# Quantum Field Theory, String Theory, and Predictions

One of the important lessons of last Tuesday’s debate about string theory is that if I’m going to talk about theories that do or don’t predict things, I’d better be very clear about

• what’s a theory?
• what’s a scientific theory expected to do?
• what’s a prediction?

On Thursday I asked my readers if they felt misled by Tuesday’s article. Most didn’t feel that way (I’m gratified), but if you’re a good scientist you focus attention on the negative feedback you receive, because that’s where you are most likely to learn something. And you also look for negative signs in the positive feedback. So thank you, especially those who were critical yet reasonable. I will respond in due course, by putting out a better, clearer article on what string theory can and cannot do, on what we know and do not know about it, a bit about its history, etc. Then I can avoid creating or contributing to confusions, such as the ones Dr. Woit expressed concerns about.

But today I want to explain why I found my conversation with Dr. Woit troubling scientifically (as opposed to pedagogically or politically). It wasn’t because I’m a string theorist — in fact, I’m not a string theorist, by anyone’s reasonable definition (except possibly Dr. Woit’s [and probably not even by his.])

I’m a quantum field theorist. Quantum field theory is the mathematical language of particle physics; quantum field theory equations are used to describe and predict the behavior of the known elementary particles and forces of nature.  Throughout my 25 year career I have mainly studied quantum field theory and some of its applications. Its applications are many. I have focused on the applications to particle physics, with some also to string theory, astronomy and cosmology, and even quantum gravity. (Other applications that I haven’t worked on include the physics of “condensed matter” — solids and liquids; magnets; electrical conductors, insulators, and superconductors; and a lot of weirder things — and phase transitions, such as the melting of a solid to a liquid, or the change of a material from magnet to a non-magnet.)

And meanwhile, while doing quantum field theory, I use every tool I can. I use fancy math. I use what I can learn from other people’s experiments, or from their big numerical simulations.  Sometimes I use string theory. Sometimes I use computers.   If loop quantum gravity were useful as a tool for quantum field theory, I’d use it. Heck, I’d use formaldehyde, bulldozers, musical instruments and/or crowds of hypnotized rats if it would help me understand quantum field theory. I’ve got a job to do, and I’m not going to stray from it just because somebody with a different job (or an axe to grind) loves or hates my tools.

The Scientific Issue

So here’s what bothers me about Dr. Woit’s argument.  First he said: “to deal with the scientific issue here and make an accurate statement, one needs to first address the following:

1. What is a prediction?
2. What is string theory?
3. What are the vacuum states of string theory?

Hard to argue with that!  [He elaborated on each of these three points, but I leave it to you to go back and read the elaboration if you like.]  And then he concludes:

What is the difference between this situation and Quantum Field Theory? That’s pretty simple: no problems 2 and 3. And those problems are not problems of calculations being hard.

Woit’s implication is that we do know what field theory is and we do understand the vacua of field theory… and that while prediction in field theory is merely hard in practice, we know what we are doing… and that we understand so little about string theory that prediction in string theory is impossible in principle.  This, as a quantum field theorist, I strongly disagree with.

If you are concerned, as you should always be in these situations, that Woit’s being misquoted or quoted out of context, you can go back and reread the comment exchange to Tuesday’s post.

What bothers me about this is that this kind of sweeping statement does a disservice to both subjects: it understates what we know about string theory and overstates what we know about quantum field theory. If only quantum field theory always made it straightforward (albeit difficult) to make predictions! My job would be a lot easier, and it might even be much easier to solve some of the deepest puzzles in nature.

Also, this blanket statement leaves it completely unclear and mysterious why string theory could be such a helpful tool for a quantum field theorist like me — which is a real loss, because the usefulness of string theory for field theory is one of the most interesting aspects of both subjects.

Our understanding of quantum field theory, while perhaps no longer in its infancy, is still clearly in adolescence, at best — and it seems likely to me that we know even less than we think. And I think that many of my readers would like to hear more about this.

What I intend to do over the coming weeks, as time and news permits, is

1. describe to you what we do and don’t know about quantum field theory
2. describe to you what we do and don’t know about string theory
3. explain how, over the past 20 or so years, we have used some of the things we do know about string theory to learn some things we didn’t know (and often didn’t know we didn’t know) about quantum field theory.
4. describe how one can use quantum field theory to learn something more about string theory

I’ll do items numbers 1 and 3 carefully.  Specifically, in number 3, I will focus on predictions made for quantum field theory using string theory [and we’ll talk very carefully, at that time, about what “prediction” means.]) Both 2 and 4 are more nebulous, and I don’t work on them directly, but I think I can do a decent job on them. I’m sure my colleagues will correct me if I get any facts wrong.

What Does “Theory” Mean to a Physicist?

First, an important, fundamental question. When I say: “quantum field theory”, or “string theory”, or “theory of relativity” — well, what is a theory?

It’s not what it means in Webster’s dictionary of the English Language.  It’s not the same as a guess or a hypothesis. It’s not the opposite of a “fact”. It’s something much more powerful than either one.  And it’s certainly not what it means in various academic departments like Literature or Art or even Sociology.

I could write a whole article on this (and someday I might) but here’s the best definition I have at the moment.  Probably there are better definitions out there.  But here’s my best shot for now: in my line of research, a theory is a set of mathematical equations, along with a set of accompanying concepts, that can be used to make predictions for how physical objects will behave, on their own and in combination — and these predictions may be relevant either in the real world or in imaginary (but reasonable, imaginable) worlds.

Wait! Why are imaginary worlds important? Why focus on anything other than the real world?  How could studying imaginary worlds be “scientific”?

