But as a test, may I ask what you think the x-axis of the graph you drew is? Ie: what are the amplitudes attached to?
Position, but it’s not meant to be an actual graph of a wavefunction pdf; just a way to depict how the concepts can be sliced up in a way I can actually draw in 2 dimensions.
If you do treat it as a pdf over position, a more accurate way to depict the “world” concept might be as a line which connects points on the diagram for each time step. So for a fixed time step, a world is a single point on the diagram, representing a sample from the pdf defined by the wavefunction at that time.
“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, but it’s not meant to be an actual graph of a wavefunction pdf; just a way to depict how the concepts can be sliced up in a way I can actually draw in 2 dimensions.
If you do treat it as a pdf over position, a more accurate way to depict the “world” concept might be as a line which connects points on the diagram for each time step. So for a fixed time step, a world is a single point on the diagram, representing a sample from the pdf defined by the wavefunction at that time.
“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.