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Why Feynman Diagrams Are So Important
- tlogan 10y agoOne simplistic thing I heard about Feynman Diagrams: Feynman Diagrams are important because they have 3 lines - not 4, 5, 6, 20, etc. The fact they have just 3 lines say something very very important about the nature and the world. Is the above correct?
- luaskldj 10y agoQED!
- willvarfar 10y agoQED as in Quantum Electro Dynamics? :)
- stared 10y agoFeynman diagrams are a series expansion, not unlike Taylor series. We do it for things which cannot be computed exactly. (I don't want to go if it is more "Nature", "our description of Nature" or "a box of numerical tricks we have mastered"... and frankly, I don't believe there is a strong distinction between these three.) 3 lines stand for the lowest non-trivial order (like 'x' in a Taylor series; '1' would be a line) - more complicated things can be made out of these.
- johncolanduoni 10y agoWhat exactly is it that it says about nature?
- Ygg2 10y agoFeynman's Diagram are just abstraction that manages to abstract away some elements of nature into a simplified version. Fetishizing them is like fetishizing the way Ancient Egyptians wrote their fractional numbers.
- coldtea 10y agoThat doesn't say much though. Something that is "just abstraction" can still be world-changing... In fact those are the most world-changing things (abstractions), the concrete stuff mostly derives from there...
- Ygg2 10y agoIf you focus too much much on current abstraction, you lose sight of better ones - that was the point of my previous post. I also don't agree concrete stuff derives from abstractions. You can make concrete stuff, using certain models/abstractions, but their behavior will always differ from the model. Because model aren't reality.
- solaris999 10y agoI heard a good rule of thumb to follow when drawing Feynman Diagrams is that the fewer lines there are, the more probable the occurrence of the event represented by the diagram. So at the simplest case, a single line representing an unchanging particle, is far far more likely than any two particle interactions (3 lines) and so on.
- misnome 10y agoRoughly, though it is actually the number of vertices and depends on the particles involved (obviously a diagram representing something very unlikely is less likely than some normal process)
- evanb 10y agoThis is true if the system you're trying to describe is weakly coupled. If the theory is strongly coupled, then in fact more and more complicated diagrams count more and more. In this case the method of Feynman diagrams because basically useless---in the case you describe you know you can get most of the answer from a simple calculation (of the simplest diagrams). But if more complicated diagrams count more (as in strong coupling) then you don't have a place to start, because whatever diagram you pick to start at I can make more complicated and be confident that my new diagram counts more than the pieces you've computed. In that case we need a different approach, the most generic of which is lattice field theory https://en.wikipedia.org/wiki/Coupling_constant#Weak_and_strong_coupling https://en.wikipedia.org/wiki/Coupling_constant#Weak_and_str... https://en.wikipedia.org/wiki/Lattice_field_theory https://en.wikipedia.org/wiki/Lattice_field_theory
- auntienomen 10y agoIn QED, each vertex has 3 lines attached to it: 2 electron/positron lines and one photon line. But in other quantum field theories, there are vertices with more edges. In QCD, for example, there are vertices where 4 gluons meet. In the Standard Model, there are vertices where 4 Higgs particles meet, and vertices where 4 electroweak bosons meet, and so on. The numbers 3 & 4 aren't really special. What's special is the numbers we assign to the edges. In 4 spacetime dimensions, any gauge boson (like the photon or gluon) gets the number 1. So does any scalar field like the Higgs. Fermions like electrons and quarks get the number 3/2. These numbers are important because you should never meet a Feynman diagram in a particle physics computation where the sum of these numbers at any vertex is larger than the spacetime dimension 4. This is a fairly deep fact about physics. Diagrams that violate these conditions are strongly suppressed at "low" energies (such as those accessible at the LHC). They contribute almost nothing to the Feynman diagram sum. Edit: This is Wilson's explanation of renormalizability, adapted to Feynman sums. It's the explanation for why physics is possible: The details of short distance physics (think Planck scale) can be very complicated, maybe involving lots of complicated Feynman diagrams. But at low energies, almost all of that complication averages out, and we can adequately approximate the laws of physics using simple ingredients.
