= 27d567bc2d48d9f40e9ccc20ea370b15)
Luke_A_Somers comments on Feynman Paths - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (28)
I know this is an old post, but I'm hoping someone will see this. I read this a long time ago and have been thinking about QM questions (non-professionally) for a while. Recently, I started to wonder about a specific question regarding this post. Specifically, I'm thinking about the idea that we are summing paths leading to "identical configurations". While the various paths the photon takes in this problem do appear to lead to the same configuration, it seems to me that this is only true if you are just looking at the configuration of the photon and the mirror. The path A takes much more time to be completed than the path G, and it seems to me that during that time, the configuration of the rest of the universe would change as well, so the two configurations aren't the same.
I think this understanding is probably wrong, but I have about twenty guesses as to mistakes I could be making, and no clue which ones are genuine. Can anyone who has studied QM more help me out?
You don't need to add them ALL up at the same time, just notice that as you get further and further from the middle, each part begins canceling with nearer and nearer neighbors. To be more concrete: at some point, you start sending your pulse. The shortest path/specular reflection gets the signal there first; other paths begin contributing later. After a short time, the time offset to get to the destination is large enough that the beginning of the pulse from one angle is cancelling with the middle of the pulse from a neighboring angle. Beyond that point, unless the packet had some special structure, there's not much in the way of reflection.
To be perfectly frank, the mirror isn't necessary for this problem to work - all it really needs to do is justify Huygens' principle.
This also goes a way towards addressing DonGeddis's question - pretend the mirror isn't there, and reflect the upward rays down. The mirror no longer exists, and this now becomes the question of why light doesn't spontaneously turn angles for no reason at all. Is that better?
That's a pretty good way of explaining it. I actually read QED last summer, after posting this, and (I believe in chapter 3) Feynman covers this topic briefly. EY just didn't describe it. Thanks for posting the clarification!