“But the two blobs are more widely separated in the configuration space. Before, each blob of amplitude had two particles in different positions; now each blob of amplitude has three particles in different positions.
Indeed, if the third particle interacted in an especially sensitive way, like being tipped off a hill and sliding down, the new separation could be much larger than the old one.
Actually, it isn’t necessary for a particle to get tipped off a hill. It also works if you’ve got twenty particles interacting with the first two, and ending up entangled with them. Then the new amplitude distribution has got two blobs, each with twenty-two particles in different places. The distance between the two blobs in the joint configuration space is much greater.”
I’m not clear on why the amplitude involving more particles means that they’re further apart in configuration space. This probably shows I simply don’t understand configuration space, so sorry if the confusion links to a previous post! Thanks for any help, and please bear in mind I’m not science educated and relying on pre-university maths only...
I don’t know what metric (method of measuring distance) you use for configuration space. But assume it’s the standard, familiar Euclidean distance metric. Then if you have one particle in two blobs separated by 1 unit, it’s 1 unit distant. If you have two, it’s now separated by 1 unit along each of two axes, so it’s sqrt(2) distant. For N particles in two blobs, the blobs are sqrt(N) distant.
“But the two blobs are more widely separated in the configuration space. Before, each blob of amplitude had two particles in different positions; now each blob of amplitude has three particles in different positions.
Indeed, if the third particle interacted in an especially sensitive way, like being tipped off a hill and sliding down, the new separation could be much larger than the old one.
Actually, it isn’t necessary for a particle to get tipped off a hill. It also works if you’ve got twenty particles interacting with the first two, and ending up entangled with them. Then the new amplitude distribution has got two blobs, each with twenty-two particles in different places. The distance between the two blobs in the joint configuration space is much greater.”
I’m not clear on why the amplitude involving more particles means that they’re further apart in configuration space. This probably shows I simply don’t understand configuration space, so sorry if the confusion links to a previous post! Thanks for any help, and please bear in mind I’m not science educated and relying on pre-university maths only...
I don’t know what metric (method of measuring distance) you use for configuration space. But assume it’s the standard, familiar Euclidean distance metric. Then if you have one particle in two blobs separated by 1 unit, it’s 1 unit distant. If you have two, it’s now separated by 1 unit along each of two axes, so it’s sqrt(2) distant. For N particles in two blobs, the blobs are sqrt(N) distant.