- danbruc 10y agoThose labels seem related to the spin, is that right?
- auntienomen 10y agoIndirectly right. Those numbers are the scaling dimensions of the field operators. (Rescale your ruler by a factor f, and the fields will get multiplied by f to the scaling dimension.) These numbers are fixed by requiring that the kinetic energy density transform correctly under scaling. The form of the kinetic energy, in turn, depends on the spin of the field quanta (i.e., the particles).
- tgb 10y agoI recommend the first two chapters of Griffiths's Introduction to Elementary Particles which gives a very readable approach of showing which Feynman diagrams occur and what they mean. After that, the book gets more technical, but the first two chpaters give historical background and make it feel like playing with tinker-toys where you can just snap together various basic diagrams.
- ttctciyf 10y agoJohn Baez's Prehistory of n-Categorial Physics [1] has some interesting nuggets about Feynman diagrams, in the "Feynman (1947)" section. In particular, "The mathematics necessary for [interesting Feynman diagrams] was formalized later, in Mac Lane's 1963 paper on monoidal categories (see below) and Joyal and Street's 1980s work on 'string diagrams.'" In other words, Feynman diagrams were (or at least can be taken as) an early precursor of diagrammatic approaches in category-theoretic mathematical physics. The paper is really great for getting some context around these diagrams and a sense of the underlying mathematics, even for a category-theory ignoramus like myself, with a little "suspension of comprehension." 1: http://math.ucr.edu/home/baez/history.pdf http://math.ucr.edu/home/baez/history.pdf
- tempodox 10y agoBeing used to live in a world of cause and effect, I'm having a really hard time of getting my head around “random fluctuations” that seem to have an effect but no cause. That's about as illogical to me as the idea of a magnetic monopole. But then, > ...particles are merely bubbles of froth, kicked up by underlying fields. Photons, for example, are disturbances in electromagnetic fields. I can get behind this, even if only by way of misunderstanding. All deviation from nonexistence (Void) is a disturbance. All existence is one giant software bug in the fabric of Nothingness (if it could have something like fabric). That's why I've got to love Physics. To me, it's the most exquisite collection of brain-racking mysteries I can imagine (modulo the narrow bounds of my imagination, of course).
- T-A 10y ago> I'm having a really hard time of getting my head around “random fluctuations” that seem to have an effect but no cause So you're saying God does not play dice with the universe? :)
- Atwood 10y agoNope. Just Craps.
- russdill 10y agoPhysics (as far as we know) doesn't care about the direction of time. Cause and effect depends on a fixed direction of time.
- rubidium 10y agoPhysics does clearly "care" about the direction of time, because physics is a description of the physical universe. Dissipation, entropy, quantum measurement... etc. all have time as a key concept. Math may not care (and it's true that most of the fundamental physics equations are often time reversible). But the universe (and any experiment to date) clearly shows that time has a direction and the equations work in that direction.
- guard-of-terra 10y agoI'm kind of confused by Feynmann diagrams where a stray gluon flies off. What happens to it then? Where does it go?
- T-A 10y agoIt goes into a vertex involving some other particle with the appropriate "color" charge. That part is not depicted because it is not relevant to the process under study, as in "and then it goes off to die somewhere, I don't care where or how".
- nhatcher 10y agoThat's just a part of a bigger diagram. Due to color confinement you can't just have one gluon.
- guard-of-terra 10y agoThey have a diagram that emits a single gluon in the head of every particle physics article in Wikipedia. Is that a make-believe diagram? I couldn't expect that from them.
- nhatcher 10y agoIt is not a make-believe diagram. It is a completely valid diagram, but it i just part of something bigger. Also the two quarks in the diagram need to ultimately couple to something else. The "in" and "out" final states must be colorless. QCD is a extremely complex theory, one usually computes a piece of the puzzle and tries to extract physical information from that.
