Quantum Field Theory, String Theory, and Predictions (Part 5)

[This is part 5 of a series, which begins here.]

In a previous post, I told you about how physicists use computers to study how the strong nuclear force combines certain elementary particles — specifically quarks and anti-quarks and gluons — into hadrons, such as protons and neutrons and pions.  Computers can also be used to study certain other phenomena that, because they involve the strong nuclear force where it is truly “strong” [in the technical sense described here], can’t be studied using simpler methods of successive approximation. While computers aren’t a panacea, they do allow some important and difficult questions about the strong nuclear force to be answered with precision.

To do these calculations, physicists study an imaginary world, as I described;

  • all forces except the strong nuclear force are ignored, and
  • all particles are forgotten except the gluons and the up, down and strange quarks (and their anti-quarks).
  • On top of this, the up, down and strange quark masses are typically changed. They are taken larger, which makes the calculations easier, and then gradually reduced towards their small values in the real world.

The Notion of “Effective” Quantum Field Theories

There’s one more interesting method for understanding the strong nuclear force that I haven’t mentioned yet, and it too involves changing the quark masses — making them smaller, rather than larger! And weirdly, this doesn’t involve the equations of the quantum field theory for the quarks, antiquarks and gluons at all. It involves a different quantum field theory altogether — one which says nothing about the quarks and gluons, but instead describes the physics of the hadrons themselves. More precisely, its equations are useful for making predictions about the hadrons of lowest masscalled pions, kaons and etas — and it works for processes

  • with rather low energy — too low to affect the behavior of the quarks and anti-quarks and gluons inside the pions — and
  • at rather long distance — too long to detect that the pions have a lot of internal structure.

This includes some of the phenomena involved in the physics of atomic nuclei, the next level up in the structure of matter (quarks/gluons → protons/neutrons → nuclei → atoms → molecules).

Notice this is the opposite regime of where the quantum field theory of quarks and gluons works well!  Successive approximation works well at short distance and high energy, for any quark masses, and computer simulations are easiest for larger quark masses.  But long distances and low energies are very important, because processes important in our lives obviously involve longer distances than protons, and also (less obviously) involve energies much lower than those involved in holding the proton together.

This kind of theory is often called an “effective quantum field theory”; it is useful for making predictions about low-energy and long-distance phenomena, but it’s not a complete theory, because it can’t predict what happens to pions and kaons and etas at higher energy and shorter distance.  [What actually does happen is that their inner structure becomes really important in their behavior.]  This is in contrast to the quantum field theory of the quarks and anti-quarks and gluons, which is supposed to apply at all energies and distances that we’ve measured so far, and perhaps even much higher energies and shorter distances. The only reason we don’t use the latter theory at long distance and low energy is that we don’t know how; it’s too difficult in practice. The effective quantum field theory of the pions etc. simplifies the problem for us, and gives us a tool that we can use in understanding how nuclei form, etc.   We don’t need to follow all the details of quarks and gluons to understand how nuclei form, just as we don’t need to follow all the details of atomic nuclei to understand how atoms form.

Fig. 1: The equations for the quantum field theory of quarks. anti-quarks and gluons can be studied using successive approximation at short distance and high energy, and using computer simulations in intermediate distances and energies.  The latter is not useful for very low quark masses.  The effective theory of lightweight hadrons is useful for low quark masses, long distances and low energies.  The real world's quark masses (blue dashed line) are low enough for the effective theory of hadrons and just barely high enough for modern computer simulations.

Fig. 1: The equations for the quantum field theory of quarks. anti-quarks and gluons can be studied using successive approximation at short distance and high energy, and using computer simulations in intermediate distances and energies. The latter is not useful for very low quark masses. The effective theory of lightweight hadrons is useful for low quark masses, long distances and low energies. The real world’s quark masses (blue dashed line) are low enough for the effective theory of hadrons and just barely high enough for modern computer simulations.

