For physicists, every day is Pi Day

An atom of the rare-earth element lutetium (right) being zapped by a laser in the vacuum chamber of Associate Professor Murray Barrett’s experimental atomic clock at the NUS Centre for Quantum Technologies. (Photo: Centre for Quantum Technologies)

Somewhere in NUS, an atom of lutetium is having a disco party. It is excited by, and gyrating in sync with, lasers in a darkened room, to the somewhat musical hum of equipment cooling fans. The outermost electron of the atom jumps up and down energetically, at an astounding speed of 350 trillion times a second. 

Associate Professor Murray Barrett is squinting at his computer screen, feverishly trying to keep the laser’s photons vibrating in sync with the dancing electron. He employs Pi to help him accomplish the task. Pi, also written as π, is, of course, the famous mathematical constant defined as the ratio of the circumference to the diameter of a circle. 

Now, the electron’s energy state goes up and down in a sine wave, which can also be represented as a point moving round and round in a circle, whose circumference is 2 times its radius times π. Using a series of mathematical equations full of π that would make one’s head spin in circles, Assoc Prof Barrett corrects for minute fluctuations in temperature and electromagnetic fields to keep the laser and electron dancing in rhythm. 

And that forms the heart of one of the most accurate atomic clocks on earth, ensconced in the bowels of the Centre for Quantum Technologies (CQT) at NUS. The lutetium atom, vibrating 10,000 times faster than the caesium atoms used in earlier-generation atomic clocks, can count time differences 10,000 times smaller. Its frequency of vibration is also much less sensitive to temperature fluctuations.

Associate Professor Murray Barrett explaining how π features in equations for correcting the frequencies of atomic clocks.

People remember π once a year on 14 March – a symbolic representation of 3.14, the approximate value of π – but for scientists like Assoc Prof Barrett, and for the dancing lutetium atom, it is Pi Day every day.

The circle was regarded as the perfect shape by early scholars from Arabia to Greece to Tibet, with divine and supernatural properties. Today, it is almost impossible to do any physics research without inviting Pi to the party.

Pi is involved in everything from quantum mechanics to cosmology, including smartphones and wi-fi, which depend on electromagnetic waves, which are calculated using π.

Researchers have shown mathematically that the decimal places of π go on and on, with no repeating pattern. Pi was recently calculated by computer to 50 trillion decimal places, and memorised by a human being to 70,000 decimal places.

Although the exact value of π will never be known, the precision to which humans have approximated it is already way too high for anything humans ever need to do. NASA’s Jet Propulsion Laboratory uses just 15 decimal places of π for interplanetary navigation. And 39 to 40 decimal places is enough to calculate the circumference of the observable universe to the accuracy of a hydrogen atom.

One of the “accidents” of quantum mechanics – an equation that ends with π for reasons physicists are unable to explain using general laws. (Photo: Professor Valerio Scarani)

Yet π, the mundane mathematical constant that physicists use as often as drinking water, can occasionally be abstract and enigmatic. In another research group in CQT, theoretical physicist Professor Valerio Scarani shares what he calls a “funny equation” in quantum mechanics. 

It pertains to the phenomenon of quantum entanglement, where two or more particles cannot be described independently of one another. The equation describes the shape of a multidimensional boundary between what can and cannot be done with quantum entanglement alone, without relying on things like communication between the particles. 

After adding and subtracting a string of variables, the result turns out to be equal to π. And no one knows why. 

To Prof Scarani, it is one of the beautiful accidents of nature. Sometimes, he says, there is simply no narrative – in quantum physics, and in physics in general, man must humbly accept what nature gives him.

This article first appeared in https://news.nus.edu.sg/for-physicists-every-day-is-pi-day/.