Out-Einsteining Einstein

By Sean Carroll | November 8, 2006 8:41 am

Among my recent peregrinations was a jaunt up to Santa Barbara, where I gave two talks in a row (although in different buildings, and to somewhat different audiences). Both were about attempts to weasel out of the need for dark stuff in the universe by trying to modify gravity.

The first talk, a high-energy theory seminar, was on trying to do away with dark energy by modifying gravity. I used an antiquated technology called “overhead transparencies” to give the talk itself, so there is no electronic record. If I get a chance sometime soon, I’ll post a summary of the different models I talked about.

The subsequent talk was over at the Kavli Institute for Theoretical Physics. There was a program on gravitational lensing going on, and they had asked Jim Hartle to give an overview of attempts to replace dark matter with modified gravity. Jim decided that he would be happier if I gave the talk, so it was all arranged to happen on a day I’d be visiting SB anyway. (Don’t feel bad for me; it was fun to give the talks, and they took me to a nice dinner afterwards.) I’m not really an expert on theories of gravity that do away with dark matter, but I’ve dabbled here and there, so I was able to put together a respectable colloquium-level talk.

MOND slide

And here it is. You can see the slides from the talk, as well as hear what I’m saying. I started somewhat lethargically, as it’s hard to switch gears quickly from one talk to another, but we built up some momentum by the end. I started quite broadly with the idea of different “gravitational degrees of freedom,” and worked my up to Bekenstein’s TeVeS model (a relativistic version of Milgrom’s MOND), explaining the empirical difficulties with clusters of galaxies, the cosmic microwave background, and most recently the Bullet Cluster. We can’t say that the idea is ruled out, but the evidence that dark matter of some sort exists is overwhelming, which removes much of the motivation for modifying gravity.

The KITP is firmly in the vanguard of putting talks online, both audio/video and reproductions of the slides. By now they have quite the extensive collection of past talks, from technical seminars to informal discussions to public lectures. Some recent categories of interest:

On Friday I’ll be at Villanova, my alma mater, giving a general talk to undergraduates on what science is all about. I’m not sure if it will be recorded, but if the yet-to-be-written slides turn out okay, I’ll put them online.

  • http://leisureguy.wordpress.com LeisureGuy

    Why is a gravity variant needed to do away with the need for dark matter? I keep seeing references at least one study (this one) that showed that using general relativity sufficed to explain the anomalies of galactic rotation, which exist only if one uses Newtonian gravity. Why isn’t general relativity enough to do away with the need for dark matter?

  • http://countiblis.blogspot.com Count Iblis

    Interesting talk!

    B.t.w., you forgot a factor Squareroot(-g) in the integrands :)

  • Belizean


    Thank you for an excellent presentation. A great way to start my day.


    Did you actually listen to Sean’s talk?

  • Haelfix

    I went to one of these string wars seminars recently and had to leave halfway through. Seriously, this topic has been beaten to death and is thoroughly boring and a great way to waste productive time. It isn’t like it hasn’t been discussed ad nauseum in every physics department coffee table, private discussions, blog posting, book review and now the public sector for the last oh five years or so (even longer if you were a QG insider or had any good old fashioned argumentative tendancies)

  • collin

    Ah, the beauty of Trackbacks.

    LeisureGuy– See this previous post by Sean which explains why that model is no good.

  • http://vagbladet.no Frodo

    Indeed. And why would anyone write “travels” when “peregrinations” is perfectly acceptable. No, this is not snark. I’m a Norwegian-speaker, and I always enjoy learning new English words.

  • http://countiblis.blogspot.com Count Iblis

    Frodo your ancestors, the Vikings, had a lot of influence on the English language, see here

  • Belizean


    What does your comment have to do with the topic of this thread?

  • http://vagbladet.no Frodo

    Hi, Count, yes I know they did. Not only verbs and nouns, but more surprisingly pronouns and prepositions (normally considered “closed” classes of words). Also, some minor grammatical/syntactical influence. But most Norse words in current English are very common words (like, say “shirt” and “skirt”, both from the Norse “skyrta”, meaning “skirt”, so I somehow doubt that “peregrinations” would be among them.) One curious story, though: The word “bag” was adopted in Britain during the Viking invasion. It later disappeared from the Scandinavian languages. But it returned during the 1960s as a loan word from English. And now it’s one of those high frequency everyday words that most people here think of as thouroughly Scandinavian. Funny how things work.