The complementary nature of the various approaches to the strong nuclear forces is illustrated in Figure 1.  Successive approximation [or  ``perturbation theory'' in jargonese] works (no matter what the quark masses are) at short distances, where the strong nuclear force isn’t strong, in the technical sense.  Computers are needed, and useful, at intermediate distances, but are easiest when the quark masses are much larger than in the real world.  And finally, the method of an effective theory for the low-energy behavior of the lowest-mass hadrons is especially powerful when the quark masses, and therefore the masses of the pions, kaons and etas, are very small.  Notice that in the real world (indicated by the blue dashes) the quarks masses are simultaneously small enough and large enough to allow some overlap between the various methods. In short, we are lucky: we can check our understanding of the strong nuclear force in multiple ways.  If the quark masses had been much smaller or somewhat larger, this would have been more difficult.  [Had they been much larger, things would have simplified again; but that's another story for another day.]

This effective theory explains that if the up, down and strange quarks’ masses were reduced to zero, then pions, and their cousins called kaons and etas, would become massless. [Technically: they would be Nambu-Goldstone particles, bosons in particular, whose presence is a consequence of the ``spontaneous breaking'', or hiding, of a subtle symmetry.] Meanwhile, protons and neutrons would change rather little from what we find in nature — their masses would be almost the same as before. [This is one of the reasons why the naive statement that the Higgs field is responsible for all mass in the universe is dreadfully wrong; even if the Higgs field were zero and the quarks were massless, the protons and neutrons that provide you with most of your mass would still have masses.]

This theory also explains why many processes involving hadrons are related to one another, and occur with the same (or similar) probabilities or rates.  Moreover, even figuring out just how changing the quark masses affects our computer simulations requires this effective theory.

Where did this effective quantum field theory come from, since it preceded the theory of quarks and anti-quarks and gluons? Well, its origin is a classic one. Essentially, it was simply guessed, based on experimental measurements of pions’ properties, made in the 1950s and 1960s, before quarks or gluons had even been imagined. Remarkably, even today, after decades of study, no one can take the quantum field theory of the elementary particles — the equations that describe the quarks, anti-quarks and gluons — and extract in a direct way the equations for the effective quantum field theory of the lightweight hadrons.   The equations for the pions, etc. must “emerge” from the equations for the quarks, etc., but so far no one has figured just how that works mathematically.  Consequently, without experimental data, it would have been much harder to guess the right effective quantum field theory, and impossible to verify the guess was correct.

So when we consider imaginary worlds for which we have no experiments to guide us, and for which no one has done extensive computer studies (if they are even possible), we often find ourselves in some difficulty figuring out what would happen in such a world…

Continued here.

51 responses to “Quantum Field Theory, String Theory, and Predictions (Part 5)

  1. Then Matt. How can we tolerate all that big bold huge declarations in detailed research papers of lots of impossible -to even guess – worlds ?

  2. LUX results are coming on 10/30/2013 so we are eager to read your assessment .

  3. Let me be honest with you , till I read this particular series I was in the very wrong impression that field equations are so direct clear-cut math. To the degree that solving the equations we directly get any answer we want in the field of quantum fields ………remember , I am structural design engineer with only general background in micro physics ………now it is all in a grand mess.

    • I didn’t say “We get any answer we want”. I said only that getting answers can be difficult.

    • Carl 'SAI' Mitchell

      If you’re a structural engineer you’ll have taken differential equations. So you know that most of them have no analytic solutions, but can be approximated by numerical methods. Much of quantum field theory consists of partial differential equations, and numerical approximations are needed. Those approximations take tons of calculation to get even a very low accuracy, and a high accuracy is required. So it’s very hard to solve them, even with supercomputers.

  4. Here I point out a great weakness point : no one even try to state in details the state of the art as you do , so I honestly appreciate your honest true sincere effort , thanks Professor Strassler.
    Aa.sh. With respect.

  5. Wait, wait, wait! How come pions etc. would become massless if the quarks did have no mass?! Why is the two-quark-system different from the 3-quark one?

    PS. I still would like to hear your explination of the excited states from the Field Theory point of view.

    • First — neither is a two- or three-quark system. This is part of why I insist on saying that hadrons are very complex objects made from quarks, antiquarks and gluons — the complexity of these systems is an essential part of why your intuition about two- and three-quark systems fails to work.

      Second — there are theories with massless proton-like objects. Our strong nuclear force doesn’t have such things, but other strong forces can have them.

