6 ms·

Kindergarten Quantum Mechanics

70 points by ColinWright 6y ago

Koshkin 6y ago
Yeah, kids are bosons...
taliesinb 6y ago
If you want to see the author riff on density matrices, check out this recent video: https://youtu.be/wP_Jsxn7BA4?t=1020 https://youtu.be/wP_Jsxn7BA4?t=1020 And by riff I mean with an actual electric guitar
mgraczyk 6y ago
Does this paper describes an early form of Coecke's ZX calculus? What is the relationship between the two systems? https://zxcalculus.com/ https://zxcalculus.com/
- mathgenius 6y ago
  Yes, very closely related. ZX is a specific set of tensors within this diagrammatic framework.
tmabraham 6y ago
I have only skimmed this paper, but the diagrams look somewhat similar to Penrose graphical notation. Is there any connection there?
- mathgenius 6y ago
  Yes, they are pretty much the same thing. There are some particular quantum-y elements though, such as the cup & cap. In general relativity these would (i think?) correspond to index raising and lowering operators.
Kednicma 6y ago
"Of course we do not expect you to know about category theory, nor do we want to encourage you here to do so." Ugh. Well, I can encourage you to do so, with some Baez [0][1]. [0] http://math.ucr.edu/home/baez/rosetta.pdf http://math.ucr.edu/home/baez/rosetta.pdf [1] https://arxiv.org/abs/quant-ph/0404040 https://arxiv.org/abs/quant-ph/0404040
- Fishysoup 6y ago
  Man everyone seems to be talking about category theory lately and I still have no idea what it is except some general sense in which different types of mathematical objects can operate on each other (which is probably wrong). Looks like I should probably actually put the effort in and learn about it.
  - themonoid 6y ago
    Study category theory if you would like to understand "monads are just monoids in the category of endofunctors." Study the flatMap function if you would like to apply category theory to life. A monad is just an object with a sensible flatMap method.
    - Fishysoup 6y ago
      Normally I'd go with the second, but I'm trying to learn physics as a hobby and, you know, technologically save the world with my messiah complex apparently, and I want to keep tabs on things that may be insightful to know about
      - themonoid 6y ago
        Just in case you are serious about having a messiah complex, I am prone to having a messiah complex, thanks to schizoaffective disorder. It took me a while to figure out which medications actually help me, without too many unpleasant side effects, but I am very grateful to have discovered the cocktail that works for me now.
        Fishysoup 6y ago
        i'm glad to hear you've found something that helps you. I was joking about the messiah complex, though it is something my therapist has made the occasional joke about too when i get over-ambitious about things i wanna do (he did specify i don't seem to actually have it, though - just good old-fashioned depression).
mncharity 6y ago
From [0] 2018: "In [1] we present an entirely diagrammatic presentation of quantum the-ory with applications in quantum foundations and quantum information.This was the result of many years of work by many, and started of as acategory-theoretic axiomatisation motivated by computer science as well asaxiomatic physics. However, I have always felt that the diagrammatic pre-sentation is of great use in its own right, be it to bridge disciplines, makequantum theory more easy to grasp, or, for educational purposes, in [2] wemade the bolt claim that using diagrams high-school kids could even out-perform their teachers, or university students. Now, we will put this claimto the test. To do so, we have written two tutorials [3,4], covering exactlythe same material, but one only using diagrams, while the other containsthe standard Hilbert space presentation. There are corresponding sets ofexamples too." [0] Quantum Theory for Kids https://repositorio.usp.br/directbitstream/95d90813-2c2f-4cc6-b513-6a8c9bf5082c/2890851.pdf#page=141 https://repositorio.usp.br/directbitstream/95d90813-2c2f-4cc... [1] Picturing Quantum Processes https://doi.org/10.1017/9781316219317 https://doi.org/10.1017/9781316219317 ; slides https://www.cs.ox.ac.uk/ss2014/programme/Bob.pdf https://www.cs.ox.ac.uk/ss2014/programme/Bob.pdf ; talk https://www.youtube.com/watch?v=7Fvjpjhimic https://www.youtube.com/watch?v=7Fvjpjhimic [2] Quantum Picturalism https://arxiv.org/abs/0908.1787 https://arxiv.org/abs/0908.1787 [3] Quantum theory in Pictures ... "Top Secret"... I didn't quickly find. A recent talk: https://www.youtube.com/watch?v=AOLoyx6EHq8 https://www.youtube.com/watch?v=AOLoyx6EHq8
mncharity 6y ago
As meta, I suggest most everyone is vastly underestimating the magnitude of potentially transformative improvement being left on the table by current science education. But that's a discussion for another time.
- zrkrlc 6y ago
  Imagine putting all of science on a common (diagrammatic) footing, implemented down to the level of types so you can immediately perform calculations...mouthwatering.
supernova87a 6y ago
Kindergarten? They just took bra/kets, Feynman diagrams and substituted block-looking shapes. The underlying logic is hardly changed to kindergarten level. The kid better have a masters in physics to follow this. "...i.e. we need to conjugate the first Hilbert space (although this gives an isomorphic copy). In the above argument establishing the bijection we used the matrix representation of Hilbert spaces and hence essentially the whole vector space structure, but in fact we need none of this, and we will show that in any picture calculus we always have..."
- tokai 6y ago
  I don't know if you are joking, but the text is not aimed at kindergarteners regardless of the title.
082349872349872 6y ago
Kindergarten Quantum Mechanics: if you ask mom for something, she will say "yes" or "no" (even if she wasn't sure before you asked). Asking her again won't change her answer. At this point, to try to get a different answer to the same question, you have to ask dad.
mathgenius 6y ago
Apparently there is an actual experiment on six-year-olds taking place [1,2]: "Experiment. Consider ten children of ages between six and ten and consider ten high-school teachers of physics and mathematics. The high-school teachers of physics and mathematics will have all the time they require to refresh their quantum mechanics background, and also to update it with regard to recent developments in quantum information. The children on the other hand will have quantum theory explained in terms of the graphical formalism. Both teams will be given a certain set of questions, for the children formulated in diagrammatic language, and for the teachers in the usual quantum mechanical formalism. Whoever solves the most problems and solves them in the fastest time wins. If the diagrammatic language is much more intuitive, it should in principle be possible for the children to win." [1] https://twitter.com/coecke/status/1285531026270367744 https://twitter.com/coecke/status/1285531026270367744 [2] https://arxiv.org/abs/0908.1787 https://arxiv.org/abs/0908.1787