  • andy.s

    So you invaded England and lost your bag, and then you later borrowed the bag back from the English?

    I’ll bet the English were all, like, “That’ll teach you to invade us, can’t even keep track of your own bag.” and you guys were like, totally embarrassed.

    Yes, I do have a couple of teenage nieces, how did you know?

  • andy.s

    On a slightly saner, note, Sean, is TeVeS renormalizeable? Haven’t seen the talk yet; it’ll have to wait till after work.

  • http://valatan.blogspot.com bittergradstudent

    TeVeS has the same power counting issues that gravity has–it does add new fields that interact with the gravitational field, but I really, really doubt that it is renormalizable.

  • Haludza

    indeed, I think it’s arguable as to whether TeVeS is modified gravity at all really. There’s a paper out there that shows it’s equivalent to normal GR + just a vector field with an odd kinetic term. Where does modified gravity end and ‘another field’ begin?

  • http://brahms.phy.vanderbilt.edu/~rknop/blog/ Rob Knop


    One thing you may want to do with your slides is indicate whether or not others can reuse them. I’ve put many (though not all) of the slides of public-outreach (and occasionally the slightly more technical) talks I’ve done online here:


    Of course, it’s infinitely messy, because I’ve borrowed some graphics from papers and the like where re-use legalities aren’t obvious, but I sort of hope I’m ducking in under fair use for educational purposes. Howver, there are also a lot of slides that I made myself, and in putting the talk slides online, I indicate that they may be used under a Creative Commons license.


  • http://brahms.phy.vanderbilt.edu/~rknop/blog/ Rob Knop

    OK, I know I have a PhD in Physics and pretend to know things about cosmology, but I have one majorly clueless question :

    The slide you quote above says that the Graviton is a spin-2 particle that couples to the metric.

    Particles in QFT are excitation of fields. I was under the impression that the metric was the field that you try to quantize in order to make gravity. In other words, gravitons should be excitations of the metric, at the very basic level of my understanding. Given that, I’m confused about the “couples” terminology.

    Do I have it all wrong?


  • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

    Haludza– you’re exactly right. There is no hard-and-fast distinction between “modified gravity” and “new degrees of freedom added to GR.” Unless you wanted to throw out the whole idea of a dynamical metric, which is probably a non-starter.

    Rob — people are welcome to use my slides. I’d be happiest if they acknowledged stealing from me, but I’m not always so good about that myself.

    It’s the energy-momentum tensor that the gravitons couple to, not the metric. You’re right, coupling to the metric is automatic. Gravitons are just small perturbations of the metric around a smooth classical solution.

  • http://brahms.phy.vanderbilt.edu/~rknop/blog/ Rob Knop

    What an idiot I am. I saw T^mu^nu, and for some reason my brain substituted in g^mu^nu.




  • andy.s

    another question I had about TeVeS was, is this scalar-vector-tensor deal some kind of multivector, like in Grassman Algebra?

  • anonymous tv junkie

    This is pretty much off-topic, but an amusing appearance of physics in pop culture: on this week’s episode of Gilmore Girls, Lorelai and Christopher visit Yale on parent’s weekend and attend a talk called “The Extravagant Universe.” They hear about supernova measurements giving evidence for accelerated expansion, and while Lorelai is distractedly writing text messages on her phone, Christopher seems interested and asks “How can we tell if dark energy is really the same thing as a cosmological constant?” I was impressed to see an accurate description of interesting physics on TV.

    The episode also featured a French restaurant called Chez Zinn-Justin, but I doubt that was an intentional physics reference. :-)

    The show is not so great these days, but the physics references compensated.

  • Aaron Bergman

    I know who wrote that scene, and I’d bet it’s all intentional.

  • Aaron Bergman

    It’s probably not too hard to figure out the author by looking at the writing credits on the episode, now that I think of it.

  • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

    Bob Kirshner’s daughter is a writer for the show. He wanted to play the professor role himself, but they hired an actual actor for the part. (Although he did claim that, because it was supposed to be a Yale audience rather than a Harvard one, they “used shorter words.”)

  • Belizean

    It’s the energy-momentum tensor that the gravitons couple to, not the metric. You’re right, coupling to the metric is automatic. Gravitons are just small perturbations of the metric around a smooth classical solution.