      So give up your atomic intuition, when you’re trying to understand hadrons. Strong forces can do things that weaker forces, like electromagnetism, cannot.

      • With all due respect, you didn’t answer my question: why are mesons different from baryons when it comes to how they get their mass?

        • In general, the mesons are not very different from the baryons. However the pions, kaons, and etas are very special particles, known as pseudo-Nambu-Goldstone particles, and their presence results from a complicated effect known as “chiral symmetry breaking”. To explain this requires a set of articles, and I can’t do it here. You can learn about Nambu-Goldstone particles many places (not on this website yet though), but to understand why the pions are such things is very subtle; there is no simple mathematics that will prove it to you. Which is precisely my point! We don’t know how to prove these things in a simple way, even though we have the right equations for the quarks and gluons…

        • Perhaps a word of caution is in order from the Particle Data Group (See Review of Quark Masses):

          “Unlike the leptons, quarks are confined inside hadrons and are not observed as physical particles. Quark masses therefore cannot be measured directly, but must be determined indirectly through their influence on hardronic properties. Although one may speak loosely of quark masses as one would of the mass of the electron or muon, any quantitative statement about the value of a given quark mass must make careful reference to the theoretical framework used to define it. It is important to keep this scheme dependence in mind when using the quark mass values tabulated in the data listings.”


          “Current lattice simulations are performed with the masses of the up and down quarks equal, mu = md = mud, electromagnetic effects are not included in the simulation. It is the average of the up and down masses that is determined directly.”

          In my opinion ideas about what’s going on inside the Proton and Neutron, like pronouncements that they are chock full of antiquarks for example, can be taken with a grain of salt.

          • Jyri Tynkkynen

            Fair enough. Yet the original question was about why three valence quarks come packaged with a zillion other particle-antiparticle couples (close enough, Matt?) and a relatively large mass even if the mass of the quarks were zero — but the two valence quarks couple up with NO such massive package.

          • There is salt, and there is salt: Just because some things are not complex and tricky does not mean nothing is known about them. We know there are gluons and anti-quarks in the proton; it’s not up for debate.


          • Until an experiment is performed to determine the gravitational acceleration of anti-hydrogen there remains the possibility that anti-hydrogen will fall up at 1g. This, despite General Relativity, despite the interpretation of the data you have so nicely presented, as well as various theoretical arguments made against antigravity since the mid-1950’s. Between 2014 and 2020 there will actually be a few experiments conducted to test this possibility. Until then please allow me my foolish belief in this possibility and understand why I mentally cringe at the idea of anti-quarks within the proton…

  6. Hello again Prof,

    Was the Big Bang a single event, one time, one location (i.e. @ | t | = 0 , F(x,y,z) = 0 )? Or was it a “external” disturbance of the plane waves where we reside now, our “visible” universe.

    I guess what I am asking, I think, :-), is was “the field” (referring to the unification theory) already in existence in “plane waves” form for a Big Bang (inflation) to occur?

    If one accepts this hypothesis then how do you handle the concepts of “zero” and “infinity”?

    Finally, did we make a wrong detour by incorporating renormalization into the equations. I understand the reason why we use the methods, but like the income tax, once we get dependent on it we cannot live without it. Have we build the walls too high to “see” outside our visible universe?

    PS; I believe this is on topic because it addresses the concept of energy and how it relates to “the field” and/or known fields.

  7. Now our dear professor , if the situation with the observed particles is like this , how can any one predict any property for the veiled unknown particles how can we ever know without observations the property of the 10/30 forthcoming star …… The neutralino for example ?

    • The Standard Model works beautifully — what “situation” are you talking about? We use successive approximation, computer simulation, and effective quantum field theories, and there are relatively few things about particle physics that we do not understand thereby.

  8. You did not answer my main question—– thanks in advance —– , you said that without experiments we cannot figure out what would happen , I ask : how then we figure out particles of DM properties ? It would be impossible to do that if as I understood all what we have of theoritical tools must be guided by observations or else we can achieve nothing .

    • Right — for pions and kaons, their properties had to be learned from experiment, then translated from there into equations which we have a lot of confidence in.