- untilted 10y agoJust to add to this: The part that comes this initial gluon emission (hadronization) is not very well understood since at this length scale the perturbative (i.e., feynman diagram) approach to QCD breaks down. See e.g. http://www.quantumdiaries.org/2010/12/11/when-feynman-diagrams-fail/ http://www.quantumdiaries.org/2010/12/11/when-feynman-diagra...
- beezle 10y agoA good read on the historical development and use of Feynman diagrams is Drawing Theories Apart The Dispersion of Feynman Diagrams in Postwar Physics https://www.amazon.com/Drawing-Theories-Apart-Dispersion-Diagrams/dp/0226422674 https://www.amazon.com/Drawing-Theories-Apart-Dispersion-Dia...
- ape4 10y agoHonest question, why does it take a super computer to come up with the animated simulation in the article. Doesn't seem that there are that many variables.
- ibab 10y agoGreat question! There is more to it than you can see in the animation. Because this is a quantum mechanical problem, it's not enough to take into account a single given field configuration at a given point in time, but we have to work with all possible field configurations at the same time. Because the number of configurations grows exponentially with the complexity of the system, we have to invest enormous amounts of memory and computing power into simulating it. Feynman actually wrote this pretty amazing paper on the topic of simulating quantum mechanical systems with computers: http://link.springer.com/article/10.1007/BF02650179 http://link.springer.com/article/10.1007/BF02650179. You should have a look, it's quite readable! (If the paywall is a problem for you, you should be able to find the paper elsewhere)
- ape4 10y agoThanks. Here it is without a paywall. https://people.eecs.berkeley.edu/~christos/classics/Feynman.pdf https://people.eecs.berkeley.edu/~christos/classics/Feynman.... Such a simple title ;)
- valarauca1 10y agoComplexity classes of algorithms. There are only 3 variables in a discrete logarithm problem but it takes super computers to solve. Same with prime number factorization. Number of inputs is completely unrelated to the time to solve depending on the algorithm being used to solve the problem.
- KenoFischer 10y agoThe simulation in question was created using Lattice QCD (which many people in the HPC world mostly know as a benchmark to optimize their compilers/systems on, but it's also a useful physics technique). Basically what you end up doing is discretizing spacetime on some grid, maybe e.g. 100x100x100x100 (not much larger than that last I checked or the problem becomes intractable even on very large computers) and then sample field configurations monte-carlo style (the way to do it is actually really clever - it turns out that there is a mathematical trick that can take you from the description of your theory right to a distribution from which you can draw your field configurations). The number of fields is decently large (some discretization introduce extra auxiliary fields for every physical one) and in general you need to consider the entire field configuration to compute an observable. Then do that a few billion times (to bring down statistical error) at a couple different lattice spacings (to be able to extrapolate to the continuum limit) and you quickly end up with a very large computations. There is a number of clever ways to reduce the amount of computation required, but in general it's a very different problem. Hope that makes some sense. I had looked into this in detail about two years ago, but looking back, I feel like I only know every other word in my write-up ;).
- madengr 10y agoWhat does he mean by "gravity responds to all kinds of energy"? What about photons?
- egjerlow 10y agoyes, those too. Light is influenced by gravitational fields!
- de_Selby 10y agoIs it not more a case of space-time being influenced rather than light?
- madengr 10y agoYes, I would think. Gravity warps space, and light just follows a line in space, which is a curve in space-time. But since gravity can affect light, does light (energy) affect gravity?
- auntienomen 10y agoYes. The gravitational field couples to any energy; it doesn't care what the source is. Light carries energy, so the gravitational field responds to it.
- OscarCunningham 10y agoYeah, in physics if A affects B then B always affects A. This idea was first formalised as Newton's Third Law.
- egjerlow 10y agoMore formally, a photon field contributes to the so-called stress-energy tensor,which acts as the 'source' of gravity in the Einstein equations, thus affecting gravity, as you say.
- XaspR8d 10y ago
- vanderZwan 10y agoMaybe a strange question, but could one of the stumbling blocks be that we still have a lot of work to do on the mathematics of infinities? I mean, saying that a positive and negative infinity might "cancel" sounds like that's where the maths gets murky.
