8 ms·
The Deconstructed Standard Model Equation
- quirkot 10y agoWell, when you put it like that... suddenly it all makes sense :p Seriously though, very neat to see the actual equation used to model the universe.
- drauh 10y agoWhen I was a wee undergrad, a grad student office-mate had printed out these equations and posted them on the office door. He wrote on it: The simplicity of the Standard Model. Or words to that effect; this was in the condensed matter physics division.
- andrepd 10y agoI've been banging my head on QFT and the Standard Model for enough time now that I can actually glimpse more or less what those terms actualy mean, as in , I can translate them into words. It's almost like learning a new language! Pretty awesome. Still, despite all this complexity, we still have several minor and major theoretical gaps to fill. Exciting times!
- alanbernstein 10y agoI, as a layman with basic college physics knowledge, and passing knowledge of the standard model, want to understand the meaning of those terms. Do you know how I can go about that? Ideally, with something a little less dense than a textbook.
- drauh 10y agoI have a PhD in physics, though not particle physics. QFT was required, since the methods appear all over in condensed matter physics. Unfortunately, there is no real shortcut to being able to understand those terms except by studying one of the standard texts. And, physics being what it is, you can expect a pretty hard slog because the texts will assume you know first quantization back and forth. Add to that, it's not just QFT but the domain-specific standard model knowledge. Dealing with QM requires PDEs, linear algebra, a fair bit of applied analysis (real and complex). Dealing with QFT requires that, plus learning a bunch of new techniques with the typical hand-wavy rigor of physics. (Hand-wavy compared to math.) If you want to get a feel of the Standard Model without knowing QFT, the text I used when I took senior-level particle physics is great: Introduction to Elementa Particles, by David Griffiths. (He's an excellent writer, btw; I recommend any of his physics books). As for the standard texts for particle physics, I'm afraid I've been out of the loop for too long to remember what books were used.
- abecedarius 10y agoA related question: Feynman's popular book QED claims to explain quantum electrodynamics enough that you could almost do calculations with it, just ridiculously inefficiently. After reading it, I can't: the details left out, I can't easily fill in from the grad-level texts, even with a pretty decent undergrad physics background. Shouldn't it be possible to explain QED to a programmer using a literate program? (Again, an inefficient one.) Was Feynman exaggerating? Or is it just the tininess of the market of programmers who want to understand what QED is really about who aren't out to become professional physicists? (For others, QED is the part of the standard model about electrons and light -- the most relevant part for everyday physics and apparently the simplest part too.)
- namin 10y agoApart the character of physical laws and the easy pieces, what's the gateway book to understand feynann more advanced work?
- abecedarius 10y agoI don't really know, because I don't understand the more advanced work like QED. But http://www.feynmanlectures.caltech.edu/I_toc.html http://www.feynmanlectures.caltech.edu/I_toc.html is one of my favorite books ever.
- ars 10y agoIf you are looking for the book, the name is "Introduction to Elementary Particles" (not Elementa which is a typo).
- tgb 10y agoI was going to recommend the Griffiths book as well. The first two chapters are readable without any demanding mathematics. The latter ones require more work, but build up nicely.
- donovanr 10y agoZee's QFT in a Nutshell is a very readable, high-level view of what's going on in QFT. Griffiths' book is his one text I haven't read, but I love his others so much I can't help but second the recommendation.
- andrepd 10y agoI'm afraid there really isn't another way around. This stuff is just very difficult. If you want to understand the standard model you need to understand Quantum Field Theory, and to understand Quantum Field Theory you need to understand Quantum Mechanics, and to understand that you need to understand classical hamiltonian and lagrangian mechanics, etc etc, and to understand all that you need lots of mathematical notions, so... There really isn't a fast way but to study the standard texts.
- proc0 10y agoCan you recommend how to get started on this? Like beginner links or something? I'm currently just a physics noob, but have some of the basic concepts of quantum theory down. I would love to just have a basic grasp of that monstrous equation.
