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:

- What is a prediction?
- What is string theory?
- 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

- describe to you what we do and don’t know about quantum field theory
- describe to you what we do and don’t know about string theory
- 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.
- 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: “S*ometimes 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…*