Because:

• By studying imaginary particles and forces, we gain insight into the real world: which properties of our universe are true of all possible universes? which properties are common but not ubiquitous? which ones are special and unique to our own?
• Sometimes the math that describes a specially chosen combination of particles and forces turns out to be much simpler than the mathematics that describes the particles and forces in our own universe. In an imaginary world described by these equations, it may be possible to solve problems that are too hard to solve in the real world.  And even though the lessons learned don’t apply directly to our world, they may still yield fundamental insights into how the real world works.
• The future may surprise us. Things that are imaginary today might actually turn up, in future, in the real world. For instance: the top quark that we find in nature was imaginary for over 20 years; the Higgs particle was imaginary for almost 50; supersymmetry is still imaginary, and no one knows if it will remain so.]
• Note Added: commenter Kent reminded me of another excellent reason, and an example of it: “Sometimes it is not possible to understand the real world until we have first understood an idealization of it. There are many examples … [including] the discovery of the laws of motion by Galileo and Newton. For hundreds of years, people followed Aristotle in believing that a moving object would return to its “natural state” of being at rest unless a force acted on it. Galileo and Newton’s breakthrough was their ability to imagine a world without friction or air resistance. Only after they understood this imaginary world could they properly understand the real one and learn that the natural state of an object is to continue moving in the same way UNLESS a force acts on it.

Notice that this strategy is not unique to physics! Biologists who want to understand humans also study flies, mice, yeast, rabbits, monkeys, etc.. From this type of research — often much easier, cheaper and safer than direct research on humans — they can perhaps learn what is common to the biology of all primates, or of all mammals, or of all animals, and/or of all life on Earth, and perhaps also ascertain what it is that makes humans unique. Many experts on Earth’s geology and climate are fascinated by Mars, Venus, and the rocky moons of Saturn and Jupiter, whose similarities to and differences from Earth give us a perspective on what makes the Earth special, and what makes it typical. Kierkegaard, the philosopher, famously uses the technique of “what-if” stories — a story retold with slight differences and a quite different outcome — to try to tease apart the meaning of religious faith within the Abraham-and-Isaac story, in his famous work “Fear and Trembling”.

The Lesson: If you want to understand a particular case, study the general case, and other similar-but-yet-different particular cases, in order to gain the insights that the particular case, on its own, cannot easily give you.  Meanwhile, what you learn along the way may have wider implications that you did not anticipate.  In short, putting one’s imagination to work, in order to learn about the real, is a powerful, tried and true approach to theoretical physics.

Continued here

### 128 thoughts on “Quantum Field Theory, String Theory, and Predictions”

1. Hello, prof. Strassler!

I’ve been following this debate and I find it quite interesting. Just a thought: perhaps you’ll like to introduce “self-consistent” in your definition of what a theory is. It might be that you can have a set of mathematical equations and concepts that you can use to make predictions but which, somewhere among their logical consequences, have an insurmountable flaw.

• This is a really excellent point. I think I’m going to leave things as they are, but I’m still thinking about it. A theory that isn’t *known* to be self-consistent, or is only mildly internally consistent, might still be useful for calculations and predictions… but would still be a theory. The Standard Model withOUT [typo!] any Higgs particle or field is such a theory; it is inconsistent but the problems don’t afflict predictions for low-energy processes. Meanwhile, some theories are so inconsistent that all predictions yield “Zero”. Such things are really fakes; they’re not theories at all. Anyway, this point can be tricky, and I think one has to leave self-consistency as something that requires separate discussion.

• Sorry. I do not understand where is inconsistency in SM. Is it in non renormalizability of strong interactions or some infinities ?
Or the fact that Higgs field does not explain baryon masses?

• There’s many examples of ‘inconsistent’ theories which are useful for calculations. Any theory which is not renormalizable falls into this category: pion models, Fermi’s theory of fermion scattering all the way up to General Relativity…

• Right — remarkably, “effective quantum field theories” like these have regions of validity where the inconsistencies are walled off, in the sense that they lead to ambiguities in your calculations that can be proven to be very small as long as the energy of the process you’re calculating is sufficiently low. That’s to be distinguished from theories that predict nonsense at all energy scales.

One minor caution: Some perturbatively non-renormalizable theories are well-defined — i.e. they are non-perturbatively renormalizable, even though you can’t see that in perturbation theory. So it can be hard to be sure if a theory is truly inconsistent.

• Matt, this is an earlier post. So I am not sure if you will see this. But let me ask question any way. To understand renormalizability of SM , I looked into Standard Model Primer (Burgess and Moore) . They say that apart from the phenomena of neutrino oscillations, which may require new physics, SM is renormalizable. Are there different opinions on this subject? Previously I understood that t’hooft proved renormalizability of weak-EM intn, but strong intn are still up in air.
I would like to understand this point. If it is too technical for this blog, please give me a reference. Thanks.

• Twistor wrote: “There’s many examples of ‘inconsistent’ theories which are useful for calculations.” I understand this stance, but I disagree with its acceptance. The purpose of a theory is conceptual modeling too, not only numerical. When you write the Dirac equation for an electron and say it is written not for electron, but for a bare electron, because our perturbative corrections are such that they needed to be absorbed (discarded), I understand it as a manipulation with calculation results for the sake of agreement with experiment. It is not a calculation, but cheating and self-fooling. Albeit “successful”, it is not a theory, it is not Physics.

• I think your understanding of renormalization needs work. May I suggest you study the problem of multiple coupled anharmonic oscillators? In this problem one ends up having to renormalize the oscillation frequency, for the same reason as one shifts the mass of the electron. The renormalization is finite, though large, and the cause is the same as in field theory. (The renormalization is infinite in the limit that the number of oscillators goes to infinity.) The physics is this: the oscillation you put into the equations is not the one that you measure, because of the anharmonic effects.

Once you understand this, you will understand that this is not about cheating and self-fooling; it is actually about not getting yourself confused between the parameters you put *into* your equations and the physics you get *out* of your equations.

• Matt Strassler wrote: “The physics is this: the oscillation you put into the equations is not the one that you measure, because of the anharmonic effects.” Matt, but the oscillation is not harmonic even for one anharmonic oscillator, so what? I do not get what special is in your “explanation”. Maybe you can give me a reference to those coupled anharmonic oscillators because I do not understand in what way they are coupled and what is calculated. If you couple many point bodies, the total mass increases, but each mass remains intact. There are things that are just calculated from the fundamental constants and have nothing to do with discarding or other ways of result modifications to obtain a desirable result from a bad one.

2. But we are left with a very strong objection , what are the rules and principles that bridge the reality-imagination tremendous gap ? Are those rules purely subjective? If yes how do we know they are correct ? If no then this NO is based on what?
Meta /multi/hyper / higher univers(s) are imaginations but can we ever be directed from them to OUR universe ? How ?