      For dark matter, we know almost nothing from theory, and, indeed, we rely on experiment. All that experiment tells us, as of now, is that dark matter is something that gravitates, does not shine, clumps and does not stream freely (i.e. is more like matter than like light), and whose interactions with itself cannot be of this sort or that (the details are complicated.) But this is for a DIFFERENT reason.

      In the case of pions, we know more fundamental equations (for quarks and gluons) and we can use them to predict relationships between the masses of pions and kaons and protons (see Part 4 of this series) but we *cannot* use them to predict how pions will scatter off one another. For this, we need the effective theory of pions, which tells us much more; a *few* pieces of experimental data about pions are used to infer the effective theory, which them makes *many* predictions for how pions behave.

      But in the case of dark matter, we don’t know the fundamental equations at all, so *of course* we can’t predict very much.

  9. I wonder what Einstein and Newton’s minds would think of this incredible machine – not being a simple bucket of water and length of rope? What experiments would they perform with it do you think? If as I suspect after its down time is concluded and you utilise more power on start up again – and you cannot move a proton any faster than the lower power – as they achieved in the 1930’s what does that mean? How will that reality cause a rethink of your targets? Will the protons be more massive ? – and hence larger collision products? A Marvellous bit of human ingenuity, pity it is only used for such a narrow bit of research. If you finally realise that the velocity of light cannot be superseded then can you use this device to make a statement “ Why Not”? and give a clear reason why not? And with such new comprehension find a new way of looking at the Universe!

  10. In your response w.r.t Dark Matter you listed what we know about it but maybe you missed something , can we be sure that there are no new force/s or field/s that only DM can feel them ? So how can we be confident that there are none ?

    • You’re confused about the logic. Everything I mentioned is what we know. Everything I didn’t mention is something that we don’t know, not something we know is absent. I didn’t say “Dark matter has no new forces or fields”, and therefore, I didn’t “miss” this possibility — I simply left it open.

      Personally I think it very likely that dark matter has new forces or fields; in fact some of my most important work is related closely to that subject. There have been hundreds of papers in the last ten years or so about this possibility. And there will be another talk at Harvard today about just that issue.

  11. kashyap vasavada

    I used to do calculations in sixties and seventies for hadrons with dispersion relations, sum rules etc just involving some simple Feynman diagrams. I did not think of that as much of field theory. I have not kept up with that . Do I understand from what you are saying that there have been advances in field theory of hadrons (without involving quarks) since that time and people do field theory calculations for hadron scattering and get some results agreeing with experiments? In that case can you give reference to some review article or a paper? Thanks.

  12. If Dark Matter is related to Black holes and Dark Energy to a chiral Higgs field, then we may assume a base for new physics?

    New Dark Matter Black Holes and a New Dark Energy Higgs Field, lead to
    a Bouncing CP symmetrical Multiverse, and new experiments. http://vixra.org/pdf/1209.0092v1.pdf

  13. Now as it is clear that Math. tools are totally dependent on experiments and tuned according to observations , I wonder , how String people’s manage to construct any Math. Structure without any observation whatsoever.?

    • You’re overstating the point again. It’s not “total” dependence. What is true in one context is not necessarily true in another.

      The reason that some progress is possible without experiment is that sometimes the math is very restricted. People worked for 40 years on various types of string theories with quantum gravity, and in the end all the math they worked on turned out, in surprising ways, to be just different ways of looking at a single theory.

      Similarly, Einstein guessed some pretty equations might be right just because they were consistent with past experiments and were particularly nice-looking. They’re probably not exactly right, but his aesthetic principles led him to the roughly right answers, even without experiment to guide him.

      This would probably not have worked for the light hadrons, though perhaps someone might have been clever enough to guess their properties even without experiments, other than the ones that discovered them and measured their masses.

      But there is no substitute for experimental guidance, in the end. That’s why physics is an experimental science, fundamentally. It was true in Newton’s day; it was true in Einstein’s; it is still true.

      Of course, if we really fully understood quantum field theory, it would not be necessary to guess at which effective theory to use; we would simply calculate the effective theory, starting with the more fundamental one. We do this type of thing in many other contexts.

