# Non geodisic motion

emanaly
What is non geodesic motion?

## Answers and Replies

Homework Helper
Obvious definition- motion that does not follow a geodesic! In relativity, geodesics are the paths followed by objects with no "outside" forces acting on them (gravity not being considered an "outside" force here) so non-geodesic motion is motion with no outside forces.

Just to elaborate quickly on what HallsofIvy said: in general relativity, the world line of a (nonspinning) test particle is a geodesic, i.e. a curve with zero path curvature. More generally, the path curvature at any event on some world line is just the magnitude of acceleration experienced by the corresponding particle. For example, a charged particle in an "electrovacuum solution" of the Einstein field equation (EFE) will experience a nonzero Lorentz force, whose magnitude (at each event on the world line of the particle) agrees with the path curvature.

non-geodesic motion is motion with no outside forces.
I'm guessing you meant either "geodesic motion is motion with no outside forces" or else "non-geodesic motion is motion with outside forces"?

Good catch, JesseM, I missed that! But I am sure HallsofIvy simply mistyped.

emanaly
Just to elaborate quickly on what HallsofIvy said: in general relativity, the world line of a (nonspinning) test particle is a geodesic, i.e. a curve with zero path curvature. More generally, the path curvature at any event on some world line is just the magnitude of acceleration experienced by the corresponding particle. For example, a charged particle in an "electrovacuum solution" of the Einstein field equation (EFE) will experience a nonzero Lorentz force, whose magnitude (at each event on the world line of the particle) agrees with the path curvature.

Why spinning particles don't have a geodesic path?