• Yes, these are fair objections. But look at the biological, planetary and philosophical analogues. A well-trained scientist knows how to keep his or her imagination under a certain level of control. It’s a part of science that has elements of art and craft — students have to be trained, by looking at examples, that wild ideas will get you nothing, whereas ideas that stray slightly from reality and permit you to still calculate things can be enormously fruitful.

3. Dear Prof Strassler,
As you are a specialist on the Quantum Field Theory, what is your opinion about the remarks from Sean Carroll made in Fermilab (july 2013) where he poses that all particles as we know, including the Higgs, are actually only excitations of a field ?
Wilhelmus

• Could this mean that “matter” as we are experiencing it is only an excitation of the field in the past. Could it be that there is only ONE field responsible for all the particle excitations as we “know” of ? IS it a reasonable thought that the “Consciousness Field” is interacting with this primal field and so realising “reality” ? A lot of things should be answered if so (spooky action at a distance, inflation, expanding universe etc etc).
Wilhelmus

• Umm… no. You need equations to go with your imagination here…

4. Based on the underdetermination of theories by data , and on the fact that we can invent many theories with huge number of equations to correlate with a given set of data ( behaviors / interactions ) , what are the meta-rules that MAY guide us in selecting the nearest Math. Structure to the veiled unknowable reality ?

• A good part of it is luck. Meta-rules like “mathematical elegance” or “simplicity” don’t always work. That’s why lots of different people have to try lots of different things.

5. Can a materialized prediction ( like the Higgs ) ever prove that the predicting Set of equations REPRESENT reality ? But then we need a meta-theory to tell us………..adinfinity
N.b. : The Higgs was not imagination but a necessary building block for the SM as you said many times.

• The point is that the STandard Model with its Higgs was still partially imaginary. In fact it still is. That’s the tricky point indeed. We have

1) the world predicted by the Standard Model
2) the real world

These are NOT necessarily the same (even at the Large Hadron Collider.) We’re comparing these two things now, using data. (1) may exist only in our minds. (2) exists of course. The question is, does (1) = (2)?

• I would add two more questions:

What part of 1) = 2)?
What part of 1) 2)?

• Matt: “The point is that the STandard Model with its Higgs was still partially imaginary. In fact it *still is*. That’s the tricky point indeed. We have
1) the world predicted by the Standard Model
2) the real world ”

Amen!!!
Most people (including many physicists) now see that the Higgs is a *fact* which is still not supported by the data, as that newly discovered boson could turn out to be something very different.

Again, the possible *difference* between 1) and 2) is the key point on the naturalness issue.

Matt: “… putting one’s imagination to work, in order to learn about the real, is a powerful, tried and true approach to theoretical physics.”

There are, at least, *two types* of imagined universes.
1. SUSY (with s-particles) and M-/F-string theories and multiverse — up to this point, they did not and cannot make contact to the *known* universe but are waiting a *dream coming true* by Nature’s mercy.
2. An invented or designed universe by arbitrary selecting a set of design criteria (a Fictitious Universe) to *design* an artificial universe — the Litmus test for this *imagined* or *artificially designed* universe is to make *contact* to the *known* physics, not from the hope of Nature’s yet to come mercy. See Fictitious Universe (http://prebabel.blogspot.com/2011/10/super-unification-in-fictitious.html ).

• The decay paths at the LHC that were measured and used to help verify the “discovery” of the Higgs boson are consistent with a ST-like Higgs particle (from that the theory says about the way it should behave, in particular, the probability for each decay path that was chosen to verify it in the sense that the theoretical probabilities have consistent values with the measured probabilities for the same paths: that is a very good reason why you need at least 5Sigma to validate!).

From that perspective, the Higgs does not seem to me as an imaginary particle any more, even though from other perspectives it could still be seemed as an imaginary particle.

• Remember: the new particle was for about a year a “Higgs-like particle”. Now most of us view it as a “Standard-Model-like Higgs particle” — definitely a Higgs, not definitely the only one, and not definitely the one predicted by the Standard Model. In fact, it is very important to consider imaginary worlds with more than one Higgs particle — maybe one of those worlds is actually the real one!

• Oops! …Where I wrote “ST-like” I meant to write “SM-like”: it looks a Sting-Theory” like but no way, meant to say Standard Model-like

6. Please, let us understand in your next posts how QFT connects to experiments, and how Could/Should ST be connected do experimental data. Once there are free parameters to adjust in QFT and none in ST I think this is a scientific question that must not be forgotten.

• I will — but you are not going to see string theory connected with data without precise specification (as Woit correctly reminds you) of which string vacuum (or at least which type of vacuum) you are talking about.

• I know that it may take an article to give a more thorough answer, but the question that lingers on mind mind is as follows:

This concept of string vacuum that is mentioned so frequently in this discusssions, is it somehow related to the fact that the uncertaintly principle does not allow for real vacuum, as any field just can’t “stay put”, cannot allow for real “emptyness”, something has to be happening where there is “nothing”, even if it starts with pairs of virtual particles (particle-antiparticle)?

Kind regards, GEN

• We’ll get there… the word “vacuum” *also* needs definition.

• The virtual particles in uncertaintly principle and to define it in equations is like comparative philology (Genetic relatedness), Ape man in darwin’s theory of evolution, Quantitative easing in Economics ect..
Max Planck knew well that this constant had a precise nonzero value. “I am unable to understand Jeans’ stubbornness — he is an example of a theoretician as should never be existing, the same as Friedrich Hegel was for philosophy. So much the worse for the facts if they don’t fit.”

Time dependent and time independent cannot coexist.

There is non zero at the fragile position of Vase at the edge of table. But we can only define the mass-energy – not the dark energy, which is not mass energy, where gravity is ?

• Ok. Let us say you are free to chose any vacuum you want, once it explains at least all phenomenology in SM with same accuracy. Dealt?

