6 ms·

How Feynman Diagrams Revolutionized Physics

219 points by furcyd 7y ago

stared 7y ago
Diagrams are very general and can be extrapolated from quantum field theory to deep learning, see: https://medium.com/@pmigdal/in-the-topic-of-diagrams-i-did-write-a-review-simple-diagrams-of-convoluted-neural-networks-6418a63f9281 https://medium.com/@pmigdal/in-the-topic-of-diagrams-i-did-w... "In particle physics, people use Feynman diagrams a lot. And these are nothing more or less than a graphical representation of summations and integrations over many variables. Also, as an ex-quantum physicist, I am a big fan of tensor diagrams [...]. You can think about it as the Einstein summation convention with no dummy indices (see Einsum in PyTorch)."
- evanb 7y ago
  You're probably better off with some kind of Penrose graphical notation https://en.wikipedia.org/wiki/Penrose_graphical_notation https://en.wikipedia.org/wiki/Penrose_graphical_notation
  - galaxyLogic 7y ago
    or: https://www.quantamagazine.org/physicists-discover-geometry-underlying-particle-physics-20130917/ https://www.quantamagazine.org/physicists-discover-geometry-... “Why are you summing up millions of things when the answer is just one function?”
  - stared 7y ago
    It’s the same.
    - evanb 7y ago
      I didn't see, for example, the circling-a-group for taking derivatives.
      - stared 7y ago
        Sure, there are other elements (derivative, (anti)symmetrization, lowering/raising indices). The core element of summation stays the same.
- srean 7y ago
  I was about to mention category theoretic connection but the post mentions Bob so I need not say anymore.
- soVeryTired 7y ago
  But... the Einstein summation convention is kind of fine in deep learning. The tensor manipulation in deep learning doesn't involve any of the gnarly contortions that physicists need to do like raising and lowering indices, taking covariant derivatives, or taking traces: and even that stuff moved along just fine without the need for diagramatic representations until the 1960s or so.
melling 7y ago
They promote their book after the video. Any opinions? “Alice and Bob Meet the Wall of Fire: The Biggest Ideas in Science from Quanta ” https://www.amazon.com/Alice-Bob-Meet-Wall-Fire/dp/026253634X https://www.amazon.com/Alice-Bob-Meet-Wall-Fire/dp/026253634...
aerovistae 7y ago
Frustrating because it doesn't actually tell you how they work.
- zinclozenge 7y ago
  Feynman diagrams are just pictorial representations of terms from a power series expansion of an overall 'master' equation representing a certain scattering process. A fairly simple one is electron positron annihilation, which yields two photons.
  - ddavis 7y ago
    Just to expand on this; the series is usually called a Dyson series (https://en.wikipedia.org/wiki/Dyson_series https://en.wikipedia.org/wiki/Dyson_series). Dyson showing the connection between perturbation theory and Feynman's formulation was very important.
  - gpsx 7y ago
    I also will expand on this. Quantum field theory is very difficult and we can't solve many problems. We can solve one in particular, free particles that do not interact. (By the way, this is like solving a simple harmonic osciallator.) Feynman diagrams use the solution to free particles as a basis - these are the lines in the diagram, like particles moving in time. Then, we add the interactions between the particles as a pertabative exapansion. This is what the parent comment refers to as the power series expansion. It is expanding in the powers of the interaction terms. As mentioned in the video, it is not quite as simple as this however. If you do this, you will get infinity as a result of the calculation. That is not a very good perterbation theory. However the real discovery of physcists from this time was renormalization. They found out you can sum many contributions from different terms in the exapansion, corresponding to different indiviaul feynmann diagrams, and you can make these infinities cancel out. What is magic is that when this process is done you can write an effective theory for the interactions that looks exactly like the original theory you started with, and only the values of the coeffiecients are changed a little. The magic involved here could be explained more, but in summary what it means is that the perterbation calculation you do is valid even thought it looks like it should be infinite. It also lets you make the simple analogy that the lines in the diagram are real and virtual particles rather than just the non-interacting approximation you starter with.
