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THE mathematical framework behind quantum theory, one of the key scientific
developments of the 20th century, could have been discovered by scientists
almost a century earlier, says a British physicist.

“It’s a generalisation of classical probability theory,” says Lucien Hardy, a
Royal Society research fellow at the University of Oxford. “A clever person
could have stumbled on it in the early 19th century.” But the realisation that
it applied to the real world would still have come about only after experiments
began to probe the realm of atoms.

Hardy sees parallels with the general theory of relativity, Einstein’s theory
of gravity. “The mathematical framework of the theory—the geometry of
curved space—was actually discovered ahead of time by Bernhard Riemann and
others in the mid-19th century,” he says. “It’s only bad luck that the same
thing did not happen for quantum theory.”

So what would it have taken for quantum theory to be discovered in the
Victorian era? Hardy highlights the crucial difference between classical
probability theory and quantum theory. Imagine two boxes and a ball; if the ball
is in one box it represents the binary digit “1”, in the other box it represents
“0”. “In classical probability theory these are the only options,” says Hardy.
“But in quantum theory, the ball can be in both boxes at the same
time—there is a continuum of states between 0 and 1.”

According to Hardy, quantum theory could have been discovered if some bright
mathematician had noticed that a jump is needed to get from 0 to 1 and had asked
the crucial question: is there any way to get there continuously? “In the 20th
century, Erwin Schrödinger complained about damned quantum jumps, but in
the 19th century nobody complained about damned classical jumps,” says Hardy.
“If they had, they might have been led to quantum theory.”

Gregory Chaitin, a mathematician at IBM’s T. J. Watson Research Center in
Yorktown Heights, near New York, says Hardy’s work is fascinating. “It would be
terrific if Hardy can show that Victorian mathematicians could have devised
quantum theory,” he says. “If he can do that, it would show he has isolated the
conceptual core of quantum theory and that the theory was inevitable, that God
had no choice in creating our world.”

To arrive at his speculation, Hardy wrote down five basic assumptions, or
“axioms”, from which quantum theory can be constructed. One of them generalises
probability theory and turns it into quantum theory, says Hardy, who has
submitted his paper to the journal Physical Review A.

Would the early discovery of the mathematics of quantum theory have made any
difference? Would we have had lasers, computers, nuclear reactors and all the
other spin-offs of the theory in 1900? Hardy thinks not. “It was making the
connection with the real world which was the important thing,” he says.