• Let’s get back to this question after I have a few more posts on the table… so we can make sure we’re all starting from the same basic understanding…

7. Scientific research: Mission —-> Vision (result of putting one’s imagination to work?) —-> Goal(s) —-> Strategy.

8. Excellent article, as usual. I am really looking forward to the series of upcoming articles you mention.

Another reason to study imaginary worlds (one closely related to your second reason) is that sometimes it is not possible to understand the real world until we have first understood an idealization of it. There are many examples of this historically. The most well-known is probably the discovery of the laws of motion by Galileo and Newton. For hundreds of years, people followed Aristotle in believing that a moving object would return to its “natural state” of being at rest unless a force acted on it. Galileo and Newton’s breakthrough was their ability to imagine a world without friction or air resistance. Only after they understood this imaginary world could they properly understand the real one and learn that the natural state of an object is to continue moving in the same way UNLESS a force acts on it. I mention this as slightly distinct from your 2nd reason because it was not the mathematical difficulty of treating friction that was the stumbling block to progress. The breakthrough was imagining the qualitative concept of a moving object on which no net forces were acting.

9. Thank you, professor Strassler. I had posed the question in your earlier post as to whether or not string “theory” should be called string “conjecture”. This helps partially answer my question.

• Yes, and thank you for your question. I got me thinking that I really needed to deal with this definition.

10. Matt, thanks for taking the time to clarify things. In my experience not only the general public but also our colleagues may have outdated information about the problems and motivation of research in high energy theory, and as a result can be confused about these issues. Also in my experience, most people would listen carefully and try to understand, even if the noisy environment would make it seem otherwise. So, again, thanks.

11. With respect to the biology analogy: flies and mice actually exist, so this is not really an analogy. And physics uses simple models to understand the real world, but these models can actually be compared to real experiments. See e.g mean field models, etc. QFT, too, is only an effective method, as is clear from the way it was originally constructed. The fact that QFT models can be compared to experimental results is the justification of these models. String theory does not have any connection with experiments beyond these of the Standard Model. An approximate/effective model is not simply a conjecture.

• Patience, sir, patience. (I suspect you think you know where I’m going with this notion that studying imaginary worlds, as a way to get insight into the real one, is important. But I don’t think you do yet.) Right now this is all just preamble. The story is complex and there’s no way to jump to the end without confusion. After a careful set of posts over about two weeks or so, it should become crystal clear.

• Thanks, I am familiar with toy models in theoretical physics. In the end, though, comparison with experiment is the real test. But I will have patience and have another look in a week or two.

12. IMHO, until it is sufficiently proven (through experiments) that a simplified/approximate model is valid to describe (within the scope of validity of the model) the real world, that the simplified model is a valid description of the real world is a conjecture, or at best, a work hypothesis.

• A conjecture is a theory that might be a description of the real world, but might not, when you don’t yet know which is the case.

• A conjecture might not really have well-defined equations to go with it. I think there are lot of very different types of conjectures, even more than theories…

13. I think the biology analogy is right on the money. The big difficulty here is that a lot of people have been taught that using the word theory to mean anything but “extremely well-tested description of the real world” is improper, mostly due to a lot of science communication efforts focusing on countering creationism. But that’s simply not what it means in theoretical physics (as I tried to get across in my ars technica article: http://arstechnica.com/science/2013/05/earning-a-phd-by-studying-a-theory-that-we-know-is-wrong/), and that’s what leads to many people being confused when we discuss string theory.

• That is why the qualifier “well-tested” is often appended.

Whether or not to include approximations, toy models and, in the end, “unreasonable” math theories is context dependent. (Some of those would be “rejected” theories, depending on your idea of approximation/effective theory et cetera.) Or in other words definition dependent, i.e. a matter of usefulness or even taste.

But yes, I can see that context dependence is a problem. I don’t think that it is a fault of some particular context though. We could as well say that the big difficulty is that theoretical physics tries to teach that using “extremely well-tested description of the real world” is improper.

14. Matt, just one comment:

It is my understanding that the main points that link quantum mechanics math (Dirac, Schrodinger, etc.) with QFT are mainly path integral formulations.

Quantum mechanics math is basically particular applications of Rational Mechanics, that is, particular applications of the Hamiltonian, with help from the Lagrangian, Lengedre transforms, Fourier Transforms: as I said, basically Rational Mechanics.

In college, I studied all this including classical QM until Dirac, but none of the later stuff, which I did study some of it, later on, on my own in my spare time, which means a lot less thorough and strict kind of studying method involved.

It would really be helpful if you could include at least some comments regarding how the new stuff relates to the basic Rational Mechanics stuff (Hamiltonian, etc.).

Besides the fact that it would be very useful for my better understanding of the things being discussed, it would be helpful in other ways, as it gives a solid grounding on general principles, like the Principle of Least (extremum) Action and Noether’s Theorem.

As you want to describe what we know and don’t know about QFT, it seems to me that including the perspective of Rational Mechanics on this could be a proper reference framework for such goal.

Kind regards, GEN

• I’m afraid this stuff is probably more technical than I can address here. The math of quantum field theory, and how it relates to the math of quantum mechanics, is a fascinating story — and no, Feynman’s path integral methods are neither the whole story nor anywhere near as simple (!! 🙂 ) as they look. Moreover, we’re still learning new things every year or two.

My approach in the coming weeks will be to focus on the physics and on our ability to calculate the physics — not on *how* we calculate it. I can understand you wanting a more advanced course, but I’m afraid this blog isn’t going to provide it… I need a larger readership.

Maybe someday I will give lectures on quantum field theory for philosophers and other non-experts, and these will be videotaped. I’m not going to be doing that this year though.

• I appreciate your candor regarding the scope of your current posts (I knew that it was a long shot, but I had to make the comment anyways!).

15. Experiments show that sporters taking paracetamol vs sporters taking placebo’s (thinking they get paracetamol) have more endurance because their bodytemperatuture stays lower. why? One doen,t know. What is the mission? Selling more paracetamol? Marketing people are very good at putting their imagination to work 🙂

Conclusion: comparing strategy’s is risky.

• Anything involving studies of humans is a LOT trickier than studies involving quarks. You have biology, sociology and psychology all wrapped up together. So — yet again we see this approach at work — if we want to see what is special to the science of studying humans, and figure out what if anything is common to all scientific study, let’s take a much simpler case: physics of particles.

