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seen Apr 21 at 14:23

Sep
27
asked What is the difference between Raman scattering and fluorescence?
Sep
27
answered How do electrons repel?
Sep
27
comment Is the principle of least action a boundary value or initial condition problem?
So should your second point be interpreted as follows: I know that a particle is at a given point at an initial time, and will be in some, yet unknown, location at a later time, which I will be able to measure to arbitrary accuracy (because I deny uncertainty). Demanding minimal action, I find the differential equation that governs the physical path between the two locations - but now, technically, I can solve the equation with initial values instead, to "find" which final position would have yielded this initial momentum had the problem been solved under boundary conditions. Am I close?
Sep
27
comment Is the principle of least action a boundary value or initial condition problem?
Thanks Qmechanic! I posed my question in a strict classical context, so while I agree that the limitation of uncertainty is indeed problematic, it is technically not existent in the Lagrangian formalism.
Sep
27
awarded  Supporter
Sep
27
comment Is the principle of least action a boundary value or initial condition problem?
I fully understand that imposing both constrains creates an overdetermined problem. Clearly, only one set of conditions is needed - what is unclear to me is which one is used in the context of least action. Why is it derived under one assumption and solved under the other?
Sep
27
awarded  Nice Question
Sep
26
comment Is the principle of least action a boundary value or initial condition problem?
As I understand you, you mean that just because the equations are differential in time, this necessitates that the problem is an initial value problem? I doubt that's really what you meant. Can you refer me to a derivation where this distinction is manifest?
Sep
26
awarded  Teacher
Sep
26
answered Overcoming Friction
Sep
26
awarded  Student
Sep
26
asked Is the principle of least action a boundary value or initial condition problem?