Non geodisic motion

  • Thread starter emanaly
  • Start date
31
0

Main Question or Discussion Point

What is non geodesic motion?
 

Answers and Replies

HallsofIvy
Science Advisor
Homework Helper
41,738
897
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
Science Advisor
2,337
8
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
Science Advisor
8,492
12
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
Science Advisor
2,337
8
Good catch, JesseM, I missed that! But I am sure HallsofIvy simply mistyped.
 
31
0
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
Science Advisor
2,337
8
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.
 
Top