After reading through the Quantum Physics sequence, I would like to know more about the assumptions and theories behind the idea that an amplitude distribution factorizes, or approximately factorizes. Where would be a good place to learn more about this? I would appreciate some recommendations for journal articles to read, or specific sections of specific books, or if there’s another better way to learn this stuff, please let me know.
In the blog posts in the sequence, an analogy comes up a few times, saying that it doesn’t make sense to distinguish between the two factors of 3 when multiplying 3 x 3 x 2 to get 18, and that similarly, the amplitude blobs in configuration space that can sometimes appear to be like particles are factors of...I’m not sure what. The wavefunction? A probability density function (but we’re calling it amplitude instead of probabilities)? Something else? I didn’t entirely follow that section, so I’m not sure how to look it up.
When I searched on Google Scholar for “quantum factorization” I got journal articles about how to use quantum computers to factor prime numbers. When I looked up “particle indistinguishability” I got papers about very small numbers of particles in a state of quantum entanglement. When I searched for “amplitude distribution factorizes” I got articles about tomography and mesons and keys for quantum cryptography.
I’m also confused about: what precisely is an amplitude distribution? Amplitude of what? Distributed over what? I can make some guesses, but how do I look it up?
I would also like to know: what needs to be true in order for this concept to be true? Does it depend on the many worlds interpretation of quantum mechanics, or would it hold true in the other interpretations? Does it require the wavefunction? Just how good is the analogy about the factors of 18, and where would the analogy break down? What do the equations look like that lead to these conclusions, and what are they called, so I can look them up? What assumptions are used to formulate the equations? What is the difference between factorizing exactly and approximately? Why does the idea of roughly factorizing come up at all, why isn’t it all exact? How accurate would it be to describe a person as a factor of the wave function, and what does that mean? Is there a technical term for “blob of amplitude”?
The Quantum Physics sequence is the best introduction to quantum mechanics that I’ve read, but it is rather incomplete about explicitly stating the assumptions it is using, or giving references to where to learn more about each topic.
But seriously, if you’re curious, try to find a textbook online, or a series of video lectures for an introductory course (you might either watch the whole course, or skip to what you want to learn and then try and figure out what the prerequisites are, then do the same thing for the prerequisites).
I think the factorization is a reference to https://en.wikipedia.org/wiki/Creation_and_annihilation_operators from quantum field theory. I haven’t learned quantum field theory though, so I can’t comment much. From what I can gather, multiplying something by the creation operator gets you the same state but with an extra particle.
I can tell you that at the very minimum, assuming Copenhagen and the minimal amount of physics to allow entanglement to happen at all, whenever two of the same kind of particle are entangled, they have a 50% chance of swapping. If you use MWI, it’s that I can find a universe with the same probability density in which those particles are swapped.
After reading through the Quantum Physics sequence, I would like to know more about the assumptions and theories behind the idea that an amplitude distribution factorizes, or approximately factorizes. Where would be a good place to learn more about this? I would appreciate some recommendations for journal articles to read, or specific sections of specific books, or if there’s another better way to learn this stuff, please let me know.
In the blog posts in the sequence, an analogy comes up a few times, saying that it doesn’t make sense to distinguish between the two factors of 3 when multiplying 3 x 3 x 2 to get 18, and that similarly, the amplitude blobs in configuration space that can sometimes appear to be like particles are factors of...I’m not sure what. The wavefunction? A probability density function (but we’re calling it amplitude instead of probabilities)? Something else? I didn’t entirely follow that section, so I’m not sure how to look it up.
When I searched on Google Scholar for “quantum factorization” I got journal articles about how to use quantum computers to factor prime numbers. When I looked up “particle indistinguishability” I got papers about very small numbers of particles in a state of quantum entanglement. When I searched for “amplitude distribution factorizes” I got articles about tomography and mesons and keys for quantum cryptography.
I’m also confused about: what precisely is an amplitude distribution? Amplitude of what? Distributed over what? I can make some guesses, but how do I look it up?
I would also like to know: what needs to be true in order for this concept to be true? Does it depend on the many worlds interpretation of quantum mechanics, or would it hold true in the other interpretations? Does it require the wavefunction? Just how good is the analogy about the factors of 18, and where would the analogy break down? What do the equations look like that lead to these conclusions, and what are they called, so I can look them up? What assumptions are used to formulate the equations? What is the difference between factorizing exactly and approximately? Why does the idea of roughly factorizing come up at all, why isn’t it all exact? How accurate would it be to describe a person as a factor of the wave function, and what does that mean? Is there a technical term for “blob of amplitude”?
The Quantum Physics sequence is the best introduction to quantum mechanics that I’ve read, but it is rather incomplete about explicitly stating the assumptions it is using, or giving references to where to learn more about each topic.
Help?
Relevant wikipedia link. The keyword is something like “many-body wavefunction.”
But seriously, if you’re curious, try to find a textbook online, or a series of video lectures for an introductory course (you might either watch the whole course, or skip to what you want to learn and then try and figure out what the prerequisites are, then do the same thing for the prerequisites).
I think the factorization is a reference to https://en.wikipedia.org/wiki/Creation_and_annihilation_operators from quantum field theory. I haven’t learned quantum field theory though, so I can’t comment much. From what I can gather, multiplying something by the creation operator gets you the same state but with an extra particle.
I can tell you that at the very minimum, assuming Copenhagen and the minimal amount of physics to allow entanglement to happen at all, whenever two of the same kind of particle are entangled, they have a 50% chance of swapping. If you use MWI, it’s that I can find a universe with the same probability density in which those particles are swapped.