beezle 7y ago
Drawing Theories Apart is an excellent book on Feynman Diagrams. You don't have to be actively involved in nuclear or hep to understand but the material is not for the faint of heart and a decent background in those areas goes a long way. https://www.amazon.com/Drawing-Theories-Apart-Dispersion-Diagrams/dp/0226422674/ref=sr_1_5?keywords=feynman+diagrams&qid=1557847023&s=books&sr=1-5 https://www.amazon.com/Drawing-Theories-Apart-Dispersion-Dia...
hepnewb 7y ago
What about Twistors, are they the future?
- musgravepeter 7y ago
  My perception (as a lapsed PhD physicist) is the community takes on a new formalism when it has to i.e. there are new results that can only be derived with the new formalism. A formalism that allows slightly better derivation of existing results does not attract attention. Twistors, Clifford algebras and other things seem to have not met this hurdle so far. Feynman diagrams, Riemannian geometry (General Relativity) did.
  - filmor 7y ago
    Clifford algebras are used whenever you use Gamma matrices, I think their a well established.
    - eigenspace 7y ago
      I think the person you're replying to was talking about Geometric Algebra, which is more of a project to reformulate all our current vector and tensor notation in terms of Clifford algebras and to move away from using specific representations of the algebra and instead just leverage the algebraic properties themselves. If you look at how most physicists use the gamma matrices, they are very reluctant to treat them as algebraic objects and rely heavily on their matrix representation. A proponent of GA would say this is like using the matrix [ 0 1 [-1 0] everywhere in your calculations instead of just using i and remembering that i^2 = -1. Sure, it's formally equivalent but you'd still miss out on a lot of the beauty of the complex numbers. For what it's worth, I have a soft spot in my heart from Geometric Algebra, but I think it still needs a lot of notational improvement before it'll ever see any real adoption. If you're curious about GA as it currently stands, I'd check out Geometric Algebra for Physicists by Doran and Lasenby.
- eigenspace 7y ago
  Just so you know, asking if twistors are the future in a thread about Feynman diagrams is like asking if smart watches are the future in a thread about cars. It's pretty off topic. That said, nobody really knows about the future of twistors in physics. Twistors have some really interesting algebraic properties that may eventually get leveraged in a main-stream theory but they could also just end up being a mathematical curiosity that never has any real impact. I think I feel pretty confident saying that twistors will never have the cultural / philosophical impact on physics that Feynman diagrams have had (for good or for ill).
andrewshadura 7y ago
Sadly, despite having read about them about a dozen times, I still don't understand how they work, or rather how to use them. Apparently, that's because of insufficient knowledge of the relevant part of physics.
- louthy 7y ago
  Feynman's own QED book is a fantastic introduction to QED and his diagrams https://www.amazon.co.uk/QED-Strange-Theory-Penguin-Science/dp/0140125051/ref=sr_1_1?crid=28BZ2MNIPKCP4&keywords=feynman+QED&qid=1557848107&s=gateway&sprefix=Feyn%2Caps%2C169&sr=8-1 https://www.amazon.co.uk/QED-Strange-Theory-Penguin-Science/...
  - guillaumec 7y ago
    Yes! I just finished it. Best vulgarization book I have ever read. Not a single equation, but still telling you exactly how the physics work, without any hand waving. I can't recommend it enough.
- mlevental 7y ago
  you need to understand perturbation theory in the context of qft. that's no small feat but since it's a pretty universally studied grad core subject there's a lot of material. this book was actually suggested to me here https://www.amazon.com/Renormalization-Methods-William-David-McComb/dp/0199236526 https://www.amazon.com/Renormalization-Methods-William-David... two good (Gentle) senior undergrad books are https://www.amazon.com/Student-Friendly-Quantum-Field-Theory/dp/0984513957 https://www.amazon.com/Student-Friendly-Quantum-Field-Theory... https://www.amazon.com/Field-Quantization-Walter-Greiner/dp/3540780483 https://www.amazon.com/Field-Quantization-Walter-Greiner/dp/... and then there's always griffiths https://www.amazon.com/Introduction-Elementary-Particles-David-Griffiths/dp/3527406018 https://www.amazon.com/Introduction-Elementary-Particles-Dav... note that you don't need to read this cover to cover if you're not interested in actually doing calculations. you can skim.
