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SaintRodriguez
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Is a worldline a curve or a trajectory? Why?
What is the difference?SaintRodriguez said:Is a worldline a curve or a trajectory? Why?
A curve is the math object like a function and the trajectory is the set of images that the function (curve) mapped.Dale said:What is the difference?
I would say “curve”, but if someone else said “trajectory” I wouldn’t correct them. I don’t know the difference in this context
What is this “set of images”? Are you just talking about the mathematical representation vs the physical thing that the math represents?SaintRodriguez said:the set of images
SaintRodriguez said:Is a worldline a curve or a trajectory? Why?
SaintRodriguez said:A curve is the math object like a function and the trajectory is the set of images that the function (curve) mapped.
That's a good question, because the terminology is a bit unclear in the physics literature. For me a curve is any smooth map between the real numbers (or an interval, if you have a finite curve) to a differentiable manifold, and spacetime is described in GR as such a differentiable manifold (with the extra properties making it a pseudo-Riemannian manifold, i.e., with a pseudometric and the uniquely defined torsion-free affine connection, compatible with this pseudometric). Another name for such a curve in relativity is "worldline".SaintRodriguez said:Is a worldline a curve or a trajectory? Why?
Why would worldline refer only to force free trajectories?vanhees71 said:If there are no forces, i.e., only gravity/aka spacetime curvature, then these are spacelike or timelike worldlines.
A worldline curve is a path that represents the movement of an object through space and time. It is different from a trajectory in that it includes both spatial and temporal components, while a trajectory only shows the spatial movement of an object.
In physics, worldline curves and trajectories are used to study the motion of objects and the effects of forces on those objects. They are also used to calculate the position, velocity, and acceleration of an object at any given time.
No, a worldline curve and a trajectory cannot be the same. A worldline curve includes both spatial and temporal components, while a trajectory only shows the spatial movement of an object. Therefore, a worldline curve provides a more complete representation of an object's motion.
In special relativity, worldline curves and trajectories differ in that worldline curves take into account the effects of time dilation and length contraction, while trajectories do not. This is because worldline curves incorporate both space and time, while trajectories only show the spatial movement of an object.
Yes, both worldline curves and trajectories are affected by gravity. In general relativity, gravity is seen as the curvature of spacetime, which affects the path of objects through space and time. Therefore, both worldline curves and trajectories will be affected by the presence of gravity.