Let’s play a little game, hopefully illustrating something about quantum field theory, quantum gravity, and all that other good stuff. We already know that particles can be viewed as excitations of fields, which are some continuous media filling up space. One way of illustrating this is by drawing a checkers board filled with black or white squares (on second thought, most of what is below might be more intuitive to the go player). We say that the square is white when the field is not excited, and black when it is excited at some location. In other words, it costs a fixed amount of energy to paint one of the squares black (actually these turn out to be dark brown, which is some kind of sad statement about my eyesight).
Obviously in the lowest energy state all the squares on the board are white, and the excitation costing least energy is obtained by painting one square black, and that could be anywhere. This is what we can call a single particle:
Here are two particles, frozen in time. In our next time slice they may move a little.
Here are those two particles, a couple of second later, they are moving!
Since they are moving towards from each other, they must have some attractive force between them. The force is weak so that it causes them to move but does not change their internal structure too much. In other words, the energy of two particles in not precisely twice the energy of each one. Rather, it just gets a tiny bit smaller when they are closer together. That tiny amount is their interaction, we have then weakly interacting particles.
Now, to make life more interesting, suppose we have dial controlling the strength of the interaction, also known as a coupling constant. We increase that coupling constant, so the particles are interacting a bit more. For example, suppose the particles like to stick together, so if we turn on the interaction between them just a little bit more, they tend to attract each other more, maybe even forming some clumps. So a typical low energy configuration may look like:
We may want to give the elongated clumps a new name, since they will look a lot like a new species of particle to us. The rectangular ones are obviously different, in fact we have a whole zoo of particles. Just imagine how complicated things could become if I managed to draw little arrows, instead of those black boxes, at each point.
Another important thing happens when we turn on the coupling. In quantum mechanics the lowest energy state (the ground state), or any other state for that matter, is some linear superpositions of many configurations. Initially, before turning on any interaction, the most likely configuration was that of an all-white checkers board. Now the likelihood of more complicated configuration increases. Many configurations like that last one will become more and more likely. From the initial viewpoint, where the energy was just proportional to the number of black boxes, this one looks like a high energy configuration, but our energy landscape started changing once we increased the interaction. When we increase the strength of the interaction, the number of possible configurations contributing significantly to the ground state wave function increases, and simple classical pictures like the ones above become less and less reliable.
Suppose we now really crank up that coupling, and look at the ground state and a few low energy excitations. Usually we get a complicated and intractable mess, which is inherently quantum mechanical, but sometimes we get lucky and life simplifies. For example, sometimes we find that the lowest energy configuration at strong coupling is:
If we invest a little energy, we may find the most likely configuration to be:
Hey, that looks familiar! if we didn’t know we are at strong coupling, we might think we have some weakly interacting particles, albeit of a different kind, which are obtained as excitations of (another kind of) field (we’d call it the white field, creating almost free white particles). In other words, we have now a different, more economical set of words to describe the situation when the coupling constant becomes very strong.
That new description is called the dual description, it is just a change of perspective- when the checkers board is more likely to be almost all white we use the original variables, when it is almost all black we might want to use the language adapted to that situation. In general we can have multiple sets of variables, multiple languages, to describe the same physical reality. Each one of them is more suitable for one limit of the theory, one set of possible phenomena, and describes everything else poorly, in an hopelessly complicated language.
Every time the theory simplifies, and mental pictures like the above account for the physics more or less accurately, we’d call the result a classical limit of the theory. In such a limit wave functions of the states we are interested in are dominated by one classical configuration. Usually, to describe physics in that limit we’d use an adapted set of variables, to use the simplifications most efficiently. When we change variables to some dual description, we do not change the physics, we just use a language convenient for a specific classical limit. But, even though we do not change the physics, our mental pictures are tied to the set of variables we use, and therefore to specific classical limit of the theory. We have to train ourselves to take those mental pictures with a grain of salt, and try to always concentrate on well-defined physical questions.
Although this simplified set of pictures may demonstrate the basic idea, it is too naive in many ways. For one thing, in this example the dual variables look fairly similar to each other, which is usually not the case. In more realistic examples the basic physics looks very different when using dual variables. In general dual descriptions of the same physics may not utilize the same kind of fields, or the same kind of interactions (one could be gravitational and the other not), or even the same number of spacetime dimensions!
Finally, if you want to know what is it like to be a theoretical physicist, how about trying to make sense out of this configuration of the checkers board?
This, in the clean language of field theorists, is a configuration that has no particle interpretation, though I am sure with a little effort you can come up with a more colorful phrase.