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Culture, history and society

Stephen Hawking coin recalled after equation error is found

01 Apr 2019
Hawking coin
Event horizon: new 50p coin honours Stephen Hawking. (Courtesy: Royal Mint)

A new coin celebrating the life of Stephen Hawking is being withdrawn because an error has been discovered in the equation for black-hole entropy that appears on the 50p piece.

Released in March by the UK’s Royal Mint, the commemorative coin contains a stylized illustration of a black hole by the artist Edwina Ellis and the Bekenstein-Hawking equation. The formula was derived in 1974 by Hawking, who built on earlier work by the Israeli-American physicist Jacob Bekenstein.

But now, the French mathematical-physics prodigy Avril Lapremiere has found an error in Hawking’s calculations that had gone unnoticed for 45 years.

Lapremiere, who at just 14 is the youngest person to study physics at France’s prestigious Sorbonne University, told Physics World, “I set myself the challenge of deriving black hole entropy from first principles in less than five minutes, but the answer I got was out by a factor of two”. Her result has an “2” in the denominator rather than Hawking’s “4”.

It’s a typical schoolboy error in counting degrees of freedom

Avril Lapremiere

Lapremiere first assumed that she had made a mistake, but quickly realized that the fault was Hawking’s. “It’s a typical schoolboy error in counting degrees of freedom,” she explains, “I’m surprised Hawking made it”.

Coe Fen – official historian of Cambridge University – thinks she could have an explanation: “We know from Hawking’s diary that he completed his derivation on a Friday afternoon”. She adds, “It was 1970s Britain, need I say more?”.

Physicists are now asking themselves why the error had gone unnoticed until now. Cambridge black-hole expert Lorenz Gage points out that no-one has actually measured the entropy of a black hole. “I suppose it shows the importance of testing theories by doing experiments,” he says.

The recall comes just days after the Royal Mint was forced to cancel the planned Brexit 50p coin, which had the date 29 March 2019 emblazoned on it. Hawking is also in the running to appear on the new Bank of England £50 note. An anonymous source at the bank echoed advice given to Hawking many years ago: “a Hawking note would not include any equations”.

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