Friday, August 14, 2009

Are Effective Field Theories The Way To Go?

For those who don't know, probably the biggest problem in theoretical physics, "the holy grail" if you will, is the fact that gravity causes physics to blow up in certain limits. Theories that do not blow up in these limits, are called renormalizable and are therefore considered "good theories". However, no theory containing gravity proposed yet is renormalizable, or free from the "blow ups" in certain limits.

(I mean theories that have made testable predictions. String theory, for example, is renormalizable, but hasn't been confirmed in experiment. This is fundamentally the reason why string theory is so popular among some. It contains gravity, the other forces and is renormalizable)

Enter effective field theory! Theorists have begun to wonder if we should care if a theory is renormalizable or not. Sweeping a lot of details under the rug, effective field theories are those theories that blow up in these limits, but as long as you stay away from those limits you get new testable predictions.

Steven Weinberg is a Nobel Prize winning physicist, who likes string theory, but recently has fallen into the pro-effective field theory camp. He has yet another paper on the subject out today, and has done some ground breaking work applying it to cosmology.

So what do our readers think? Should theoretical physicists spend more time trying to crack open the "holy grail" egg, or should they turn to effective field theories that can never be "the theory of everything" but can at lease make testable predictions as long as you stay away from those places where they blow up?


  1. How will the LHC affect our (ok, your...kind =:) ability to test these field theories? Are there any direct or indirect predictions relating to string theory that are just waiting for some functional magnets? (and maybe a few other spare parts)

  2. Stan, good question.

    First: If we are lucky the LHC with start doing collisions later this year. Now, the last big accelerator, the tevatron at Fermilab took ~3 years, after it turned on, to start making real discoveries. The point is, these machines are complex enough that it should take at least a couple years before discoveries begin to be announced.

    Second, the problem with string theory isn't actually that it doesn't predict things, the problem is it has the ability to detect just about anything. In an earlier post I mentioned string theory has ~10^500 solutions so just about anything can be predicted making it really hard to verify the theory.

    However, there are a few things that seem to be true about all string theories. A couple examples:

    1. They all seem to suggest there is a symmetry in nature called supersymmetry. (I'll blog more on this later.)
    2. That there are more than the 4 dimensions we experience (remember time) they are just so small we can't see them.

    Now, both of the above two things we hope to be able to test at the LHC. If supersymmetry is real we should start seeing it rear its head at ~1 TeV. The LHC should be able to reach energies about ~10 TeV. (The actual number is debatable given all the issues they are having, but 10 TeV should eventually work for sure.) So we will hopefully see supersymmetry. (Although, even if supersymmetry is manifested at 1 TeV, it might be too tricky for scientists to extract it. It's a mess but many physicists are hopeful. Most say it is a 50-50 chance).

    Second, if the extra dimensions are big enough we may be able to detect them as well. (I'll do a post on how we do this in the future as well. Lots of posts.) But, if they are too small they will still go unnoticed.

    Now, if we discover both supersymmetry and extra dimensions at the LHC, string theorists will start parting in the streets.

    However, they will need to hold on. It is possible to have a non-string theory with both supersymmetry and extra dimensions, but the string theorists will still argue "yeah, but only mine doesn't blow up, and these are techniaclly predictions that almost all string theory models make and are now confirmed." They will have a point, but that still won't cut down on the 10^500 solutions out there so they are still not out of the woods.


    With an effective field theory you say: "even though it will blow up at extremes, I can add one piece and see what predictions that one piece makes." You then know whether that one piece is true. And you do it again and again adding one more piece at a time. In theory, after you add enough pieces it will converge on a renormalizable theory that won't blow up.

    So with the effective field theory approach, you can immediately start testing specific things right now, with the price that you only confirm a partial theory. But this partial theory grows with time. Many think this approach is best. String theorists think if we just keep working on string theory eventually we will have the whole whole theory at once.

    Anyways, my point is, yes, string theorists have some real things at the LHC that they hope to see that for them will confirm large pieces of their theory. However, whether string theory is true or not, the effective field theorists will also have a lot to look forward too.

    Sorry this comment is so long. I obviously have lots to blog about for the next while. :)

  3. Despite the problems with string theory, I would like to see more effort in that field. However, as an engineer, I can't help but feel the value of moving toward effective field theory as it is certainly the most practical.

    In engineering we do this all the time. Yeah, we know the theoretical physicists would whine at the way we do things, but you know what, they work!

  4. jmb275, good observation.

    "However, as an engineer, I can't help but feel the value of moving toward effective field theory as it is certainly the most practical."

    Physics would benefit from some more practically minded theorists. That's for sure!

  5. As a theorist that works in a field where we can check our results against real data, I can tell you that the engineering mentality is useful in basic science but only to a point. I do computer simulations of the sun where we treat it as a huge ball of rotating, convecting, turbulent fluid. Engineers have worked for decades on ways to model turbulence in a variety of settings and they've come up with some methods that work very well in specific applications, but since they are not general theories, they break down. For example, when you move from oil flowing through a pipe to the interior of a star, almost all turbulence models simply fall apart.

    The effective theories are nice, but something general should always be the goal.

  6. Field theories are the way to go, however at this stage I think we ought be looking for anything that we can tie to empirical oddities. Otherwise we get something elegant but too broad to be useful. (Ala M-Theory)

    Also, for the record, I'm amazingly skeptical that the LHC (if they ever get it working) will do much for string theory. Even the theoretical discoveries some hope for seem to not really be sufficient to ebb the tide of string skeptics.

  7. This post reminded me strongly of some things I learned in my Computer Science training. There is a field in Computer Science called Complexity Theory:

    It focuses on categorizing problems into various classes so that scientists and mathematicians can more easily determine things about them, such as how much time and effort should be put into solving them. For example, some problems are decidable or undecidable, some problems can be solved in polynomial time and/or space and other problems require exponential time and/or space in relation to the problem set. This field is very important because it sets boundaries about what can and cannot be done by computers (or people, for that matter).

  8. Thanks Carl. I'm glad you brought this up and that in general we are having people with so many different backgrounds share their thoughts.

    I can see why this is so important for computer science too. I remember being in a lecture by a mathematician on cryptography who said "this problem on modern computers would take about 1 billion years."

  9. The funny thing is that computer scientists laid the foundation of complexity theory long before computers were ever practical. I'm surprised that physicists are only starting to discuss these kinds of issues. It seems to make so much sense, from a practical perspective, to circumscribe the boundaries of various fields of study so that people can practically determine where best to direct their efforts.

  10. Carl, your right, it is unfortunate that in some respects different fields seem to evolve independent of other fields. I'm sure it would do physics a lot of good if physicists were thinking in terms of complexity theory more often.

    I myself don't know about the subject as well as I should. I think many physicists, especially theoreticians hope that though a problem is difficult, the solution will "just come top them while thinking hard like it did Newton or Einstein".

    But, there needs to be more practicality in this process for sure.


To add a link to text:
<a href="URL">Text</a>