    Gravitons, unlike photons, also couple to their own energy. I suppose you could make this self-coupling look as though it’s sourced by a stress-energy tensor, but it really isn’t.

  • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

    In the linearized theory (which is where talk of “gravitons” makes sense), gravitons couple precisely to their own energy-momentum tensor. Then you notice that such a coupling contributes to the energy-momentum tensor, so you add another term, and start an infinite series, which (as was discovered by a bunch of people in the 60’s) gives you the full nonlinear Einstein equation.

  • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

    andy.s — “tensor-vector-scalar” isn’t a new kind of mathematical beast; it just refers to the fact that the theory includes a dynamical tensor field, a vector field, and a scalar field.

  • Belizean

    In the linearized theory (which is where talk of “gravitons” makes sense), gravitons couple precisely to their own energy-momentum tensor. Then you notice that such a coupling contributes to the energy-momentum tensor, so you add another term, and start an infinite series, which (as was discovered by a bunch of people in the 60’s) gives you the full nonlinear Einstein equation.

    You’re right. Except that the gravity-self interaction contribution to the energy-momentum tensor gets moved over to the left side of the Einstein equations. It is not part of ususal definition of this tensor (which is restricted to the matter contribution).

    So when you say that gravitons couple to energy-momentum, you mean that in the broad sense of an energy-momentum tensor augmented by a gravitational-self interaction piece. [This is a just a silly quibble on my part that boils down to whether “energy-momentum” = “standard energy-momentum tensor”.]

  • Shantanu

    Sean, what’s the latest story on apsidal motion of DI Hercules and its observed discrepancy with GR? I can’t recall any recent papers on this? Since you have worked on this system ,
    could you give a brief overview of what accoridng to you (and also the general
    community) is the consensus on this issue?

  • http://leisureguy.wordpress.com LeisureGuy

    Hi, Belizean. No, I didn’t listen to the talk. Indeed, I probably would not have understood it. I came across this posting on the Web, and asked the question that’s been bothering me. I figured asking a question was okay, and maybe I’d get an answer.

    And indeed I did. Thank you, Collin. I much appreciate the pointer.

  • Pingback: Coast to Coast | Cosmic Variance()

  • Rod Hartman

    I’ve had a thought for quite a while that the universe may expand and contract, rather than expand endlessly – and we wuld never be able to tell which part of the cycle we were in.

    In a contracting universe, bodies and matter would be accelerating toward the center of the universe, but bodies further out would be going slower. This would give the appearance that from any observation point, bodies closer to the center would be moving faster – giving the illusion of an expanding universe. And bodies further out would be moving slower – also giving the illusion of an expanding universe.

    So as the universe expands, stops, and then collapses on itself we would have have an endless series of “big bangs”. Is this possible??

  • Sonny

    Dark matter is exactly that it is dark to the naked eye
    Because it is faster than the speed of light and can only be observed through Gravity
    As an object approaches the speed of light, it condenses and becomes invisible
    Undetectable is more like it. Matter is neither created nor destroyed.
    Dark matter can pass through galaxies, because it is moving just past the speed of light.
    It is hard to detect light in the dark
    Dark matter and light enjoy a dance that to some is like doing the two – step for others the waltz
    Just fast enough to be seen by gravitation but not fast enough to be observed without.
    So we do see shapes and shadows, without light and dark matter we would not.
    The reason dark matter appears slow because of the observation point.
    Gravity is a bit more substantial than we thought
    A famous man once stumped many with a theory called relativity
    Dark matter too will be bent by space we just haven’t seen that effect yet.
    I think maybe Einstein was on to something…

    Einstein’s theory still holds. It is all relative.

    Smokyjinx 2006

  • Sonny

    Use Germanium Calthrates (university of Houston) to capture dark matter at cryogenic temperatures. More surface area equates to more particles seen. Gotta slow down the train to see it.

    Smokyjinx 2006


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About Sean Carroll

Sean Carroll is a Senior Research Associate in the Department of Physics at the California Institute of Technology. His research interests include theoretical aspects of cosmology, field theory, and gravitation. His most recent book is The Particle at the End of the Universe, about the Large Hadron Collider and the search for the Higgs boson. Here are some of his favorite blog posts, home page, and email: carroll [at] cosmicvariance.com .


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