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By Hamish Johnston
Paul Dirac famously said “A physical theory must possess mathematical beauty”.
This morning Radio 4’s Today programme asked Dirac’s biographer Graham Farmelo “How can a theory of physics possess beauty?”.
Farmelo was joined on-air by Jim Al-Khalili, professor of physics at the University of Surrey, and together they discussed if aesthetics and logical thinking can go together.
You can listen to the conversation here — scroll right down to the last item of the programme. The audio clip will be available for about one week.
Although Al-Khalili and Farmelo did their best to explain, Radio 4’s normally razor-sharp John Humphrys seemed humbled by the concept.
The piece ended with Humphrys asking Al-Khalili for a concrete example of how the beauty of mathematics led Dirac to ground-breaking physics.
Al-Khalili recounted how Dirac used mathematics to predict the existence of antimatter several years before the stuff was actually seen in an experiment.
“…and antimatter is?”, replied Humphrys.
Typical of Al-Khalili to pick the perfect example – as you know, Dirac always attcahed great importance to beauty in equations, and claimed that beauty guided him in deriving the Dirac equation.
I’ve been watching repeats of Al-Khalili’s TV series ATOM, they are absolutely superb….Regards, Cormac
What does beauty mean in physics and mathematics is unfortunately something you need to experience by studying them, so I understand poor Humphrys reaction. Trying to explain it to someone who hasn’t studied them is very much like trying to explain the beauty of a sunset or of a visual work of art to a blind. Although you can try, it will be impossible to convey it fully.
As I understand it, beauty in physics and mathematics is related to the economy in proving or explaining something. Thus, the Copernican model, being a simpler description of the solar system, is beautiful as compared to the Ptolomean one, and is also closer to the “truth,” whatever that means.
Symmetry is also an important element in the beauty of physical theories, just as it is in some conception of art. Therefore the success of group theory as a tool in physics.
On the other hand, the idea that “beauty” and “true” must be necessary linked has been largely abandoned in the past few decades, probably for good reasons. I’d love what people here have to say about this.
I think the problem here is that physics is far from beautiful. How can you say there is beauty in physics when we don’t understand what causes electrostatic charge, gravity or any other fundamental force? There’s a hole you could drive a supertanker through. What would be beautiful would be if the universe consisted of nothing more than positrons and electrons and all forces were fundamentally electrostatic and were driven by wave interactions between positron/electron particles. Not this zoo of forces and particles and half-answers that we have now.
If beauty is linked to economy in explaining and if explanations become more intricate as one approaches “truth” (whatever that means,again), can one deduces that “truth” is ugly?
Franklin Hu said: “What would be beautiful would be if the universe consisted of nothing more than positrons and electrons and all forces were fundamentally electrostatic and were driven by wave interactions between positron/electron particles. Not this zoo of forces and particles and half-answers that we have now.”
That’s one of the reasons why one of the main quests of modern physics is to achieve “grand unification.” Indeed, when Maxwell posed the electromagnetic theory as a unified theory of electricity and magnetism, or when Weinberg and Salam unified electromagnetic and weak forces, those were “beautiful steps,” and recognized as such. Yet another example is Einstein’s theory of relativity, in which space and time were also unified in a certain way. But of course physical theories aren’t finished, and the last three decades have been difficult ones.
Concerning economics, that’s another story. Too much asymmetry…
Prof VS Ramachandran made interesting commenst about art and beauty in his Reith Lecture of 2003, http://www.bbc.co.uk/radio4/reith2003/lecture3.shtml
His 10 univerwsal laws of art are:
1. Peak shift
2. Grouping
3. Contrast
4. Isolation
5. Perception problem solving
6. Symmetry
7. Abhorrence of coincidence/generic viewpoint
8. Repetition, rhythm and orderliness
9. Balance
10. Metaphor
They seem to me to give useful insights into the consilience of art, beauty and science.
Jonathan Wilson
The pointer to Ramachandran’s talk was really appreciated.
Physics is always a beautiful subject when we understand it thoroughly and when any physics problem agrees quiet well with that of experimental values.When any complicated problem is solved very quickly physics/mathematics finds pleasure as one get pleasure while seeing an art or painting. I love physics , like to teach physics and I live for physics.
Dr.S.Chitra, Reader in Physics, Sri Parasakthi colleg for women, courtallam, Tamil Nadu-627802.India