  - mhh__ 7y ago
sillyquiet 7y ago
PBS Space Time, as usual, has an excellent layperson's explanation of the diagrams. https://www.youtube.com/watch?v=fG52mXN-uWI https://www.youtube.com/watch?v=fG52mXN-uWI
alephu5 7y ago
I don't really know how you can understand Feynman diagrams without seeing how annihilation and creation operators act on the vacuum. They are the mathematical building blocks of qft; formally they are linear operators that represent the creation or annihilation of particles. If you apply an annihilation operator to a state containing no particles then the string gets deleted from your equation. Moreover if you swap the order of two operators you get an artifact (they're matrices after all), so a•b = b•a + c and so in qft calculations you swap your strings of operators around until you end up distilling it down to just a few non-vanishing artifacts that can be calculated. There's something called wick's theorem that the result of this process can actually be mapped onto a graph if you specify the initial and final state.
- mnl 7y ago
  Yeah, normal ordering and contractions, if we're expanding the fields in terms of such operators when doing canonical quantization using Fock spaces. There's a lot of stuff going on there. The fact that we can draw nice pictures representing the terms of a perturbation theory doesn't mean that you can skip a regular course on QFT to understand what practitioners mean when they use them. Again, not stressing this while showing tree level Feynman diagrams as if they were straight representations of particle interactions may give wrong ideas to the unsuspecting readers.
wizardforhire 7y ago
For anyone interested in a deeper (but not dense) introduction to how and why Feynman diagrams work I’ve found a lot of pleasure going through this blog post below. https://www.quantumdiaries.org/2010/02/14/lets-draw-feynman-diagams/ https://www.quantumdiaries.org/2010/02/14/lets-draw-feynman-...
- jarvist 7y ago
  Chapters 0 and 1 in this book by Mattuck are also a fantastic read for a general audience interested in what's going on 'under the hood'. https://www.amazon.co.uk/Feynman-Diagrams-Many-body-Problem-Physics/dp/0486670473 https://www.amazon.co.uk/Feynman-Diagrams-Many-body-Problem-... Feynman's own book 'QED: the strange theory of light and matter' is another good read, but strangely it is a bit lacking in illustrations. (And the illustrations that are there are a bit dry compared to Mattuck!)
xorand 7y ago
In case anybody interested in graphic lambda calculus, there are 5! X 5! = 14400 possible alternatives for the beta rewrite only. So it beats me why among all the possible calculi in CS the lambda calculus is special. I made a page which gives random alternatives http://imar.ro/~mbuliga/betarand.html http://imar.ro/~mbuliga/betarand.html
- danharaj 7y ago
  Because of the Curry-Howard-Lambek correspondence.
  - xorand 7y ago
    Agree, but I don't say that lambda calculus is not interesting, I say that there are so much more alternatives, unexplored. If we do the same with the IC of Lafont, I think that the possible (right patterns) of rewrites (which preserve the no of half-edges and nodes) are about 10^13. A conjecture, which I don't know if it holds water, is that analoguous to CA, Wolfram style, perhaps 1/3 (or anyway a significant proportion) of the 10^13 possible graph rewrite systems, alternative to IC, are Turing universal.
- xorand 7y ago
  An update: added more explanations about how these random variants of the beta rewrite are generated. You can see also the generated rewrites written in lambda calculus style, although they are graphical rewrites which go outside lambda calculus. I state again what I believe: that analogously with cellular automata, probably a big proportion of these random generated calculi are as rich as the original (Turing complete at least).
Myrmornis 7y ago
I really like Quanta and I'm disappointed that they are spending resources on creating video content (and presumably reducing the written content accordingly). I don't know if it's obviously elitist of me (to wish to deny people the opportunity to educate themselves via video if that's what they like) or absurd of me to think that it could possibly be elitist to try to retain the tradition of education-via-writing-and-reading. Anyway, I like reading quanta, and I don't watch videos unless they are extremely special (3b1b) or I'm in an odd mood.

