When does a Geodesic Represent a Free-Falling Particle's Worldline?

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SUMMARY

A geodesic represents a possible worldline for a particle in free fall under specific conditions, primarily that the metric ds squared is positive. Additionally, the particle must be massive, as this ensures proper time is non-zero. The discussion emphasizes that free fall excludes the influence of nongravitational forces, aligning with the principles of General Relativity (GR) which incorporates only gravitational forces into the metric. Thus, a particle's worldline can be accurately described as a geodesic when these conditions are met.

PREREQUISITES
  • Understanding of General Relativity (GR) principles
  • Familiarity with the concept of geodesics in differential geometry
  • Knowledge of proper time and its significance in physics
  • Basic grasp of metrics in spacetime
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  • Study the mathematical formulation of geodesics in General Relativity
  • Explore the implications of proper time in relativistic physics
  • Investigate the role of mass in defining worldlines of particles
  • Learn about the effects of nongravitational forces on particle motion
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This discussion is beneficial for physicists, students of theoretical physics, and anyone interested in the intricacies of General Relativity and the behavior of particles in spacetime.

deadringer
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"Under what conditions does a geodesic represent a possible wordline for a particle in free fall, parametrized by proper time."

I can only think of one conditions - the fact that the metric ds squared is positive. Is this enough?
 
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Possibly something like, "if acted on by no nongravitational forces". GR only absorbs gravitational forces into the metric. Though possibly that violates the condition of 'free fall'.
 
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Nope. I think you are basically right to begin with. 'Free fall' should exclude nongravitational forces. But I think the condition that they might be looking for is that the particle is massive. Otherwise proper time=0 is quite acceptable.
 

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