@sonhouse saidWell I think every school-boy studying dynamics knows
https://www.forbes.com/sites/startswithabang/2020/03/12/we-all-learned-physics-biggest-myth-that-projectiles-make-a-parabola/#227c6d3a5d2e
that a parabola is a (really good) approximation.
Hadn't thought about the actual path.
An ellipse does make sense though.
@wolfgang59 saidI would cautiously use the word “actual”. Is there an actual path? It seems to me, that all the paths we can “know” are just approximations of something truly unknowable.
Well I think every school-boy studying dynamics knows
that a parabola is a (really good) approximation.
Hadn't thought about the actual path.
An ellipse does make sense though.
@joe-shmo saidThat the actual path is unknowable doesn't, of itself, prevent it from existing. At the level of "absolute truth" we'd expect it's flight to be governed by Quantum Field Theory (total overkill for working out the trajectory of a macroscopic projectile) and there isn't a single path, but a sort of averaging over all possible trajectories.
I would cautiously use the word “actual”. Is there an actual path? It seems to me, that all the paths we can “know” are just approximations of something truly unknowable.
1 edit
@deepthought saidI've obviously never studied QM, so I don't know how the machinery works. However, it appears to the layman that the averaging is ( by definition ) an approximation, is it not?
That the actual path is unknowable doesn't, of itself, prevent it from existing. At the level of "absolute truth" we'd expect it's flight to be governed by Quantum Field Theory (total overkill for working out the trajectory of a macroscopic projectile) and there isn't a single path, but a sort of averaging over all possible trajectories.
@joe-shmo saidWell, the average of 5 and 7 is exactly 6, no approximations are involved. What is the case in quantum mechanics is that the path itself is somewhat blurry. What we tend to be interesting in is the correlation function between <x(t)|x(0)> where |x(0)> represents the initially prepared position of the particle and |x(t)> the probability amplitude of finding it at position x at time t. Since we don't attempt to observe it in the meantime we can't even be sure the thing exists in between measurements, never mind what route it took.
I've obviously never studied QM, so I don't know how the machinery works. However, it appears to the layman that the averaging is ( by definition ) an approximation, is it not?
1 edit
@deepthought said"Well, the average of 5 and 7 is exactly 6, no approximations are involved"
Well, the average of 5 and 7 is exactly 6, no approximations are involved. What is the case in quantum mechanics is that the path itself is somewhat blurry. What we tend to be interesting in is the correlation function between <x(t)|x(0)> where |x(0)> represents the initially prepared position of the particle and |x(t)> the probability amplitude of finding it at positio ...[text shortened]... ntime we can't even be sure the thing exists in between measurements, never mind what route it took.
I wasn't trying to convey that the mean couldn't be exactly defined, but that for instance in this example you presented 6 is an approximation of 5 and 7?
I think I understand what you are saying about the particle being "here or there" when it is measured, and possibly "nowhere or everywhere" in between? But in that case its our notion of a continuum/trajectory that is the approximation. The true reality seems to be something unknowable?
- Joined
- 18 Jan 07
- Moves
- 12477
@wolfgang59 saidNeither is any good at approximating reality outside the classroom, and none of you have ever fired a shell.
Well I think every school-boy studying dynamics knows
that a parabola is a (really good) approximation.
Hadn't thought about the actual path.
An ellipse does make sense though.
Have none of you armchair artillerists ever heard of drag!?
@shallow-blue saidThe article referenced in the OP does specify that air resistance is neglected. They're saying it would still not be an ellipse on the moon, and make the rather tedious point that really it's an ellipse, but if we want to be really pedantic we have to take the local mass distribution and general relativity into account and use a supercomputer to solve it.
Neither is any good at approximating reality outside the classroom, and none of you have ever fired a shell.
Have none of you armchair artillerists ever heard of drag!?
This is an A-level mechanics problem and taking drag into account makes the problem non-linear, it's not reasonable to make them take it into account.