3 What is a theory?

What do we mean when we talk about a ‘theory’? Think about the examples you’ve seen in this course: Newton’s theory of gravity and Einstein’s theory of gravity (part of his general theory of relativity). In the end, a theory is a model (usually framed in the language of mathematics) of some aspects of the natural world, which is meant to describe how things behave, and explain the outcome of experiments. Such experiments play a key role here – they allow us to test our model, and are often used to inspire new models. Throughout the history of science, our theories have evolved. New experiments test our models in more and more detail, and we find deviations that show that the model is, at best, incomplete.

The two theories of gravity are a good example of this process. Einstein’s theory can explain small deviations observed by experiments, such as providing a precise explanation for the motion of the planet Mercury. It can be seen as a generalisation of Newton’s theory, in the sense that the latter is a good approximation of Einstein’s theory for many everyday purposes.

But how do we choose one theory over another? If one theory successfully explains more observations than another, you would assume that it provides more insight into nature, and is therefore superior. But what if you have two (or more) different theories in your hands, each of which explain some observation equally well? What can you do then? One approach to this dilemma is to come up with an experiment which gives different answers depending on which theory has been applied, and then use this experiment to make a choice. Similarly, when a new theory predicts something which has not yet been observed, and you then go out and observe it exactly as predicted, it lends strong credence to the theory. A good example of this approach, discussed earlier in the course, is how support was gathered for Einstein’s theory of general relativity.

Another approach would be to look at the power of prediction of the theory. Here’s how this works. Suppose you have two different theories which both explain the behaviour of a system equally well. One of the theories uses a few fundamental constants (such as the speed of light in vacuum, or Planck’s constant) while the other contains tens or hundreds of parameters (numbers that enter the equations in the theory) which all have to be chosen correctly for the theory to work, without any information as to where these parameter values come from. You can argue that the first theory possesses more ‘predictive power’ than the second, because it requires less input to describe the behaviour of the system. Trying to reduce the number of parameters is a common approach to find a more ‘fundamental’ theory.

In fact, one reason why scientists are not completely happy with the current Standard Model of particle physics is that it includes quite a few parameters (many of them related to particle masses and the way that particles ‘mix’ when considering different interactions). The theory does not predict values for these parameters; they have to be determined by experiment. Many scientists believe that there should be a ‘reason’ for the values that these parameters take, and that there should be a theory that will predict their values.

Another highly significant aspect is the relationship between theories explaining different aspects of nature. There is a belief that there should be a ‘theory of everything’ that describes all natural processes consistently. Currently, we have quantum theory, which works well to predict physics at the smallest scales, and Einstein’s theory of general relativity, which works well to describe the structure of the universe. However, as far as we know right now, there seems to be no way to consolidate these two theories into a single theory that would encompass both. If an alternative theory were found for either that would allow for such a unified theory – while agreeing with experiments – it would certainly be favoured.

The discussion of theories can reach into more subjective territory. For example, the ‘beauty’ of the mathematical theory has become a matter of some controversy since the late 2010s, as will be discussed in the next section.