- nhatcher 10y ago"Quantum Field Theory for the Gifted Amateur" by Stephen Blundell and Tom Lancaster. It might be right for you if you know the basics of Quantum Mechanics and electromagnetism
- MengerSponge 10y agoI love how everybody uses Gutierrez's typesetting. If I ever meet him and have the presence of mind to put two and two together, I'll buy him a beer. If you want the TeX source for your own purposes, it's here: http://nuclear.ucdavis.edu/~tgutierr/files/stmL1.html http://nuclear.ucdavis.edu/~tgutierr/files/stmL1.html
- hossbeast 10y agoWhat is the sum of terms supposed to be equal to?
- dnautics 10y agoAnything. It's a state function measuring energy, so pick a number and keep it the same. Usually zero is a good choice.
- deleted 10y ago[deleted]
- dhoe 10y agoIt's a Lagrangian, so this is the function nature tries to minimize. In common everyday systems, the Lagrangian is kinetic energy minus potential energy.
- Chrisatorain 10y agoI visit this blog first time and inspire by this good stuff work. Incredible post keeps up posting such great information. You can use this <a href="http://www.clazwork.com">best http://www.clazwork.com">best essay writing service</a> for any kind of academic writing work.
- adrianratnapala 10y agoTrue, but with nitpick that it is the Lagrangian density so nature minimises its total over a region of 4-space. And with the more important nitpick that this Lagrangian is a quantum operator rather than a number. In some sense nature does try to minimise it even so, but I never got an intuitive grasp on what that sense is.
- cygx 10y agoAnd with the more important nitpick that this Lagrangian is a quantum operator rather than a number. I don't think that's true when dealing with the formulation in terms of path integrals as we do here...
- partycoder 10y agoI haven't seen an article so math intensive in a while... since I saw this one: http://www.scholarpedia.org/article/Bayesian_Ying_Yang_learning http://www.scholarpedia.org/article/Bayesian_Ying_Yang_learn...
- adrianratnapala 10y agoThe article displays a big equation somewhat carefully. But it doesn't have any maths.
- ars 10y agoAm I correct in understanding that this takes every kind of interaction that particles can have, and simply adds them all together? How does it deal with some particles only interacting in certain ways and not others? Is the user of the equation supposed to make sure to enter zero for those terms, or does the equation capture that knowledge as well?
- sprash 10y agoIf you apply an operator of such an interaction to the Lagrangian the equations of motions automatically return zero (e.g. similar to a derivation of a constant).
- T0T0R0 10y agoGiven the world we live in, right now, why does mathematics continue to insist on minified expressions? Given the option, most development teams would choose to read and write against verbose source code, rather than scrape obfuscated variables and method signatures out of a minified, transpiled, compressed package. So why do we continue this archaic practice of obscure, inscrutable symbols in mathematics? Cultural inertia? The cycle of madness must end!
- vlasev 10y agoYour assessment is somewhat unfair and kind of misguided. The differences between math and programming are quite large. I think there are two main reasons for why we have symbols in math and more verbose expressions in programming. 1. Medium. Math is mainly done with pen/pencil on paper, or chalk on a blackboard, or marker on a whiteboard. Programming is mainly done with keyboard on a computer. Those media are quite different. In a way, it's about ease of input - it's easier to write out a longer name with keyboard than with a pen. 2. Nature of the activity. A lot of math boils down to manipulating expressions given rules. It involves a lot of scratch work with a lot of backtracking and trying new things. A lot of programming boils down to easily reading and writing code and reasoning about how things work. Imagine writing "integral from a to b of f(x) dx" or "integral(f(x), x, a, b)" by hand a hundred times vs in an IDE and you'll see what I mean.
- mirosam 10y agoYour comment shows a common misunderstanding of what mathematicians are trying to do. Modern mathematical notation is not obfuscated, it is in fact making the object being described much easier to perceive for humans. Explaining the equation you see in English words is what every physics book does, however the equation itself represents a concept that is not human. It comes from an alien universe of symmetries and relations and we have spent centuries to arrive at the current way of writing these down in a way which makes them easy to work with. You can formulate the solution to a quadratic equation as: The negative linear term, added and subtracted from the square root of the quantity which is the difference between the square of the linear term and the product of four times the constant term and the quadratic term, all divided by twice the quadratic term. Modern mathematicians write: x = (-b +- sqrt(b^2 - 4ac)) / 2a The difference is night and day. You cannot remove the essential complexity from a problem. You can only try to get close to its representation.