219 points by furcyd 7y ago

Diagrams are very general and can be extrapolated from quantum field theory to deep learning, see: https://medium.com/@pmigdal/in-the-topic-of-diagrams-i-did-write-a-review-simple-diagrams-of-convoluted-neural-networks-6418a63f9281 https://medium.com/@pmigdal/in-the-topic-of-diagrams-i-did-w... "In particle physics, people use Feynman diagrams a lot. And these are nothing more or less than a graphical representation of summations and integrations over many variables. Also, as an ex-quantum physicist, I am a big fan of tensor diagrams [...]. You can think about it as the Einstein summation convention with no dummy indices (see Einsum in PyTorch)."

evanb 7y ago
You're probably better off with some kind of Penrose graphical notation https://en.wikipedia.org/wiki/Penrose_graphical_notation https://en.wikipedia.org/wiki/Penrose_graphical_notation
- galaxyLogic 7y ago
  or: https://www.quantamagazine.org/physicists-discover-geometry-underlying-particle-physics-20130917/ https://www.quantamagazine.org/physicists-discover-geometry-... “Why are you summing up millions of things when the answer is just one function?”
- stared 7y ago
  It’s the same.
  - evanb 7y ago
    I didn't see, for example, the circling-a-group for taking derivatives.
    - stared 7y ago
      Sure, there are other elements (derivative, (anti)symmetrization, lowering/raising indices). The core element of summation stays the same.
srean 7y ago
I was about to mention category theoretic connection but the post mentions Bob so I need not say anymore.
soVeryTired 7y ago
But... the Einstein summation convention is kind of fine in deep learning. The tensor manipulation in deep learning doesn't involve any of the gnarly contortions that physicists need to do like raising and lowering indices, taking covariant derivatives, or taking traces: and even that stuff moved along just fine without the need for diagramatic representations until the 1960s or so.

melling 7y ago

They promote their book after the video. Any opinions? “Alice and Bob Meet the Wall of Fire: The Biggest Ideas in Science from Quanta ” https://www.amazon.com/Alice-Bob-Meet-Wall-Fire/dp/026253634X https://www.amazon.com/Alice-Bob-Meet-Wall-Fire/dp/026253634...

aerovistae 7y ago

Frustrating because it doesn't actually tell you how they work.

zinclozenge 7y ago
Feynman diagrams are just pictorial representations of terms from a power series expansion of an overall 'master' equation representing a certain scattering process. A fairly simple one is electron positron annihilation, which yields two photons.
- ddavis 7y ago
  Just to expand on this; the series is usually called a Dyson series (https://en.wikipedia.org/wiki/Dyson_series https://en.wikipedia.org/wiki/Dyson_series). Dyson showing the connection between perturbation theory and Feynman's formulation was very important.
- gpsx 7y ago
  I also will expand on this. Quantum field theory is very difficult and we can't solve many problems. We can solve one in particular, free particles that do not interact. (By the way, this is like solving a simple harmonic osciallator.) Feynman diagrams use the solution to free particles as a basis - these are the lines in the diagram, like particles moving in time. Then, we add the interactions between the particles as a pertabative exapansion. This is what the parent comment refers to as the power series expansion. It is expanding in the powers of the interaction terms. As mentioned in the video, it is not quite as simple as this however. If you do this, you will get infinity as a result of the calculation. That is not a very good perterbation theory. However the real discovery of physcists from this time was renormalization. They found out you can sum many contributions from different terms in the exapansion, corresponding to different indiviaul feynmann diagrams, and you can make these infinities cancel out. What is magic is that when this process is done you can write an effective theory for the interactions that looks exactly like the original theory you started with, and only the values of the coeffiecients are changed a little. The magic involved here could be explained more, but in summary what it means is that the perterbation calculation you do is valid even thought it looks like it should be infinite. It also lets you make the simple analogy that the lines in the diagram are real and virtual particles rather than just the non-interacting approximation you starter with.