70 points by ColinWright 6y ago

Yeah, kids are bosons...

If you want to see the author riff on density matrices, check out this recent video: https://youtu.be/wP_Jsxn7BA4?t=1020 https://youtu.be/wP_Jsxn7BA4?t=1020 And by riff I mean with an actual electric guitar

mgraczyk 6y ago

Does this paper describes an early form of Coecke's ZX calculus? What is the relationship between the two systems? https://zxcalculus.com/ https://zxcalculus.com/

mathgenius 6y ago
Yes, very closely related. ZX is a specific set of tensors within this diagrammatic framework.

tmabraham 6y ago

I have only skimmed this paper, but the diagrams look somewhat similar to Penrose graphical notation. Is there any connection there?

mathgenius 6y ago
Yes, they are pretty much the same thing. There are some particular quantum-y elements though, such as the cup & cap. In general relativity these would (i think?) correspond to index raising and lowering operators.

Kednicma 6y ago

"Of course we do not expect you to know about category theory, nor do we want to encourage you here to do so." Ugh. Well, I can encourage you to do so, with some Baez [0][1]. [0] http://math.ucr.edu/home/baez/rosetta.pdf http://math.ucr.edu/home/baez/rosetta.pdf [1] https://arxiv.org/abs/quant-ph/0404040 https://arxiv.org/abs/quant-ph/0404040

Fishysoup 6y ago
Man everyone seems to be talking about category theory lately and I still have no idea what it is except some general sense in which different types of mathematical objects can operate on each other (which is probably wrong). Looks like I should probably actually put the effort in and learn about it.
- themonoid 6y ago
  Study category theory if you would like to understand "monads are just monoids in the category of endofunctors." Study the flatMap function if you would like to apply category theory to life. A monad is just an object with a sensible flatMap method.
  - Fishysoup 6y ago
    Normally I'd go with the second, but I'm trying to learn physics as a hobby and, you know, technologically save the world with my messiah complex apparently, and I want to keep tabs on things that may be insightful to know about
    - themonoid 6y ago
      Just in case you are serious about having a messiah complex, I am prone to having a messiah complex, thanks to schizoaffective disorder. It took me a while to figure out which medications actually help me, without too many unpleasant side effects, but I am very grateful to have discovered the cocktail that works for me now.
      - Fishysoup 6y ago
        i'm glad to hear you've found something that helps you. I was joking about the messiah complex, though it is something my therapist has made the occasional joke about too when i get over-ambitious about things i wanna do (he did specify i don't seem to actually have it, though - just good old-fashioned depression).

