## Physics: Mathematical or Theoretical or Experimental?

Fresh from doing two Open Day talks last week I thought I’d write a few words here about something that cropped up in the question-and-answer session.

For a start, I should explain that here at Maynooth University there are two Physics departments, one the Department of Theoretical Physics (of which I am a Faculty member) and the other the Department of Experimental Physics. These two units are in the same building but are largely separate in terms of teaching and research.

For instance, when students enter on our General Science degree programme they have to choose four subjects in the first year, including Mathematics (much as I did when I did my Natural Sciences degree at Cambridge back in the day). Picking `double physics’ (i.e. Experimental Physics and Theoretical Physics) uses up two of those choices, whereas Physics was a single choice in the first year of my degree.

To confuse matters still further, the Department of Theoretical Physics only recently changed its name from the Department of Mathematical Physics and some of our documentation still carries that title. I got asked several times at the weekend what’s the difference between Theoretical Physics and Mathematical Physics?

As far as Maynooth is concerned we basically use those terms interchangeably and, although it might appear a little confusing at first, having both terms scattered around our webpages means that Google searches for both `Mathematical Physics’ and `Theoretical Physics’ will find us.

It’s interesting though that Wikipedia has different pages for Mathematical Physics and Theoretical Physics. The former begins

Mathematical physics refers to the development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines the field as “the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories”. It is a branch of applied mathematics, but deals with physical problems.

while the latter starts

Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experimental tools to probe these phenomena.

The difference is subtle,and there is obviously a huge amount in common between these two definitions, but it is perhaps that Theoretical Physics is more focused on the use of mathematics to account for the results of experiment and observations whereas Mathematical Physics concerns itself more with the development of the necessary mathematical techniques, but I’m sure there will be readers of this blog who disagree with this interpretation.

For the record here is what Wikipedia says about Experimental Physics:

Experimental physics is the category of disciplines and sub-disciplines in the field of physics that are concerned with the observation of physical phenomena and experiments. Methods vary from discipline to discipline, from simple experiments and observations, such as the Cavendish experiment, to more complicated ones, such as the Large Hadron Collider.

I’d say that theoretical physicists are more likely than mathematical physicists to be working closely with experimentalists. I count myself as a theoretical physicist (that’s what I did in Part II at Cambridge, anyway) though I do work a lot with data.

Anyway, as an experiment, I asked the audience at my Open Day talks if they could name a famous physicist. Most popular among the responses were the names you would have guessed: Einstein, Hawking, Feynman, Dirac, Newton, Schrodinger, and some less familiar names such as Leonard Susskind and Brian Greene. Every single one of these is (or was) a theorist of some kind. This is confirmed by the fact that many potential students mention similar names in the personal statements they write in support of their university applications. For better or worse, it seems that to many potential students Physics largely means Theoretical (or Mathematical) Physics.

Although it is probably good for our recruitment that there are so many high-profile theoretical physicists, it probably says more about how little the general public knows about what physics actually is and how it really works. For me the important thing is the interplay between theory and experiment (or observation), as it is in that aspect where the whole exceeds the sum of the parts.

It might seem a bit strange to have two Physics departments in one University – though it seems to work alright in Cambridge! – but I think it works pretty well. The one problem is that there isn’t a clear entry point for `Physics’ without an adjective. Students can carry Theoretical Physics and Experimental Physics through all the way to final year and get a joint honours degree (50% theory and 50% experiment) or they can pick one to do single honours, but we might attract a few more students if the former possibility were just called `Physics’. Perhaps.

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November 26, 2018 at 1:36 pm

Another big issue is the balance in physics departments between basic and applied physics, and whether any particular department gets that balance right in terms of resources and esteem.

November 26, 2018 at 2:25 pm

Yes, another grey area is between Applied Physics and Engineering.

November 26, 2018 at 3:41 pm

Yes.

November 27, 2018 at 2:04 pm

Has anybody written on the difference?

November 26, 2018 at 1:53 pm

You were wise not to mention applied mathematics. 🙂

November 27, 2018 at 2:03 pm

I did some rabble-rousing on that subject courtesy of Peter here:

https://telescoper.wordpress.com/2010/04/20/guest-post-the-emperors-new-math/

November 26, 2018 at 3:21 pm

I would add that many people who say they do “mathematical physics” are in fact mathematicians — that is, they’re housed in mathematics departments.

November 26, 2018 at 3:44 pm

Yes, that’s the way I see things: `mathematical physics’ is the term mathematicians give to the field, while `theoretical physics’ is what physicists call it. Of course, mathematicians and physicists tend to approach the field from slightly different perspectives, but the differences are relatively modest.

November 26, 2018 at 3:48 pm

Penrose is a mathematician, for example, but has done stuff interesting for physics. And Witten is a physicist (though he studied history first) but won the Field Medal.

November 27, 2018 at 1:07 pm

Has it worked alright in Cambridge? DAMTP was founded in 1959 and I do not think it has won a single Nobel Prize, in marked contrast to the university’s Physics Department.

I don’t hold with the phrase “mathematical physics”, because *all* analysis in physics is expressed using mathematics. As for the alternative definition which Peter quotes, ie mathematics developed with physical application in mind, this is mathematics and so should be called physical mathematics, not mathematical physics.

That the best-known physicists are all theoreticians reflects more the interests of the media and general public, surely?

For me the important thing is the interplay between theory and experiment (or observation), as it is in that aspect where the whole exceeds the sum of the parts.A thousand times Yes! I have seen it described beautifully as a dialectic between theory and experiment. Nowadays I like to subcategorise “observation” as “observation of systems we cannot influence” using superior technology, as in astrophysics, and “observations from designed interventionist experiments” – i.e., if I do this *here*, what effect will it have on that *there*?

November 27, 2018 at 2:01 pm

DAMTP does have at least on IgNobel Prize, though. 🙂

Seriously, winning a Nobel Prize, especially in a theoretical field (remember: the will said “invention or discovery”, even if it is not always interpreted strictly), does not correlate that well with excellence.

November 27, 2018 at 2:05 pm

That’s a great consolation to me!

November 27, 2018 at 4:25 pm

Well, it works in the sense that the Cavendish and DAMTP have survived for quite a while. Whether the split has been good for Physics at Cambridge I couldn’t possibly say!

November 27, 2018 at 4:29 pm

And the Institute of Astronomy is part of neither, right? Often, there is a “Department of Physics and Astronomy”. While the MRAO is part of the Cavendish, when the RGO was still in Cambridge, there were thus 4 institutes which did astronomy/astrophysics/cosmology in some sense. There aren’t many places like that—maybe Garching, Heidelberg, Boston.

November 27, 2018 at 4:46 pm

There are also many physicists in the Engineering Department at Cambridge…

December 1, 2018 at 8:27 pm

You seem to have forgotten that Newton “with his prism and silent face” was at least as famous for his Optiks (largely recording experimental work) as for the Principia. And the Principia records some more of Newton’s own experimental results, especially on fluid mechanics. Richard Westfall’s biography claims that Newton’s experimental work was far and away the most meticulous and accurate of any of his contemporaries.

Still, it’s a shame that Michael Faraday isn’t often mentioned. These days physics A-levels usually include a module on “fields” but the content doesn’t seem to explain how the field concept extends Newtonian action-at-a-distance, nor mention Faraday’s crucial role in coming up with it.