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In GR. What's the worldline of a quantum particle before and after it undergoes state reduction (before and after Born rule applied)?
Worldlines are paths traced by particles moving through spacetime in the theory of General Relativity. They represent the complete history of a particle's motion, including its position and velocity at every point in time.
In classical mechanics, particles follow well-defined trajectories in 3-dimensional space. In GR, however, particles follow worldlines that exist in a 4-dimensional spacetime, which takes into account the curvature of spacetime caused by massive objects.
Yes, the worldline of a particle can change over time due to various factors such as the presence of other massive objects or the effects of gravitational waves. This is in contrast to classical mechanics, where the trajectory of a particle is considered to be fixed.
The curvature of spacetime, as described by Einstein's field equations in GR, directly influences the path that a particle follows through spacetime. The curvature is determined by the distribution of mass and energy in the universe, meaning that the worldline of a particle can be altered by the presence of other massive objects.
While the concept of worldlines is most commonly associated with GR, it can also be applied to other theories of physics that involve spacetime, such as special relativity and quantum mechanics. In these contexts, worldlines represent the evolution of a system over time in a similar way to how they represent the motion of a particle in GR.