And when you add up all the ways the photon can go from S to P, you find that most of the amplitude comes from the middle part of the mirror—the contributions from other parts of the mirror tend to mostly cancel each other out, as shown at the bottom of Feynman’s figure.
Eliezer, one thing that is confusing me is that you are trying to show that the billiard ball and the “particles have identities” analogy is wrong. At the same time you keep speaking from “the photon”. In the quotation the impression I get is that “the photon” splits up into the different paths it travels. Why does it split up in the first place? Again the “splitting up” assumes that there is a particle(alias small billiard ball) but your writing seems to imply this.
Btw, I have posted a question to your last entry “The quantum arena” which unfortunately wasn’t answered and has to do with this confusion.
Thanks, Roland
PS: I’m no physicist and from reading the other comments I have the impression that most who are following this are physicists or at least have quite an advanced knowledge of QM. Please don’t subestimate the inferential distance for those of us who don’t have all that knowledge.
I think that the splitting of the photon’s path is pretty much entirely a human construction—the smaller the components it is split into, the more accurate the calculation, and each partition is itself an approximation that can be refined by splitting it up further in exactly the same manner. Essentially, it’s a shortcut to doing a path integral over the entire range down to the planck level. Maybe… I’m not sure!
And when you add up all the ways the photon can go from S to P, you find that most of the amplitude comes from the middle part of the mirror—the contributions from other parts of the mirror tend to mostly cancel each other out, as shown at the bottom of Feynman’s figure.
Eliezer, one thing that is confusing me is that you are trying to show that the billiard ball and the “particles have identities” analogy is wrong. At the same time you keep speaking from “the photon”. In the quotation the impression I get is that “the photon” splits up into the different paths it travels. Why does it split up in the first place? Again the “splitting up” assumes that there is a particle(alias small billiard ball) but your writing seems to imply this.
Btw, I have posted a question to your last entry “The quantum arena” which unfortunately wasn’t answered and has to do with this confusion.
Thanks, Roland
PS: I’m no physicist and from reading the other comments I have the impression that most who are following this are physicists or at least have quite an advanced knowledge of QM. Please don’t subestimate the inferential distance for those of us who don’t have all that knowledge.
Very late response:
I think that the splitting of the photon’s path is pretty much entirely a human construction—the smaller the components it is split into, the more accurate the calculation, and each partition is itself an approximation that can be refined by splitting it up further in exactly the same manner. Essentially, it’s a shortcut to doing a path integral over the entire range down to the planck level. Maybe… I’m not sure!