- proc0 10y agoIf I was a physics phd working on QFT, I would tattoo this equation as a sleeve. Unfortunately, as a mere programmer, I could never pick a sufficiently perfect code snippet to use. I would constantly look at it and try to refactor it.
- sdenton4 10y ago"Note: ...In Gutierrez’s dissemination of the transcript, he noted a sign error he made somewhere in the equation. Good luck finding it!" Anyone see the flipped sign?
- lordnacho 10y agoThere must be some smarter notation that captures the model with less verbosity? Also, how on earth did various people put this together? Is there a good book about it?
- deleted 10y ago[deleted]
- zbyszek 10y agoThere is; the equation on the CERN mug in the photo is an example. For example, the gluon Lagrangian (Section 1) may be more compactly written -1/2 Tr F_{\mu\nu} F^{\mu\nu} for a suitably defined F. Or further abbreviated to something like L_g. It just depends on how much detail you need to expose.
- nonbel 10y ago"To clean up these redundancies, theorists use virtual particles they call ghosts. This part of the equation describes how matter particles interact with Higgs ghosts, virtual artifacts from the Higgs field. [...] This last part of the equation includes more ghosts. These ones are called Faddeev-Popov ghosts, and they cancel out redundancies that occur in interactions through the weak force." So the second half this equation is used to describe invisible things needed to cancel out wrong stuff from the first half? Sounds ad hoc to me, were these "ghosts" predicted by anyone beforehand? Even if not, as a model it can still be useful though.
- cygx 10y agoFaddeev–Popov ghosts in particular are artifacts of covariant quantization in the path integral formalism. One way to think of them is as a kind of Jacobian determinant of the transformation to physical degrees of freedom.
- auntienomen 10y agoIt doesn't really make sense to ask if the ghosts were predicted. They're mathematical artifacts of a particular computational formalism. There are other computational formalisms for QFT which don't feature ghosts, and which give the same answers for any observable quantities.
- psi-squared 10y agoThe two types of "ghosts" here are very different. In both cases, though, they're mathematical artefacts rather than anything "physical", but I'll try to explain them as well as I know. Disclaimer: The most advanced physics I've done was a first course in this stuff, so I might be wrong about some things. For what they're calling "Higgs ghosts": There are two different ways of describing the electromagnetic and weak forces, and which one is best depends on how much energy the particles you're dealing with have. At really high energies, it makes the most sense to talk about a combined "electroweak force", described in terms of four fields with 2 components each (often called W1, W2, W3 and B), and one 4-component field (the Higgs field). In contrast, at low energies, it makes more sense to talk about the electromagnetic force, with one 2-component field (y), and the weak force, with three 3-component fields (W+, W-, Z0) and a 1-component field (the Higgs field, again). So, where did the other three components of the Higgs field go? Well, we just rearranged things - if you check, the total number of components stayed the same. There are various names for this rearrangement, and I haven't seen this one before, but I guess they're calling these "missing" components "ghosts". As for the other type, the Faddeev-Popov ghosts, those are more obviously mathematical artefacts. Normally, you'd start by writing down a "physical" Lagrangian ("physical" here meaning something like "written in terms of actual physical fields"). But it turns out that you can't actually calculate with the physical Lagrangian. So you have to rewrite it in a (mostly) mathematically-equivalent way, which involves extra fields. These fields come along with extra rules which basically say "no state you can actually measure involves the ghost fields in any way". Really, they're just there as a calculational aid and aren't physically "real", and they're called "ghosts" to reflect that. Hope that's at least vaguely comprehensible, it's difficult to explain this stuff without assuming a lot of background knowledge.
- dzdt 10y agoI would love to see this article, about 5-10 times longer. Dig one level deeper into what the notation means, how it relates to the zoo of fundamental particles, etc. Compare and contrast the sections dealing with different forces/particles. Talk something about the history of how this came out as a unification of models for gravity, electricity and magnetism, weak force, strong force.