Non Geodesic Motion: Definition & Explanation

[emanaly]

What is non geodesic motion?

 

[HallsofIvy]

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.

 

[Chris Hillman]

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.

 

[JesseM]

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"?

 

[Chris Hillman]

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?

 

[Chris Hillman]

Spin-spin forces plus an essential PF link

Why spinning particles don't have a geodesic path?

I didn't quite say that. However, in gtr, a spinning object immersed in a nonzero gravitational field (perhaps caused by a much larger nearby and spinning object) will in general experience a tiny "spin-spin" force and thus will be pushed off a geodesic path. However, these forces would be much too small to measure in any currently envisioned solar system experiments (at least, not any I know of). See for example "Dixon-Papapetrou equations" in Stephani, General relativity.

By the way, I urge all members to carefully read https://www.physicsforums.com/showthread.php?t=5374 if they have not already done so, and indeed to bookmark it for future reference.