Core Theory T-Shirts

Way back when, for purposes of giving a talk, I made a figure that displayed the world of everyday experience in one equation. The label reflects the fact that the laws of physics underlying everyday life are completely understood.

So now there are T-shirts. (See below to purchase your own.)

Core Theory T-shirt

It’s a good equation, representing the Feynman path-integral formulation of an amplitude for going from one field configuration to another one, in the effective field theory consisting of Einstein’s general theory of relativity plus the Standard Model of particle physics. It even made it onto an extremely cool guitar.

I’m not quite up to doing a comprehensive post explaining every term in detail, but here’s the general idea. Our everyday world is well-described by an effective field theory. So the fundamental stuff of the world is a set of quantum fields that interact with each other. Feynman figured out that you could calculate the transition between two configurations of such fields by integrating over every possible trajectory between them — that’s what this equation represents. The thing being integrated is the exponential of the action for this theory — as mentioned, general relativity plus the Standard Model. The GR part integrates over the metric, which characterizes the geometry of spacetime; the matter fields are a bunch of fermions, the quarks and leptons; the non-gravitational forces are gauge fields (photon, gluons, W and Z bosons); and of course the Higgs field breaks symmetry and gives mass to those fermions that deserve it. If none of that makes sense — maybe I’ll do it more carefully some other time.

Gravity is usually thought to be the odd force out when it comes to quantum mechanics, but that’s only if you really want a description of gravity that is valid everywhere, even at (for example) the Big Bang. But if you only want a theory that makes sense when gravity is weak, like here on Earth, there’s no problem at all. The little notation k < Λ at the bottom of the integral indicates that we only integrate over low-frequency (long-wavelength, low-energy) vibrations in the relevant fields. (That's what gives away that this is an "effective" theory.) In that case there's no trouble including gravity. The fact that gravity is readily included in the EFT of everyday life has long been emphasized by Frank Wilczek. As discussed in his latest book, A Beautiful Question, he therefore advocates lumping GR together with the Standard Model and calling it The Core Theory.

I couldn’t agree more, so I adopted the same nomenclature for my own upcoming book, The Big Picture. There’s a whole chapter (more, really) in there about the Core Theory. After finishing those chapters, I rewarded myself by doing something I’ve been meaning to do for a long time — put the equation on a T-shirt, which you see above.

I’ve had T-shirts made before, with pretty grim results as far as quality is concerned. I knew this one would be especially tricky, what with all those tiny symbols. But I tried out Design-A-Shirt, and the result seems pretty impressively good.

So I’m happy to let anyone who might be interested go ahead and purchase shirts for themselves and their loved ones. Here are the links for light/dark and men’s/women’s versions. I don’t actually make any money off of this — you’re just buying a T-shirt from Design-A-Shirt. They’re a little pricey, but that’s what you get for the quality. I believe you can even edit colors and all that — feel free to give it a whirl and report back with your experiences.

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29 Responses to Core Theory T-Shirts

  1. Ray Gunn says:

    @Sean: “… feel free to give it a whirl and report back with your experiences.”

    So you’re requesting Peer Review?

  2. Ben Goren says:

    I’d be afraid to wear one unless I could actually explain the equation. To myself first, and then to a layperson.

    Um…Sean? Maybe you could put together a YouTube video doing exactly that? You’re wearing the shirt, somebody stops you on the CalTech mall, and you explain it all?

    …and I think a good way to short-circuit the tiresome objections would be by describing these as the rules of the game for humans. You can learn the rules of the game for chess easily, but not only does that not make you a grandmaster, it also doesn’t tell you what the chessboard is made of or how to carve the wood to make the pieces. But, whatever the board and pieces are made of, if you want to play chess with what you’ve got, those’re the rules. Your (Sean’s) own day job is figuring out if the pieces are carved from wood, cast from plastic, or even just simulated on a computer…and, while the answers to those questions will assuredly be mind-blowing, they won’t change the way the chess game is actually played.



  3. Bee says:

    I like the name Standard Model better. It’s a model. It’s not a theory. The theory is quantum field theory. Also, other fields have their core theories too…

  4. Ryan says:

    Done. Thanks!

  5. Neil says:

    “There a little pricey…” tch tch

  6. Elaine says:

    You are one of my favorite physicists….really…have read your books…buy you still needed an editor for this one…..I’m with Neil….”they’re”

  7. Ray Gunn says:

    Don’t know what Sean is implying, but these are the first shirts I’ve ever seen that go up to size 6XL.

  8. Antonio (AKA "Un físico") says:

    “The core theory”: what an awful name!. W looks like a functional that mixes gravity and quantum fields; but the key point in that formula is the cutoff momentum lambda: how do you renormalize that?.

  9. Shecky R says:

    probably make a few more sales if you had just collaborated with Sidney Harris 😉 :

  10. rob s says:

    I would love a lecture devoted to more in-depth discussions on Quantum Field Theory. My limited understanding of all this stuff went up immensely with some of your recent lectures that touched on it. I can’t find much of anything that gives a decent treatment of the subject while still accessible for non-physicist types. I’ve really learned a lot reading and listening to you, thank you.

  11. Toni Orrill says:

    I want a 2 larges. How do I order?

  12. Thanks so much for your order sir. We love scientists!

  13. Sean Carroll says:

    Thanks for making great shirts! The only real problem is an apparent lack of international shipping?

  14. Well, we CAN ship internationally, but of course it’s not free like our 10-day U.S. shipping and we cannot guarantee arrival times like we do in the U.S. This usually restricts us to U.S. customers which we very happily serve. We can quote international shipping if details on the shipping address is sent to

  15. Sean Carroll says:

    Got it. Will let people know.

  16. Daniel Kerr says:

    I don’t understand the Dg component, I don’t know what it means to integrate over metric configurations. Wearing this shirt in public would mean overselling my mental faculties I’m afraid.

  17. Pingback: This! I need to get this for myself! Core Theory T-Shirts | One Good Thing

  18. arch1 says:

    Daniel, how about: Until you understand Dg (and all the rest), Dg stands for Diogenes, the shirt is your lantern, and your search is for someone who can explain it to you?

  19. Grant B says:

    No long-sleeved options (besides sweatshirts)?

  20. James Gallagher says:

    Some people may be wondering if this W has anything to do with the W in the Boltzmann Epitaph on your blog header picture, S = k. log W.

    It doesn’t, but a T-Shirt with the Boltzmann epitaph would maybe be even more cool, since that will never be obsolete.

  21. Simon Packer says:

    Unless time become obsolete….

  22. Oss Ickle says:

    Are you and Jennifer the models? 😀

  23. Andrew Beeching says:

    To paraphrase Ben, I’d love to be able to confidently WEAR a shirt like this, but I think I’m too poor. The real/hidden cost is the 5-year MSc that it’d take for me to understand it sufficiently to be able to explain it without getting that unfocussed stare of confusion creep into my eyes… Any chance of explaining it with rocks? We geologists are much better at understanding things when they’re explained relevant to rocks 😉