Backwards and Forwards in Science

I spent a few hours today involved with our Open Day at Maynooth University, including – as I mentioned here – giving a presentation about Theoretical Physics to complement one about Experimental Physics followed by a couple of hours of Q&A. It was a bit of a shame to be cooped up inside on such a lovely Spring day but we had a lot of interesting questions and it was all quite enjoyable.

One of the things that I tried to stress in my talk is that while there theorists and experimentalists (or observers), real science is about the interplay between the two, which I’ve illustrated in the above diagram which I use sometimes when talking about cosmology though it applies to other disciplines.

We have theoretical models – normally including a set of free parameters which we don’t know how to fix a priori. What we can do though is calculate the consequences if we did know the values of these parameters. That forward calculation is represented by the upward arrow, using theory to predict the result of a measurement. The backward calculation (inverse reasoning) involves using the measurements to infer values for the free parameters; that’s represented by the downward arrow. There’s usually a considerable amount of back-and-forth between theory space and measurement space as scientific knowledge develops. If one version of a model doesn’t fit we can adjust its parameters until it does, then we might need new data to test this iteration. It is only when the theoretical slack is sufficiently tight and freedom to adjust parameters is eliminated or severely restricted can we really test a theoretical idea definitively.

In cosmology we have only a handful of free parameters and this process has worked pretty well in providing a model in which these parameters are tightly constrained by a host of observational results. This is the standard model and although there a “tensions”, most prominently concerning the Hubble Constant, the model has survived very well. The same situation holds for the standard model of particle physics, though there is tension concerning the muon magnetic moment that I blogged about here.

I’ve written quite a lot on this blog about the inverse reasoning step – partly because I think there are many people (even professional scientists) who don’t understand this part very well and partly because cosmology provides a good example of a model with elements that can’t be calculated from first principles.

It struck me this morning, however, in answering a question about the muon magnetic moment that we often tend to assume that the forward calculation is somehow trivial. In fact the theoretical calculation of (g-2) is nothing of the sort: it requires lengthy supercomputer computations before the theory can make a prediction and there is some doubt over whether the current values of the theoretically expected value of the muon dipole moment are correct within the model.

The same issue arises in cosmology. It is not at all easy to calculate, for example, detailed properties of galaxy clustering in a given cosmological model. The forward calculation here uses huge N-body experiments. This is why a very considerable part of the effort being expended in preparation for the European Space Agency’s Euclid mission is on the simulation side.

Both particle physics and cosmology – and no doubt other fields – are thus limited by how well we can do the forward calculation and that is not going to change very soon. Nevertheless it is the interplay between theory and measurement that has driven the progress so far, and it will continue to do so even if it is the case that the more progress we make the harder it gets to go further.

9 Responses to “Backwards and Forwards in Science”

  1. One of the most common misunderstandings of crackpots, and even of some serious scientists, is the idea that it is somehow bad for a theory if it needs input from observation and cannot calculate everything from first principles.

    I won’t mention any names. 🙂

  2. My sister told me today that one of her friends was suprised to learn that ‘theoretical physicists’ are actual real people!

    • telescoper Says:

      I don’t believe in “real people”.

    • And electrical engineers are some sort of robot?

      Actually, that is an interesting case, as a robot who is an engineer would presumably be an electric engineer. There is a slight difference. Elliptical or elliptic? But there is no word magnetical, though the adverb magnetically exists.

      What has a high energy physicist been smoking?

      I recently read a book which mentioned some naked eye observers. My observing trips were never that much fun.

  3. One of the arguments by fundamentalists against evolution is that it is only a theory. But so is the theory of gravity and everyone believes in it – although not according to Family Guy – see

  4. […] people who were there often remind me of it. Coincidentally, I thought of that event when I wrote Saturday’s post. Since the forthcoming colloquium is via Zoom I think I’ll be safe from any such intervention […]

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