3 ms·
Is it not the case that F=ma and other Newtonian laws are encoded in the Lagrangian, and therefore not derived from symmetries? After all nature and her symmetr
by ajkjk 3y ago
Is it not the case that F=ma and other Newtonian laws are encoded in the Lagrangian, and therefore not derived from symmetries? After all nature and her symmetries alone do not tell us how her physics works; there has to be some rule for time-evolution as well, and that's what's encoded in L (L's form is essentially a list of pairings of variables and their costs of evolution, which for classical mechanics is L = T - V = ∫ p·dv + ∫ F·dx, which says "the cost of changing v is p and the cost of changing x is F").
(QFT sort-of has an explanation for time evolution in terms of symmetries alone, but it requires a lot more machinery. But afaik classical mechanics does not.)
- om2 3y ago> the cost of changing v is p and the cost of changing x is F I’m sure the equation is right and all but this seems sideways in terms of an intuitive explanation - velocity changes position, and force changes momentum. Force doesn’t directly change position (only indirectly via changing momentum) and momentum doesn’t change velocity, having momentum is consistent with a constant velocity. It doesn’t even make much sense to me to think of integrals as being about “costs of changing”, would that not be a derivative?