• Simpler? More straightforward I think, at least the way you do it.

16. The first self-inconsistent theory was Classical Electrodynamics of a point particle. Unfortunately, its flaws were “understood” as due to “unknown physics of short distances” rather than our mathematical and physical errors, so QFT inherited this self-inconsistency too.

• Thanks, I will read it carefully.

• Well, after browsing the article by Coleman’s, I found the same mass renormalization and runaway solutions (the equations are the same as everywhere else). Nothing is resolved in a sense of correctly coupling mechanical and field equations, unfortunately. To see what I mean, please read my article http://pubs.sciepub.com/ijp/1/4/2/index.html

17. It seems to me that physicists use the word “theory” with at least two different meanings. I’ll give examples of both:

1) In the article above: “Quantum field theory is the mathematical language of particle physics“.

In this case “theory” means a theoretical framework, a kind of template or (as you wrote) a language with a particular syntax. It does not tell you, for example, which fields you have and how the Lagrangian (a mathematical object that governs the dynamical behavior of the fields) looks. But it tells you, which kinds of fields you could possibly have, and which methods you can apply to find out how these fields would behave.

2) From the Wikipedia article on “Landau pole”: “the Landau pole […] is the momentum (or energy) scale at which the coupling constant (interaction strength) of a quantum field theory becomes infinite” (emphasis mine, notice the article).

In this case “theory” means something else. It refers to a particular instance within the theoretical framework, an instance that has specific fields, a specific Lagrangian, etc. In this sense there are many “theories” you can think of within the framework of quantum field theory.

From what I read, one interesting aspect of string theory is that the situation might be somewhat different there. It seems that string theory – the framework – has only a single unique inhabitant: string theory – the instance. I do not yet understand what the arguments are for this uniqueness, but it is obviously interesting. Unfortunately there is (and here my understanding gets very vague) another conceptual layer beneath the layers of “framework” and “instance”: The layer of “solutions” or “vacua” or “backgrounds” of a theory (instance). And there can be lots of them, or maybe better: lots of different classes of them.

• This issue is actually addressed at the beginning of tomorrow’s post. Stay tuned.

18. If we still do not have experimental measurements that can either verify or disprove a mathematical model that is able to explain a sub-set of existing experimental evidence and also might explain other related phenomena (for which do not have yet complete evidence to verify or disprove), then, that is also a theory, and for many cases, this is the starting point of many theories that now have been verified and proven consistent with existing evidence.

19. Matt I wasn’t too keen on the imaginary worlds or which properties of our universe are true of all possible universes?. I’ve just searched this page for the word “evidence”, and the only instances are in Gaston’s comment above. IMHO you need to pay special attention to the evidence. Evidence like the Einstein-de Haas effect.

• Patience, patience. Rome wasn’t built in a day.

• I would tend to argue that evidence tell us about which theories do or do not provide good descriptions of the real world, not about what gets to count as a theory.

• Well put. I agree.

• Noted Matt.

No problem Parlyne. The thing is, the Einstein-de Haas effect demonstrates that spin angular momentum “is indeed of the same nature as the angular momentum of rotating bodies as conceived in classical mechanics”. Which means there’s something going round and round in there. Magnetic moment is further evidence. What might it be? IMHO there lots of things like this that theoretical physicists don’t pay enough attention to. But noting Matt’s remark above, I’ll see how his next few blog entries pan out.

• The Einstein-De Haas effect is one of such situations where a summation of quantum effects of many particles can be measured as a macroscopic effect.

Kind regards, GEN

20. I have a feel that some confusion about String Theory (ST) capabilities may have originated from the statement of Stephen Hawking that in his view the ST is somewhat “oversold” ( his word ) in a way that it has no outcome and cannot do predictions to current experiments ( we cannot reach today the required hi energy levels and so we should focus on theories that can do predictions today using theories other than ST ).

Matt, please correct me, if my feeling is wrong.
Yours, bob

• I don’t think that’s wrong’, no. String Theory (in Application Number 1 = Theory of Everything candidate = String Unification) has been oversold, now and again, since the 1980s… it goes in waves.

But still, there’s a subtle point:

When you say “we should focus on theories that can do predictions today using theories other than String Theory” — my response is “yes, sort of, but don’t forget that I sometimes NEED string theory, as a tool (Application Number 2), in order to make the predictions that you’d like me to make — certainly for imaginary worlds that somewhat resemble our own, and perhaps even for the real world.”

21. Bob, many other scientists besides Hawking (some of them very prominent), have fielded their concerns regarding the validity of String Theory and its variations.

So far, regarding String Theory, or SUSY, or even other theories, the jury is still out.

It is my understanding that part of this is due to the fact that many theories for at least the last 100 years are very complex and insights are very difficult to be gained, so, there are many possible interpretations that take the place of insights when these are scarce.

As we have to navigate through this “sea of interpretations”, opinions abound and get into the conversations.

Kind regards, GEN

22. In Physics there are many experts, but no Authorities, so, it is OK to field your concerns, but we should all follow the Scientific Method to solve any doubts and problems.

23. This is definitely very helpful for my continued understanding of what you “theoretical scientists,” do. I appreciate it. So it would be safe to say you like to use your imagination lots? 🙂

HOW to BECOME a GOOD THEORETICAL PHYSICIST- http://www.staff.science.uu.nl/~hooft101/theorist.html by Gerard ‘t Hooft is quite helpful too.

24. Interesting post. It’s surprising how hard it is to pin down what we mean by ‘theory’ even now. I notice wikipedia distinguishes between ‘theory’ and ‘scientific theory’ but not between scientific theories that, while no doubt incomplete, are strongly supported by evidence (.eg.gravity) and theories that are at the stage of an entirely theoretical edifice (GR in the early years, SUSY today etc).
The word ‘model’ has even worse connotations as far as the public is concerned- a lot of climate scientists have their work regularly rubbished by commentators who understand nothing of how models are constructed and constrained!

25. Allow me to mention what Mulla Sadra of Shiraz discovered in his transcendental philosophy about the primary fundamental movement where every thing in the cosmos is in a continuous change /birth/rebirth , doesn’t this refer to how physics view the fundamentals now ?
What can we call this ? A theory or a glimpse to the veiled ? Or a extra-cosmic capacity of the human mind?

