Whichever coordinate system we choose, the charge will keep flowing in the same “arbitrary” direction, relative to the magnetic field. This is the conundrum we seek to explain; why does it not go the other way? What is so special about this way?
If I’m a negligibly small body, gravitating toward a ~stationary larger body, capture in a ~stable orbit subtracts exactly one dimension from my available “linear velocity”, in the sense that, maybe the other two components are fixed [over a certain period] now, but exactly one component must go to zero.
Ptolemaically, this looks like the ~stationary larger body, dragging the rest of spacetime with it in a 2-D fixed velocity [that is, fixed over the orbit’s period] around me—with exactly one dimension, the one we see as ~Polaris vs ~anti-Polaris, fixed in place, relative to the me/larger-body system. That is, the universe begins rotating around me cylindrically. The major diameter and minor diameter of the cylinder are dependent on the linear velocity I entered at [ adding in my mass and the mass of the heavy body, you get the period ] - but, assuming the larger body is stationary, nothing else about my fate in the capturing orbit appears dependent on anything else about my previous history—the rest is ~erased—even though generally-relative spacetime doesn’t seem to preclude more, or fewer, dependencies surviving. My question is, why is this? Why don’t more, or fewer, dependencies on my past momenta [“angular” or otherwise] survive?
Whichever coordinate system we choose, the charge will keep flowing in the same “arbitrary” direction, relative to the magnetic field. This is the conundrum we seek to explain; why does it not go the other way? What is so special about this way?
If I’m a negligibly small body, gravitating toward a ~stationary larger body, capture in a ~stable orbit subtracts exactly one dimension from my available “linear velocity”, in the sense that, maybe the other two components are fixed [over a certain period] now, but exactly one component must go to zero.
Ptolemaically, this looks like the ~stationary larger body, dragging the rest of spacetime with it in a 2-D fixed velocity [that is, fixed over the orbit’s period] around me—with exactly one dimension, the one we see as ~Polaris vs ~anti-Polaris, fixed in place, relative to the me/larger-body system. That is, the universe begins rotating around me cylindrically. The major diameter and minor diameter of the cylinder are dependent on the linear velocity I entered at [ adding in my mass and the mass of the heavy body, you get the period ] - but, assuming the larger body is stationary, nothing else about my fate in the capturing orbit appears dependent on anything else about my previous history—the rest is ~erased—even though generally-relative spacetime doesn’t seem to preclude more, or fewer, dependencies surviving. My question is, why is this? Why don’t more, or fewer, dependencies on my past momenta [“angular” or otherwise] survive?