“position” is nearly right. The more correct answer would be “position of one photon”.
If you had two electrons, say, you would have to consider their joint configuration. For example, one possible wavefunction would look like the following, where the blobs represent high amplitude areas:
This is still only one dimensional: the two electrons are at different points along a line. I’ve entangled them, so if electron 1 is at position P, electron 2 can’t be.
Now, try and point me to where electron 1 is on the graph above.
You see, I’m not graphing electrons here, and neither were you. I’m graphing the wavefunction. This is where your phrasing seems a little weird: you say the electron is the collection of amplitudes you circled: but those amplitudes are attached to configurations saying “the electron is at position x1” or “the electron is at position x2″. It seems circular to me. Why not describe that lump as “a collection of worlds where the electron is in a similar place”?
If you have N electrons in a 3d space, the wavefunction is not a vector in 3d space (god I wish, it would make my job a lot easier). It’s a vector in 3N+1 dimensions, like the following:
where r1, r2, etc are pointing to the location of electron 1, 2, 3, etc, and each possible configuration of electron 1 here, electron 2 there, etc, has an amplitude attached, with configurations that are more often encountered experimentally empirically having higher amplitudes.
“position” is nearly right. The more correct answer would be “position of one photon”.
If you had two electrons, say, you would have to consider their joint configuration. For example, one possible wavefunction would look like the following, where the blobs represent high amplitude areas:
This is still only one dimensional: the two electrons are at different points along a line. I’ve entangled them, so if electron 1 is at position P, electron 2 can’t be.
Now, try and point me to where electron 1 is on the graph above.
You see, I’m not graphing electrons here, and neither were you. I’m graphing the wavefunction. This is where your phrasing seems a little weird: you say the electron is the collection of amplitudes you circled: but those amplitudes are attached to configurations saying “the electron is at position x1” or “the electron is at position x2″. It seems circular to me. Why not describe that lump as “a collection of worlds where the electron is in a similar place”?
If you have N electrons in a 3d space, the wavefunction is not a vector in 3d space (god I wish, it would make my job a lot easier). It’s a vector in 3N+1 dimensions, like the following:
where r1, r2, etc are pointing to the location of electron 1, 2, 3, etc, and each possible configuration of electron 1 here, electron 2 there, etc, has an amplitude attached, with configurations that are more often encountered experimentally empirically having higher amplitudes.