• I would say it’s called stating the obvious, but that’s just me.

26. PS. : That was around 4 centuries ago .

27. Normally, if you know that a theory merely describes an imaginary world and you know at the outset that it does not describe the real world, you call it as “toy model” rather than a theory in the august sense used in this post.

28. Matt,
It’s extremely unclear who’s a “string theorist” these days or what that even means, and despite what people seem to believe, I think many of those now calling themselves “string theorists” are doing interesting things. But, no, in the current sociological use of the term, you’re not the kind of person generally being referred to that way.

The “implication” you attribute to my few words contrasting QFT and string theory in the context of unified theories doesn’t correspond to anything I actually think. “Quantum Field Theory” refers to a very large class of theories, and of course the question of how well we understand them and their vacuum structure is an extremely complicated one. I’m very well aware that there are interesting QFTs which we don’t understand non-perturbatively, even in principle.

As for “string theory”, in this day and age of M-theory and AdS/CFT, it’s not at all clear exactly what that term means, and that’s part of the problem I was referring to. Sure, there are some things you can call “string theory” that are reasonably well-understood, others where there isn’t even a viable definition. As I wrote in a comment that you don’t quote, the history of trying to use some kind of “string theory” to study strongly coupled qfts is a long and interesting one.

Good luck with your multi-part series trying to explain some of these complexities. I wish though you would avoid taking sentences I wrote in blog comment sections out of the argument they were part of and using them to put arguments in my mouth that I don’t believe in.

• Peter — you are always welcome to set the record straight regarding your opinions. I do not wish to misrepresent them — especially when they are reasonable.

Still, in one of your comments you did make a very strong statement that string theory, unlike QFT, is not defined, and that string vacua, unlike QFT vacua, are not understood at all. I am not misquoting you there, am I? (Set me straight if I am; or alternatively, feel free to add nuance to your comment.) This statement was, from my scientific perspective, simply inaccurate. And either

* you did not know it was inaccurate (in which case I feel obligated to set you and my readers straight) or
* you did know it was inaccurate (in which case, why did you make that statement?)

Separately:

“As I wrote in a comment that you don’t quote, the history of trying to use some kind of “string theory” to study strongly coupled qfts is a long and interesting one.”

You did write this, and I’m glad you think this. But I still feel that in this remark you do not give the unified string/M theory its due. Yes, string theories of various sorts — ones without quantum gravity, with no pretensions to unification — have been used in the past for quantum field theory, with a certain degree of success. The shocking thing that happened in the late 90s, however, is that THE unified string/M theory — the one that *has* quantum gravity and extra dimensions and is used by the string unification folks — turns out to be *better* for studying quantum field theories with strong forces than all of the previous string models — and that having extra dimensions of space and quantum gravity turns out to be crucial in this application!!

In particular, the unified string/M theory is the first string theory to give rigorous, quantitatively precise, and even potentially testable predictions for any quantum field theory. Moreover, some of those predictions are counter-intuitive and rather astonishing. So even though “some kind of string theory'” has been used before, those attempts never gave us what the unified string/M theory has given us.

• /I’m very well aware that there are interesting QFTs which we don’t understand non-perturbatively, even in principle./

My humble question..
If this perturbative nature (approximation) is filled with axiomatic equations like virtual particles, comparative philology (Genetic relatedness), Ape man in darwin’s theory of evolution, Quantitative easing in Economics ect..

This world can only increase The 1%
The 1% is a process, which will end in chaos further engulfing within 1% – not leading to any scientific Enlightenment ?

29. Matt,
I never wrote “string theory, unlike QFT is not defined”, what you quote is just a reference to the fact that non-perturbative string theory has a much more serious problem with what its definition is than QFT does. For more, reread my last comment.

I never wrote “string vacua, unlike QFT vacua are not understood at all”, my comment was explicitly about string vacua that are supposed to give a unified theory and the problems with understanding those (i.e., what is the “landscape”). Again, reread my last comment.

Look, physics is an extremely complex subject, and the topics under discussion here are among the most complex and poorly understood there are. If you want to have a serious discussion of them, that’s great. If you want to play the stupid game of taking sentences I write (which inherently can never capture the full complexity of the situation) rewriting them to make them completely incorrect and then using this to show the world that I don’t know what I’m talking about, yes you can do that. Maybe it will help you make the “no one should listen to that ignoramus Peter Woit case”, but it won’t further anyone’s understanding of anything.

Let me just show you that if I wanted to, I could play too:

“Matt Strassler writes that M-theory is the best way to study strongly-coupled quantum field theories, an inaccurate statement showing that he doesn’t realize that M-theory doesn’t apply to all sorts of strongly-coupled QFTs, so he must just be sadly really sunk deep in ignorant fanaticism about string theory”

Now, wasn’t that fun?

No, actually it was really stupid.

• So is it fair to say that you think the primary difference between a generic quantum field theory and string theory is both the difficulty of definition and the existence of a landscape of solutions in the latter rendering it unpredictive?

• I think Peter is saying that’s not fair. I must admit I thought that’s what he said on Tuesday… but he seems to be saying I misunderstood him, or maybe that the whole thing is more nuanced. Which I’m prepared to accept, despite being puzzled.

• “Generic quantum field theory” is a meaningless term, and these days “string theory” is not much better. If you want to engage in arguments of this kind, you need to specify exactly what QFTs you want to talk about and what aspects of them are at issue, as well as tell me exactly what you mean by string theory. My objection to a lot of these arguments is that what is going on is often sophistry designed to avoid the obvious contrast between the most successful fundamental theory in human history, and one of the least successful ideas (string unification) ever tried. I understand the point Matt is trying to make here, but I object to the “string theory is more predictive than QFT” sloganeering and the attempt to claim that the only problem with string theory unification is that our accelerators aren’t large enough. He may be trying to avoid this, but he’s operating in an environment of an active campaign to mislead people about these issues.

