For the
first time, scientists have discovered a classic formula for pi in the world of
quantum physics. Pi is the ratio between a circle's circumference and its
diameter, and is incredibly important in pure mathematics, but now scientists
have also found it "lurking" in the world of physics, when using
quantum mechanics to compare the energy levels of a hydrogen atom.

Why is that
exciting? Well, it reveals an incredibly special and previously unknown
connection between quantum physics and maths.

"I find
it fascinating that a purely mathematical formula from the 17th century
characterises a physical system that was discovered 300 years later," said one of the lead researchers, Tamar Friedmann, a mathematician at the University
of Rochester in the US. Seriously, wow.

The
discovery was made when Carl Hagen, a particle physicist at the University of
Rochester, was teaching a class on quantum mechanics and explaining to his
students how to use a quantum mechanical technique known as the 'variation principle'
to approximate the energy states of a hydrogen atom.

While
comparing these values to conventional calculations, he noticed an unusual
trend in the ratios. He asked Friedmann to help him work out this trend, and
they quickly realised that it was actually a manifestation of the Wallis
formula for pi – the first time it had even been derived from physics.

"We
weren't looking for the Wallis formula for pi. It just fell into our
laps," said Hagen. "It was a complete surprise," added Friedmann. "I jumped up and down when we got the Wallis formula out of
equations for the hydrogen atom."

Since 1655
there have been plenty of proofs of Wallis's formula, but all have come from
the world of mathematics, and the new results have people freaking out. The
results have been published in the Journal of Mathematical Physics.

You can see
two pages from Wallis's book Arithmetica Infinitorum below:

Digitized by
Google

"This
almost seems like magic," writes maths contributor Kevin Knudson for Forbes. "That a formula for π is hidden inside the quantum mechanics of
the hydrogen atom is surprising and delightful."

"Nature
had kept this secret for the last 80 years," said Friedmann. "I'm
glad we revealed it."

We just
can't help but wonder what other secret connections are lurking between quantum
mechanics and pure mathematics.

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