      • He is overstating the point in yet another way. A great deal of mathematics is actually abstraction of physical experience. In this sense, countless “experiments” are already “behind” many mathematical ideas with the greatest impact on physics – above all various kinds of symmetry, that we observe in many forms in nature. Many fundamental and profoundly new physical discoveries have been made by applying these mathematical ideas to already “known” facts, without the input of any experiments. People frequently talk in this context about “aesthetics” but this “aesthetics” is not, as some people imagine, just a subjective “matter of taste”, but is based on certain well tested ideas about the structure of physical reality in the greatest generality.
        The most famous example of this was special relativity. In fact, although the invariance of the speed of light is a well tested empirical fact, it can be derived by purely mathematical methods from certain very general and very natural hypotheses about the properties of space-time : preservation of physical laws by inertial transformations, homogeneity of space time, isotropy of space, and the group structure of the set of inertial transformations. None of these needs to be tested by “experiment” because they have already been tested by countless implicit experiments. Nevertheless, applying mathematical reasoning to these very general ideas leads to very profound, surprising (and unique) conclusions with strong practical implications.

  14. You keep talking about the difficulty of doing calculations. Would a quantum computer running quantum algorithms solve the problem? I know they aren’t better at all problems but the system you are studying is inherently quantum.

    • By “difficulty” he does not mean the complexity of a computational algorithm in any sense known to computer science. He means that there is no known algorithm that gives a meaningful (i.e. finite) answer. A quantum computer would be of no help in this situation: what you need is a better quantum physicist/mathematician.

      • Well yes I understand that but that is why I asked about quantum computers. It opens an entire new category of algorithms to think about.

        The universe solves these computational problems. And does it very fast. There is no reason we can’t use components of the universe to solve these types of problems ourselves. Maybe we will need to think in quantum algorithms before we can even understand the problem.

        We will of course need better quantum physicist/mathematician but in the end it may simply not be possible to do these calculations with a classical computer no matter how good our theory may be. Worse it may not be possible to discover a good theory without a quantum computer to explore possibilities.

        • Well, if you want to simulate the universe you will indeed need a “quantum computer”. The whole point of using mathematics is to avoid the need for such a device (which right now belongs to the realm of science fiction or even “science fantasy”).

          • I don’t want you simulate the entire universe, only a tiny relevant piece of it. And that is what any mathematical model gives you the power to do. If I want to understand the weather I must understand fluid dynamics and then I can simulate weather. If I want to understand planetary orbits I must have a mathematical model of gravity and then I can build solar systems in my computer.

            If the underlying mathematical model of a system is inherently quantum then having the model may not allow you to do many calculations or make many predictions with a classical computer. For example if the universe factors very large numbers in very little time then your mathematical model will be mostly useless unless you have the computational ability to do the same. You may think your model is good but until you can do the calculations you cannot know it is good.

            It is increasingly difficult to believe that quantum computers are impossible even as we discover how technically challenging they are. If they do turn out to be impossible or so challenging as to be impractical it may mean that a deeper understanding of physics is impossible or impractical.

  15. @Lucretius : I reached my “overstated ” stand just from what Dr. Strassler wrote in his series , as for GR and SR these are talking about the cosmos , here we are talking about the field , particles , forces realm where –as I see it now — no Math. Tool can go directly from quarks/ gluons to the nucleus and beyond……that is what Matt. Said and that is what I am saying , please read his opinion that maybe a smart physicist some day can go directly from the fundamental theory to all known properties of the hadrons bypassing the effective theories all together.

  16. My point is : Do we have a clear cut Math. Tool by which we can go directly from quarks , gluons to hadrons ? NO

    • There are countless unsolved problems both in mathematics and in physics (I am working on some of the former myself). The fact that they can’t be solved today does’t mean that they won’t be solved in the future. Certainly, there is nothing in Matt’s article that suggests otherwise (I don’t understand what you mean by Math. Tool – how is that different from just mathematics? )

  17. Math. Tool is any Math. That is used to get answers in any other field , as for the dogma of knowing tomorrow what we don’t know today , this is just a dogma , it could be very easly what we don’t know today will be proved un-knowable tomorrow………right ?