• No one, especially not me, has made the statement “string theory is more predictive than QFT” on this website. That statement would be somewhere between manifestly false and meaningless, for the reasons you state. As I emphasized on Tuesday, you have to specify the string theory vacuum, and the specific QFT, and what “predictive” means in the context of interest, before you can make a comparison. There are specific cases where one theory does better than the other. We all agree QFT is older, simpler, and much better understood than string/M/whatever theory.

As for “the only problem with string theory unification is that our accelerators aren’t large enough.”, of course I didn’t say that, but you made your point that a reader might misread what I wrote, and I added a note in response. I said that just as one has to specify a QFT, one has to specify a string vacuum before one can hope to calculate and predict anything. We don’t disagree about the need to be clear about that.

I am aware of the active campaign of hyping, some of it intentional, some of it unintentional, and many parts of it without scientific justification. (It’s not an accident that my talk on string theory from 2006 was called “Beyond the Hype”.) I think many readers who come to my site do so because they recognize hype when they see it, and they want the straight story. They will get it, if you give me a couple of weeks to churn out the relevant articles.

• Peter: My goal is not to attack you, it is to get the science right and to explain it properly to the public. [I will, however, defend myself against attacks on my writing, my science and on my integrity.] If you agree with my presentations on the science in the next weeks, and I’ve said nothing you disagree with, then — great. If not, let’s discuss the disagreements when they arise.

• “Never argue with a fool, onlookers may not be able to tell the difference”

30. One can only wish there was less of politics in science and more of science in politics.

31. Prof. Strassler: In your preceding 6:19 PM post I don’t understand the statement “…unified string/M theory is the first string theory to give rigorous, quantitatively precise, and even potentially testable predictions for any quantum field theory.” Does the statement mean that the Heisenberg uncertainty principle is automatically generalized to an hbar/alpha-prime uncertainty principle given the quantum field theory?

• No it doesn’t. It’s more subtle than that.

32. Hi Matt,

You have usefully defined what you mean by “a theory.” A definition is just that — it makes explicit what you are talking about — and your definition of “theory” corresponds well with the language of theorists. However, you have made it clear that the primary goal of your blog is to present a correct, unvarnished picture of a subset of physics where you have substantive knowledge, so I feel an urge to “complain” that your definition as it stands could unintentionally obscure or even mislead some of your audience.

What bothers me is that your definition makes no distinction at all between mathematically consistent theories (whether simple toy theories or complex frameworks) and consistent theories that have also passed stringent experimental or observational tests (like QM and GR). While the distinction is obvious to you and other scientifically trained people, it may be less so to the interested public. My strong impression is that the general public has little idea just how strong the empirical evidence is for QM and GR, and to define QM and GR as theories on the basis of mathematical consistency and predictivity alone risks cheapening their status or, by lumping them (by default) into the same category as speculative or toy theories that also meet your definition, unjustifiably increasing (by association) their stature as carrying verified “truth” about the physical world. This is misleading, and I think that conflating the two “types” of theories has been a significant factor in fostering and perpetuating the “string wars” and their collateral damage

For example, since you allow that consistency and predictivity are the hallmarks of a theory, and moreover that a theory may be a theory of imaginary worlds, it looks to me like we have a situation of “once a theory, always a theory;” a theory loses no stature by your definition no matter how many times its predictions fail experimental tests. Yes, a highly speculative theory must be appropriately mathematical to fulfill your definition, but I imagine much of that distinction can easily be lost to people who also propose their own speculations (or speculations by others they found interesting) as a “theory” with no attempt at intellectual rigor whatsoever.

• Clarification (hopefully obvious) in the second paragraph:

… and to define QM and GR as theories on the basis of mathematical consistency and predictivity alone risks cheapening their status or, by lumping them (by default) into the same category as speculative or toy theories that also meet your definition, unjustifiably increasing (by association) the stature of the speculative/toy theories as carrying verified “truth” about the physical world.

• I can’t deny that the terminology we use leads to confusions. It’s hardly the only case; look at the word “mass”, http://profmattstrassler.com/articles-and-posts/particle-physics-basics/mass-energy-matter-etc/more-on-mass/the-two-definitions-of-mass-and-why-i-use-only-one/ .

One cannot alter language of 100 years by fiat. We have no choice but to work hard to compensate; we are not going to be able to change entrenched terminology like “theory of relativity” — a well-established theory, well-defined and well-understood — or “string theory” — a poorly-understood, barely-defined, speculative theory. The language of particle physics involves modifiers of the word theory:

“untested theory”
“speculative theory”
“poorly-understood theory”
“inconsistent theory”

“partially-tested theory”
“well-established theory”
“consistent theory”
“accepted theory”

The key is to find compelling modifiers (maybe there are better ones?) that speak more clearly to the public about the difference between things that nobody understands and things that everyone accepts as descriptive of nature, and the gradations between. I do view this as one of the key pedagogical problems of our time, as far as science outreach.

• I agree with everything in your reply. If those who wish to educate/communicate with non-experts were to include the appropriate modifier(s) when discussing a theory, there would be less confusion, and the hype-o-meter used by cautious readers would give more accurate readings…

33. Matt Strassler wrote: “The physics is this: the oscillation you put into the equations is not the one that you measure, because of the anharmonic effects.” Matt, but the oscillation is not harmonic even for one anharmonic oscillator, so what? I do not get what special is in your “explanation”. Maybe you can give me a reference to those coupled anharmonic oscillators because I do not understand in what way they are coupled and what is calculated. If you couple many point bodies, the total mass increases, but each mass remains intact. There are things that are just calculated from the fundamental constants and have nothing to do with discarding or other ways of result modifications to obtain a desirable result from a bad one.

34. Matt, one problem with string theory or in papers which quote “string theory” is that one often finds conflicting statements.
For example in Cliff Will’s review paper gr-qc/0103036, he has claimed
that string theory predicts violation of equivalence principle because of dilaton fields. whereas many others claim that string theory does not predict any violations of equivalence principle. question is who is right?
tomorrow if some experiment detects violation of equivalence principle,
would that rule out string according to second camp?

Shantanu

• Without reading *exactly* what Will said, I believe (experts may correct me)

1) Will’s statement is correct, but…

2) There is no prediction in string theory that suggests the dilaton must have an extremely low mass; quantum fluctuations of other fields will correct this mass and can make it moderate or very large.

