{ 1 if t > 0 x(t) = { { 0 if t <= 0
If I remember my calculus correctly, x'(0) is undefined, while x(t) = 0. Does it therefore follow that at time t=0, the particle has a position and is moving but has no velocity? Would it be physically possible (i.e. compatible with the laws of physics as we currently understand them) for a particle with that behaviour to actually exist?  SJK
In classical (nonquantum) mechanics a particle with mass cannot make such an instantaneous jump in position. It implies infinite acceleration which implies infinite force. So this case is not physically possible in classical mechanics (assuming zeromass particles are not physically possible).  Eob
the derivative of the step function x(t) you wrote above is the Dirac delta function.  :RAE
I am in browse mode tonight... but at some point mention will have to made of tangent spaces and tie the discussion back to differential geometry.
Eob: What about in quantum mechanics? IIRC, quantum mechanics predicts instantaneous jumps in position (consider e.g. the Bohr model of the atom). And it has a zeromass particle, the photon...  SJK
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