beezle 7y ago

Drawing Theories Apart is an excellent book on Feynman Diagrams. You don't have to be actively involved in nuclear or hep to understand but the material is not for the faint of heart and a decent background in those areas goes a long way. https://www.amazon.com/Drawing-Theories-Apart-Dispersion-Diagrams/dp/0226422674/ref=sr_1_5?keywords=feynman+diagrams&qid=1557847023&s=books&sr=1-5 https://www.amazon.com/Drawing-Theories-Apart-Dispersion-Dia...

hepnewb 7y ago

What about Twistors, are they the future?

musgravepeter 7y ago
My perception (as a lapsed PhD physicist) is the community takes on a new formalism when it has to i.e. there are new results that can only be derived with the new formalism. A formalism that allows slightly better derivation of existing results does not attract attention. Twistors, Clifford algebras and other things seem to have not met this hurdle so far. Feynman diagrams, Riemannian geometry (General Relativity) did.
- filmor 7y ago
  Clifford algebras are used whenever you use Gamma matrices, I think their a well established.
  - eigenspace 7y ago
    I think the person you're replying to was talking about Geometric Algebra, which is more of a project to reformulate all our current vector and tensor notation in terms of Clifford algebras and to move away from using specific representations of the algebra and instead just leverage the algebraic properties themselves. If you look at how most physicists use the gamma matrices, they are very reluctant to treat them as algebraic objects and rely heavily on their matrix representation. A proponent of GA would say this is like using the matrix [ 0 1 [-1 0] everywhere in your calculations instead of just using i and remembering that i^2 = -1. Sure, it's formally equivalent but you'd still miss out on a lot of the beauty of the complex numbers. For what it's worth, I have a soft spot in my heart from Geometric Algebra, but I think it still needs a lot of notational improvement before it'll ever see any real adoption. If you're curious about GA as it currently stands, I'd check out Geometric Algebra for Physicists by Doran and Lasenby.
eigenspace 7y ago
Just so you know, asking if twistors are the future in a thread about Feynman diagrams is like asking if smart watches are the future in a thread about cars. It's pretty off topic. That said, nobody really knows about the future of twistors in physics. Twistors have some really interesting algebraic properties that may eventually get leveraged in a main-stream theory but they could also just end up being a mathematical curiosity that never has any real impact. I think I feel pretty confident saying that twistors will never have the cultural / philosophical impact on physics that Feynman diagrams have had (for good or for ill).

andrewshadura 7y ago

Sadly, despite having read about them about a dozen times, I still don't understand how they work, or rather how to use them. Apparently, that's because of insufficient knowledge of the relevant part of physics.

louthy 7y ago
Feynman's own QED book is a fantastic introduction to QED and his diagrams https://www.amazon.co.uk/QED-Strange-Theory-Penguin-Science/dp/0140125051/ref=sr_1_1?crid=28BZ2MNIPKCP4&keywords=feynman+QED&qid=1557848107&s=gateway&sprefix=Feyn%2Caps%2C169&sr=8-1 https://www.amazon.co.uk/QED-Strange-Theory-Penguin-Science/...
- guillaumec 7y ago
  Yes! I just finished it. Best vulgarization book I have ever read. Not a single equation, but still telling you exactly how the physics work, without any hand waving. I can't recommend it enough.
mlevental 7y ago
you need to understand perturbation theory in the context of qft. that's no small feat but since it's a pretty universally studied grad core subject there's a lot of material. this book was actually suggested to me here https://www.amazon.com/Renormalization-Methods-William-David-McComb/dp/0199236526 https://www.amazon.com/Renormalization-Methods-William-David... two good (Gentle) senior undergrad books are https://www.amazon.com/Student-Friendly-Quantum-Field-Theory/dp/0984513957 https://www.amazon.com/Student-Friendly-Quantum-Field-Theory... https://www.amazon.com/Field-Quantization-Walter-Greiner/dp/3540780483 https://www.amazon.com/Field-Quantization-Walter-Greiner/dp/... and then there's always griffiths https://www.amazon.com/Introduction-Elementary-Particles-David-Griffiths/dp/3527406018 https://www.amazon.com/Introduction-Elementary-Particles-Dav... note that you don't need to read this cover to cover if you're not interested in actually doing calculations. you can skim.
- mhh__ 7y ago

