The world lines having constant magnitude of four-acceleration are Minkowski-circles i.e. hyperbolas The scalar product of a four-velocity and the corresponding four-acceleration is always 0. Even at relativistic speeds four-acceleration is related to the four-force such that where m is the invariant mass of a particle. In general relativity the elements of the acceleration four-vector are related to the elements of the four-velocity through a covariant derivative with respect to proper time. In special relativity the coordinates are those of a rectilinear inertial frame, so the Christoffel symbols term vanishes, but sometimes when authors uses curved coordinates in order to describe an accelerated frame, the frame of reference isn't inertial, they will still describe the physics as special relativistic because the metric is just a frame transformation of the Minkowski space metric. In that case this is the expression that must be used because the Christoffel symbols are no longer all zero.

### Numerology

1. Chaldean Numerology

The numerical value of FOUR-ACCELERATION in Chaldean Numerology is: 9

2. Pythagorean Numerology

The numerical value of FOUR-ACCELERATION in Pythagorean Numerology is: 4

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