- ssivark 10y agoIt sounds murky because we were being silly the first time around. The physically relavant quantity was always the sum of all those contributions and we decided to (arbitrarily, in the grand scheme of physics) split things up under some scheme. So, in hindsight, the positive and negative infinities were artificially manufactured by our segregation scheme... there's not much to be bothered about in that regard. That might still mean that there's more to be understood regarding notions of infinity or the convergence of amplitudes in quantum field theory.
- darkmighty 10y agoAs an example (not sure if applicable), you could do some calculation and get an alternating series as the result: R = 1 - 1/2 + 1/3 - 1/4 ... If you "explain" the positive part as being contribution from field A, and the negative part as a contribution from field B, both would be infinite, but the reality might be that splitting them is nonsensical.
- arcanus 10y agoFull disclosure: I don't work in particles but have solved Feynman integrals for class work. Renormalization is indeed 'black magic'. But I don't think it is due to our limited mathematical knowledge. In my experience in mathematical physics, singularities appear when you have incomplete modeling ansatz, and so in this sense renormalization would just be a 'hack' that is necessary because of writing down imperfect equations. In other words, formulating the problem a different (and closer to truth) way would eliminate these infinities. I know some extensions of the standard model (string theory, in particular) do not have cutoff scales. But that is largely beyond my knowledge base.
- gaze 10y ago
- jballanc 10y agoWell for one thing without them we wouldn't have Penguin diagrams! (https://en.wikipedia.org/wiki/Penguin_diagram https://en.wikipedia.org/wiki/Penguin_diagram)
- lisper 10y agoAnother cool use of diagrams in abstract algebra: https://graphicallinearalgebra.net https://graphicallinearalgebra.net
- mlpinit 10y agoThis is a fantastic resource! The writing is really enjoyable.
- tmaly 10y agoIf you have read any of the books like Surely Your Joking, the first thing that sprung to my mind were those diagrams he drew on napkins
- justinpombrio 10y agoIs there a list somewhere of all of the basic particle interactions we know of, represented as Feynmann diagrams? My understanding is that there is a small, finite number of them; it would be neat to see them enumerated.
- gpsx 10y agoMaybe someone reading this can enlighten me on the utility of thinking about virtual particles in the vacuum. This is not related that directly to the article, but it is mentioned in it. Feynman diagrams are a perturbation theory expanding around a problem we can solve - non-interacting free fields. The lines in the diagram represent the particles in the free theory, not the interacting theory. Renormalization does allow us to make some correspondence between the two, but that can only be taken so far, at least to my understanding. (And perhaps this is my limitation.) There are lots of vacuum diagrams, for example. These represent the difference between the vacuum in the free theory and the interacting theory. That does not mean there is frothing going on in the interacting theory that is not in the free theory. The vacuum wave function is still a combination of field configurations each with an associated amplitude density. (And, relating to the article, of course, this creates an associated non-zero vacuum energy.) It looks just like the vacuum in a particle Schroedinger equation model, but just a lot more degrees of freedom. What are the virtual particles? I'd appreciate if someone could explain what people mean and why when they talk about these.
- KenoFischer 10y agoThere is many ways to think about virtual particles. From a particle point of view one can think of it as quantum mechanics allowing you to create a high energy particle for a short amount of time, even if that would not be allowed classically. From a field theory point of view, you can have excitations in the fields that are not sufficient to be a particle, but can still interact locally.
- gpsx 10y agoI was looking for an explanation of why the lines of a Feynman diagram are called virtual particles when they are really particles in the unperterbed (or free) model. So why do you think of this as creation of a particle for a short amount of time?
- KenoFischer 10y agoGenerally if you look at the Feynman diagram for an interaction, you'll have some number of external legs which one thinks of as physical particles, as well as a number of interactions. The lines between the interactions may be particles whose mass exceeds the total amount of energy of the incoming particles, so they obviously can't be real. They are thus generally called virtual (or off-shell particles). How one can think of this is what I tried to address in the original response.