3) If the dilaton has a sufficiently large mass, any larger than a typical neutrino, then Will’s statement is correct but useless, because the violations he mentions will be at such short distances that no one will ever measure them.

4) There are plenty of string/M vacua that have no dilaton at all (although it is common to have other fields that, if lightweight, might play a similar role.)

So they’re both right to a degree, but I would say the statement “string theory does *not* predict violations of the equivalence principle” is more correct. And really I think you need to say:

“string theory does *not* predict practically-measurable violations of the equivalence principle”, and
“yet string theory does not forbid measurable violations of the equivalence principle”, and
“other theories of quantum gravity are similar, predicting violations of the equivalence principle, but by amounts that may or may not be measurable.”

So if we saw such violations in data, we’d have no idea what they meant, and we’d have a lot of work to do.

35. I would tend to draw a distinction between two uses of “imaginary.”

To me, an idea we know (or strongly suspect) isn’t part of the real world is imaginary. Such ideas may help us understand aspects of the real world. These imaginary ideas are sometimes referred to as “spherical cows” (extreme simplifications useful for some types of analysis), and spherical cows are pretty definitely imaginary.

But an idea that we suspect is part of the real world (the Top, the Higgs), to me those things aren’t “imaginary” (just undiscovered country). We went looking for the Top and Higgs, because we expected to find them in our real world. I have a hard time considering those things imaginary.

But my legion of hypnotized, bulldozer-driving musical rats? Definitely imaginary…. 😕

36. Professor Strassler, you talk about these beautiful scientific buildings: Quantum Field Theory, String Theory, sometimes General relativity. Their logic, their computations, their implications, their wonderful symmetries (gauge, abelian or not, local or global, any other kind science will discover…). Their use, their deductions, appear to be a negative-slope path, from the top of abstraction (laws, principles, invariances, constants, and all those things we think of but we do not see as objects around us) to the bottom of pure empirical facts (all those things we see, we touch, we control with instruments, with empirical acts).
I wonder, I ask you: do you think there may be another viewpoint on all these “scientific landscape”? I mean: could QFT one day be considered from a point of view of environmental other than from that of abstraction?
Could it be done a theory centered on “variations” more than on “invariances”? Could faster computers help doing that sort of revolutions?
Is mathematical language that keeps endorsing abstractions/invariances/constants, or is it a wrong considerations?
To end: do you think physics will continue being mathematical or there will be a all-computer/computations-based science?

• One thing I’ve learned from history and from my own personal experience is that speculation about the future of physics leads off cliffs. Imagine if you’d asked Newton or Maxwell whether the fundamental laws of physics might end up being probabilistic, as they are in quantum mechanics! The only thing I’m confident of is that there are surprises yet to come.

37. Matt, please give me references to the renormalization of coupled anharmonic oscillators so that I could better understand what it is. Regards, Vladimir.

38. Is there a specific reason why you chose to not moderate Dilaton’s comment about him leaving this site ?

39. Hello again Professor, I am very excited that you finally decided the share your views on quantum field theory and it’s potential reach beyond our understanding of the tug of war between the real and imaginary domains of nature.

You write: “Why are imaginary worlds important? Why focus on anything other than the real world? How could studying imaginary worlds be “scientific”?”

My question is, does the scientific community (particle physicists) have a robust system in place to ensure that the invalid new theories get removed quickly enough to prevent wasted careers of gifted people?

As Daric once put it “hocus pocus physics”.

• Does companies have a robust system in place to ensure that the invalid new products get removed quickly enough to prevent wasted careers of gifted people?

The proof is in the pudding, it works and it is more economical problems than new theories that wastes careers of gifted people. (Or invalid old theories and data, which you seem to have forgotten – people have to keep track of them as we learn more. A bigger, but not insurmountable, problem.)

• Apples and oranges … a good, successful company welcomes risk takers and as you say, the proof is in the pudding” (the market will dictate the validity of the new idea (product).

Physics is very different. Physicists, and in particular the professors, lure undergraduates to either remain and.or transfer over to their faculty to do their thesis in subjects practically dictated by the professors. As a professor you must be extremely careful how to handle this monumental of guide a young and vulnerable apprentice.

As we allow (invent, or as Daric put it, use hocus pocus) the different branches grow more and more on the tree of physics we must make sure that we don’t over load the capacity of the trunk and kill the tree.

The scientific method must be adhere to in the most robust procedure to ensure the integrity of the faculty.

41. Extremely interesting look forth to coming
back.

42. /*…Heck, I’d use formaldehyde, bulldozers, musical instruments and/or crowds of hypnotized rats if it would help me understand quantum field theory. I’ve got a job to do, and I’m not going to stray from it just because somebody with a different job (or an axe to grind) loves or hates my tools…*/

If so, why not to use the dense aether model for it? The end just justifies the means at the end…

In AWT the subject of quantum field theory aren’t some esoteric artifacts and phenomena at the whole boundary of the observable Universe – but just the common life physics [RES ignored duplicate image][1] BETWEEN scale of relativity and quantum mechanics. I.e. just the physics of formaldehyde, bulldozers, musical instruments and/or crowds of hypnotized rats. If you want to reconcile the worlds of quantum physics and general relativity, then the very first step should be, what actually exists between these worlds…

The memo is, the first step in understanding of your job is to realize, what this job is actually about… It’s not about choice of tools you can use, it’s about just these tools.

43. In general relativity all massive objects should collapse into singularity with no mercy. All right, but the general relativity isn’t the only theory describing the world, the quantum mechanics is relevant as well. And in quantum mechanics all wave packets of free particles should expand into infinity – this is exactly what the Dirac/Schrodinger equations predict. Apparently both theories are deeply flawed at the human observer scale, as nothing expands, neither collapses in our real life. What we can assume here is, the predictions of both theories are sorta averaged, which leads to quasi-stable behavior of objects in real life. The (principally) futile search of the exact way how to average these theories is the subject of quantum gravity theories, like the various stringy and loopy models. But at the moment, when two theories already predict the qualitatively different outcome for the same object it’s evident, these two theories can be never reconciled at the strictly rigorous formal level.

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