sillyquiet 7y ago

PBS Space Time, as usual, has an excellent layperson's explanation of the diagrams. https://www.youtube.com/watch?v=fG52mXN-uWI https://www.youtube.com/watch?v=fG52mXN-uWI

alephu5 7y ago

I don't really know how you can understand Feynman diagrams without seeing how annihilation and creation operators act on the vacuum. They are the mathematical building blocks of qft; formally they are linear operators that represent the creation or annihilation of particles. If you apply an annihilation operator to a state containing no particles then the string gets deleted from your equation. Moreover if you swap the order of two operators you get an artifact (they're matrices after all), so a•b = b•a + c and so in qft calculations you swap your strings of operators around until you end up distilling it down to just a few non-vanishing artifacts that can be calculated. There's something called wick's theorem that the result of this process can actually be mapped onto a graph if you specify the initial and final state.

mnl 7y ago
Yeah, normal ordering and contractions, if we're expanding the fields in terms of such operators when doing canonical quantization using Fock spaces. There's a lot of stuff going on there. The fact that we can draw nice pictures representing the terms of a perturbation theory doesn't mean that you can skip a regular course on QFT to understand what practitioners mean when they use them. Again, not stressing this while showing tree level Feynman diagrams as if they were straight representations of particle interactions may give wrong ideas to the unsuspecting readers.

wizardforhire 7y ago

For anyone interested in a deeper (but not dense) introduction to how and why Feynman diagrams work I’ve found a lot of pleasure going through this blog post below. https://www.quantumdiaries.org/2010/02/14/lets-draw-feynman-diagams/ https://www.quantumdiaries.org/2010/02/14/lets-draw-feynman-...

jarvist 7y ago
Chapters 0 and 1 in this book by Mattuck are also a fantastic read for a general audience interested in what's going on 'under the hood'. https://www.amazon.co.uk/Feynman-Diagrams-Many-body-Problem-Physics/dp/0486670473 https://www.amazon.co.uk/Feynman-Diagrams-Many-body-Problem-... Feynman's own book 'QED: the strange theory of light and matter' is another good read, but strangely it is a bit lacking in illustrations. (And the illustrations that are there are a bit dry compared to Mattuck!)

xorand 7y ago

In case anybody interested in graphic lambda calculus, there are 5! X 5! = 14400 possible alternatives for the beta rewrite only. So it beats me why among all the possible calculi in CS the lambda calculus is special. I made a page which gives random alternatives http://imar.ro/~mbuliga/betarand.html http://imar.ro/~mbuliga/betarand.html

danharaj 7y ago
Because of the Curry-Howard-Lambek correspondence.
- xorand 7y ago
  Agree, but I don't say that lambda calculus is not interesting, I say that there are so much more alternatives, unexplored. If we do the same with the IC of Lafont, I think that the possible (right patterns) of rewrites (which preserve the no of half-edges and nodes) are about 10^13. A conjecture, which I don't know if it holds water, is that analoguous to CA, Wolfram style, perhaps 1/3 (or anyway a significant proportion) of the 10^13 possible graph rewrite systems, alternative to IC, are Turing universal.
xorand 7y ago
An update: added more explanations about how these random variants of the beta rewrite are generated. You can see also the generated rewrites written in lambda calculus style, although they are graphical rewrites which go outside lambda calculus. I state again what I believe: that analogously with cellular automata, probably a big proportion of these random generated calculi are as rich as the original (Turing complete at least).

Myrmornis 7y ago

I really like Quanta and I'm disappointed that they are spending resources on creating video content (and presumably reducing the written content accordingly). I don't know if it's obviously elitist of me (to wish to deny people the opportunity to educate themselves via video if that's what they like) or absurd of me to think that it could possibly be elitist to try to retain the tradition of education-via-writing-and-reading. Anyway, I like reading quanta, and I don't watch videos unless they are extremely special (3b1b) or I'm in an odd mood.