    • No, not at all right. Nothing has ever been proved “unknowable”, except, arguably, the existence of God and such things. (Some mathematical statements have been shown to be independent of other mathematical statements and it has been shown that one can’t prove the consistency of an axiomatic system within that system, but this has nothing to do with anything “being unknowable”).
      As for “Math Tool” for quantum field theory – yes, there is one actually and it is called Quantum Field Theory. But it is not a robot like tool that driven by some algorithm will work by itself, but is rather like a paintbrush in the hand of an artist. It still needs skill, talent and sometimes even genius, to use the tool well and in the hands of the incompetent it is no better than Krushchev’s famous “donkey’s tail”.

  18. I wonder how anyone can deny the unknowable !!
    Meta/multi/ verses are unknowable.
    Mechanism of configurating space due to M/E distributions is U-K.
    Mechanisms to generate cosmic laws , constants , boundary conditions are UK
    Mechanisms of all life morphogenesis are UK ……..
    Do you need more
    Maybe even DM is UK , note that LUX excluded all low mass WIMPS ( 60 minutes ago ) .

  19. God and unicorns are also unknowable, in the same sense. Asking questions about such things makes about as much sense as asking if unicorns are green. Of course, I never denied that people ask questions of this kind – in fact I specifically wrote “the existence of God and such things”. It is you who mentioned “things that will be proved to be unknowable” and I asserted that nothing of this kind has ver been proved or will be proved. The only questions to which the answers are “unknowable” are those that are “unknowable” to start with, by their very nature. This includes meaningless questions, such as “whether the present King of France is bold” or equally meaningless questions about the value of measurements of two complementary properties in (e.g. position and momentum of an electron) in quantum mechanics.

  20. Most illogical response !! , Sir: Is the extra universes knowable or unknowable ?it is of no use to bypass the main question by such tactics.

    • Nothing has been proved or can be proved about this matter. Since there is no way (at least at this time) of knowing if any such things exist or not, there is no way of proving that they can’t be known. In order to prove that something can’t be known you have to first prove that it exists. Not being “able to know” what does not exist, does not count.
      Of course, you can “postulate” such things, just like you can postulate “hidden variables” or an “undetectable ether” or an unknowable “thing in itself” but defining something as unknowable make its unknowability a tautology which does not require a proof.

  21. Is it just the pleasure of having the last word ?
    What about position and momentum which you know are existing but knowing both in detail is unknowable , I am not seeking to have the last word but I feel you are.

  22. Multiverses are unknowable in themselves by their very nature , so unknowables exist ,so what are you arguing about after you admitted it in your reference to UCP……..is it just the urge to be seen as superior ? calm down we are not in a contest for the better.
    Back to the start : we can never be sure that the future will give all answers , it may well be the case that answers are veiled , unknowable, why this is hurting you so much? Maybe since it demolish Naturalism foundations? Maybe it shakes the bases of atheism ? ……rest in peace .

  23. Does anyone know why Be9 is more stabile than Be8, same for F19 or Na23, etc. ?

    • kashyap vasavada

      Honestly I do not know the exact answer! Perhaps a nuclear physicist on this blog would answer. But here is my 2 cents worth!! Alpha particles are extraordinarily stable. So Be(8) ->2 alphas has a strong probability. In fact that was a big problem for cosmology ,how did periodic table advance after Be(8) to form carbon etc. Fred Hoyle explained that there was a resonant capture of other alpha particle to form C(12) because of closeness of some nuclear energy level. This gave rise to anthropic argument. The extra neutron adds stability to Be(9) by additional attractive force. I do not know about the other two nuclei you mentioned. It probably depends on the shell structure. I do not have it handy. In any case I would also be interested in the answer from cosmology point of view. Let us see what Matt says about this.

  24. Thanks for your interest. The other cases were similar, so are Al27, P31, Se45, V50, Mn55. etc. All single odd stabile isotopes. So the point is something very different and interesting is happening. And the second point is with all the high powered math, someone ought to have an answer if the math is any good !!!

  25. Pingback: Quantum Field Theory, String Theory, and Predictions (Part 7) | Of Particular Significance

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