4 ms·

Sure, if you would know the spin direction before the measurement, you could align your measurement device accordingly and get a predictable answer and spin sta

Sure, if you would know the spin direction before the measurement, you could align your measurement device accordingly and get a predictable answer and spin state would remain unchanged as the particle is not in a superposition for that measurement basis. But if measurement basis and spin direction are not aligned, then the measurement result will be random in proportion to the misalignment and the spin state will be non-unitarily changed by the measurement, projected onto the measurement basis. It the second scenario that lacks proper understanding, the first one seems much less interesting, you measure something that you already know and you get the value that you expect. It is certainly an interesting fact that being in a superposition is not an absolute statement, but it also seems not to uncommon. In additive color mixing magenta is a combination of red and blue, in subtractive color mixing it is one of the base colors.

gus_massa 2y ago
Rhere are a few interesting cases where superposition is inevitable. A) In a molecule with two electrons, the wavefunction of the electrons is written as |aa> + |bb> + ... combining one electron with spin up and one with spin down. [1] [2] It would be nice to choose the base carefully and write only |aa>. That is the Hartree-Fock method [3] and the result is like 95% or 99% accurate, sometimes you get 100% accurate, but it's not usual. To get the small difference, you must allow combinations like Sqrt(99%) |aa> + Sqrt(1%) |bb>. [4] It would be very nice to be able to use the simple form because calculations would be much faster. B) In a different area, IIUC the neutrino osculation is caused because it's impossible to choose the bases for leptons and neutrinos and their transformations in a way there is no superpositions. [1] Actually, in some cases you must use |ab> + |cd> + ... , but the simple version is good enough. [2] And with more electrons it's even worse. [3] https://en.wikipedia.org/wiki/Hartree%E2%80%93Fock_method https://en.wikipedia.org/wiki/Hartree%E2%80%93Fock_method [4] https://en.wikipedia.org/wiki/Electronic_correlation https://en.wikipedia.org/wiki/Electronic_correlation [5] https://en.wikipedia.org/wiki/Neutrino_oscillation https://en.wikipedia.org/wiki/Neutrino_oscillation

gus_massa 2y ago

Rhere are a few interesting cases where superposition is inevitable. A) In a molecule with two electrons, the wavefunction of the electrons is written as |aa> + |bb> + ... combining one electron with spin up and one with spin down. [1] [2] It would be nice to choose the base carefully and write only |aa>. That is the Hartree-Fock method [3] and the result is like 95% or 99% accurate, sometimes you get 100% accurate, but it's not usual. To get the small difference, you must allow combinations like Sqrt(99%) |aa> + Sqrt(1%) |bb>. [4] It would be very nice to be able to use the simple form because calculations would be much faster. B) In a different area, IIUC the neutrino osculation is caused because it's impossible to choose the bases for leptons and neutrinos and their transformations in a way there is no superpositions. [1] Actually, in some cases you must use |ab> + |cd> + ... , but the simple version is good enough. [2] And with more electrons it's even worse. [3] https://en.wikipedia.org/wiki/Hartree%E2%80%93Fock_method https://en.wikipedia.org/wiki/Hartree%E2%80%93Fock_method [4] https://en.wikipedia.org/wiki/Electronic_correlation https://en.wikipedia.org/wiki/Electronic_correlation [5] https://en.wikipedia.org/wiki/Neutrino_oscillation https://en.wikipedia.org/wiki/Neutrino_oscillation