mncharity 6y ago

From [0] 2018: "In [1] we present an entirely diagrammatic presentation of quantum the-ory with applications in quantum foundations and quantum information.This was the result of many years of work by many, and started of as acategory-theoretic axiomatisation motivated by computer science as well asaxiomatic physics. However, I have always felt that the diagrammatic pre-sentation is of great use in its own right, be it to bridge disciplines, makequantum theory more easy to grasp, or, for educational purposes, in [2] wemade the bolt claim that using diagrams high-school kids could even out-perform their teachers, or university students. Now, we will put this claimto the test. To do so, we have written two tutorials [3,4], covering exactlythe same material, but one only using diagrams, while the other containsthe standard Hilbert space presentation. There are corresponding sets ofexamples too." [0] Quantum Theory for Kids https://repositorio.usp.br/directbitstream/95d90813-2c2f-4cc6-b513-6a8c9bf5082c/2890851.pdf#page=141 https://repositorio.usp.br/directbitstream/95d90813-2c2f-4cc... [1] Picturing Quantum Processes https://doi.org/10.1017/9781316219317 https://doi.org/10.1017/9781316219317 ; slides https://www.cs.ox.ac.uk/ss2014/programme/Bob.pdf https://www.cs.ox.ac.uk/ss2014/programme/Bob.pdf ; talk https://www.youtube.com/watch?v=7Fvjpjhimic https://www.youtube.com/watch?v=7Fvjpjhimic [2] Quantum Picturalism https://arxiv.org/abs/0908.1787 https://arxiv.org/abs/0908.1787 [3] Quantum theory in Pictures ... "Top Secret"... I didn't quickly find. A recent talk: https://www.youtube.com/watch?v=AOLoyx6EHq8 https://www.youtube.com/watch?v=AOLoyx6EHq8

mncharity 6y ago

As meta, I suggest most everyone is vastly underestimating the magnitude of potentially transformative improvement being left on the table by current science education. But that's a discussion for another time.

zrkrlc 6y ago
Imagine putting all of science on a common (diagrammatic) footing, implemented down to the level of types so you can immediately perform calculations...mouthwatering.

supernova87a 6y ago

Kindergarten? They just took bra/kets, Feynman diagrams and substituted block-looking shapes. The underlying logic is hardly changed to kindergarten level. The kid better have a masters in physics to follow this. "...i.e. we need to conjugate the first Hilbert space (although this gives an isomorphic copy). In the above argument establishing the bijection we used the matrix representation of Hilbert spaces and hence essentially the whole vector space structure, but in fact we need none of this, and we will show that in any picture calculus we always have..."

tokai 6y ago
I don't know if you are joking, but the text is not aimed at kindergarteners regardless of the title.

082349872349872 6y ago

Kindergarten Quantum Mechanics: if you ask mom for something, she will say "yes" or "no" (even if she wasn't sure before you asked). Asking her again won't change her answer. At this point, to try to get a different answer to the same question, you have to ask dad.

mathgenius 6y ago

Apparently there is an actual experiment on six-year-olds taking place [1,2]: "Experiment. Consider ten children of ages between six and ten and consider ten high-school teachers of physics and mathematics. The high-school teachers of physics and mathematics will have all the time they require to refresh their quantum mechanics background, and also to update it with regard to recent developments in quantum information. The children on the other hand will have quantum theory explained in terms of the graphical formalism. Both teams will be given a certain set of questions, for the children formulated in diagrammatic language, and for the teachers in the usual quantum mechanical formalism. Whoever solves the most problems and solves them in the fastest time wins. If the diagrammatic language is much more intuitive, it should in principle be possible for the children to win." [1] https://twitter.com/coecke/status/1285531026270367744 https://twitter.com/coecke/status/1285531026270367744 [2] https://arxiv.org/abs/0908.1787 https://arxiv.org/abs/0908.1787