I don’t disagree with your second sentence. Regarding the first, I don’t think there’s really any argument about whether or not it’s handwaving. The question is whether or not it’s justified handwaving in the pursuit of a pseudo-rigorous understanding of quantum mechanics.
I’m comfortable with him saying that time evolution is linear, because there are intuitive reasons for it to be so, and he presents those reasons elsewhere.
I’m less comfortable with the use of them in this article. Take the following quote:
There are no plausible Feynman paths that end up with both LEFT and RIGHT sending amplitude to the same joint configuration. There would have to be a Feynman path from LEFT, and a Feynman path from RIGHT, in which all the quadrillions of differentiated particles ended up in the same places. So the amplitude flows from LEFT and RIGHT don’t intersect, and don’t interfere.
It’s really hard to make sense of this given the way Feynman paths are treated earlier. I can make sense of it if I rely on what traditional training I’ve had in quantum mechanics, but not everyone has that background.
‘Handwaving’ describes vagueness. Yet, just how much vagueness qualifies as ‘handwaving’ is not well-defined!
This builds on the result of ‘joint configurations’, which is that for interference to occur, everything needs to line up. EVERYTHING. Otherwise, it’s offset in some dimension or other, and not really in the same ‘place’ at all. With that in place, this is a short step to take.
‘Handwaving’ describes vagueness. Yet, just how much vagueness qualifies as ‘handwaving’ is not well-defined!
I don’t disagree? I’m making essentially an aesthetic point.
I thought I qualified how much vagueness was acceptable—there is vagueness that is pedagogically useful, and there is vagueness that is not pedagogically useful, and my accusation of handwaving is isomorphic to saying that the vagueness with Feynman paths here is not pedagogically useful.
This builds on the result of ‘joint configurations’, which is that for interference to occur, everything needs to line up. EVERYTHING. Otherwise, it’s offset in some dimension or other, and not really in the same ‘place’ at all. With that in place, this is a short step to take.
I can’t follow this explanation at all. Too many ambiguous pronouns. But this is okay; the goal isn’t to explain it to me—I have all the training in quantum mechanics that I care to have.
“Everything needs to line up” is the key point, and it once you understand it it’s really quite simple. It just means that there is more than one way to get to the same configuration state. Think about history seeming to branch out in a tree-like way, as most people tend to imagine. But if two branching paths are not far apart (e.g. differing by just a single photon) then it is easy for then to come back together. History changes from a tree to a graph. Being a graph means that some point has two history paths (actually every point has an infinite amount of ancestry but most of it cancels out). When you more than one history path both constructive and destructive interference can take place, and destructive means that the probability of some states goes down, i.e. some final states no longer happen (you no longer see a photon appearing in some places).
Is this making it clearer or have I made it worse? ;-)
Well, true, a graph implies a discreteness that does not correlate closely to a continuous configuration space. I actually think of it as the probability of finding yourself in that volume of configuration space being influenced by “significant” amplitudes slowing from more than one other volume of configuration space, although even that is not a great explanation as it suggests a ticking of a discrete time parameter. A continuously propagating wavefront is probably a much better analogy. Or we can just go into calculus mode and consider boxes of configuration space which we then shrink down arbitrarily while taking a limit value. But sometimes it’s just easier to think “branches” ;-)
Nobody seems to think EY’s exposition is an issue, and you’re the second person who’s tried—and I can’t understand the motivation for this—to explain the underlying QM to me in vague metaphors that neither reflect the underlying theory nor present a pedagogical simplification.
But it does reflect the underlying theory (though it does take special cases and simplifies), and it does present a pedagogical simplification (because it’s a hell of a lot easier than solving huge quantum systems. Heck, it’s not even a metaphor. A DAG is blank enough—has few enough intrinsic properties—to be an incomplete model instead of a metaphor.
Does anything other than a fully quantum description of a system using only an interacting-particle hamiltonian with no externally applied fields count as a non-vague non-metaphor?
I don’t disagree with your second sentence. Regarding the first, I don’t think there’s really any argument about whether or not it’s handwaving. The question is whether or not it’s justified handwaving in the pursuit of a pseudo-rigorous understanding of quantum mechanics.
I’m comfortable with him saying that time evolution is linear, because there are intuitive reasons for it to be so, and he presents those reasons elsewhere.
I’m less comfortable with the use of them in this article. Take the following quote:
It’s really hard to make sense of this given the way Feynman paths are treated earlier. I can make sense of it if I rely on what traditional training I’ve had in quantum mechanics, but not everyone has that background.
‘Handwaving’ describes vagueness. Yet, just how much vagueness qualifies as ‘handwaving’ is not well-defined!
This builds on the result of ‘joint configurations’, which is that for interference to occur, everything needs to line up. EVERYTHING. Otherwise, it’s offset in some dimension or other, and not really in the same ‘place’ at all. With that in place, this is a short step to take.
I don’t disagree? I’m making essentially an aesthetic point.
I thought I qualified how much vagueness was acceptable—there is vagueness that is pedagogically useful, and there is vagueness that is not pedagogically useful, and my accusation of handwaving is isomorphic to saying that the vagueness with Feynman paths here is not pedagogically useful.
I can’t follow this explanation at all. Too many ambiguous pronouns. But this is okay; the goal isn’t to explain it to me—I have all the training in quantum mechanics that I care to have.
“Everything needs to line up” is the key point, and it once you understand it it’s really quite simple. It just means that there is more than one way to get to the same configuration state. Think about history seeming to branch out in a tree-like way, as most people tend to imagine. But if two branching paths are not far apart (e.g. differing by just a single photon) then it is easy for then to come back together. History changes from a tree to a graph. Being a graph means that some point has two history paths (actually every point has an infinite amount of ancestry but most of it cancels out). When you more than one history path both constructive and destructive interference can take place, and destructive means that the probability of some states goes down, i.e. some final states no longer happen (you no longer see a photon appearing in some places).
Is this making it clearer or have I made it worse? ;-)
See the comments on How Many Worlds? for why introducing the graph metaphor is confusing and negatively helpful to beginners.
Well, true, a graph implies a discreteness that does not correlate closely to a continuous configuration space. I actually think of it as the probability of finding yourself in that volume of configuration space being influenced by “significant” amplitudes slowing from more than one other volume of configuration space, although even that is not a great explanation as it suggests a ticking of a discrete time parameter. A continuously propagating wavefront is probably a much better analogy. Or we can just go into calculus mode and consider boxes of configuration space which we then shrink down arbitrarily while taking a limit value. But sometimes it’s just easier to think “branches” ;-)
I’m tapping out.
Nobody seems to think EY’s exposition is an issue, and you’re the second person who’s tried—and I can’t understand the motivation for this—to explain the underlying QM to me in vague metaphors that neither reflect the underlying theory nor present a pedagogical simplification.
But it does reflect the underlying theory (though it does take special cases and simplifies), and it does present a pedagogical simplification (because it’s a hell of a lot easier than solving huge quantum systems. Heck, it’s not even a metaphor. A DAG is blank enough—has few enough intrinsic properties—to be an incomplete model instead of a metaphor.
Does anything other than a fully quantum description of a system using only an interacting-particle hamiltonian with no externally applied fields count as a non-vague non-metaphor?