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Most people at some time or other have taken part in a lottery where the winning ticket is drawn ‘at random’ from all those entered in the draw. But what do we mean by ‘random’?
A sequence of numbers is random if there is no pattern behind it, no law to predict which number will come next. So how could we make such a sequence?
Researchers in the EU-funded RANPHYS project developed a mathematical model of unpredictability and found they could assess the degree to which a source of randomness was truly unpredictable.
“We were interested in the industrial realisation of random number generators,” says RANPHYS’ researcher Karl Svozil of the Vienna University of Technology, Austria. “We located instances of quantum randomness so that you could say - if you believe in quantum mechanics - that this process is guaranteed, certified by authority of quantum mechanics, to be totally lawless in a very strict sense.”
Svozil worked with colleagues in France and New Zealand to gain deep insights into the nature of randomness and unpredictability and help scientists navigate what he describes as the “weird interface between physics and mathematics”.
Quantum randomness
Many random number generators available today are only ‘pseudo-random’ as they employ algorithms to produce sequences of numbers that appear random but are actually pre-determined by the starting conditions and will eventually repeat. Computer programs to generate random numbers are of this nature and are not suitable for high-stakes applications such as encryption and lotteries.
Much better are generators that use a physical source of randomness such as electrical or atmospheric noise, but most physicists believe that the ultimate source of randomness lies in quantum mechanics, the behaviour of matter at atomic or sub-atomic scales.
On such scales events are inherently random and unpredictable. Radioactive decay is an example - no-one can predict when a nucleus will emit a particle - and has been used to generate sequences of truly random numbers. But can we do better?
Codebreaking and lotteries
But why does this matter? Random sequences of numbers are used as keys in cryptography, to protect all manner of information transmitted over the internet. If there was any doubt whether the sequence was truly random then an adversary may be able to find a way to break the code.
What the RANPHYS model does is point to a way of certifying a random sequence as truly random and unpredictable, based firmly on what is believed to be irreducible quantum uncertainty. Other possible applications are in national lotteries, where prizes of millions of euros are allocated according to ticket numbers drawn at random.
“They would be advised to use our device if they wanted the public to believe in them,” Svozil says. “This is the best way of generating randomness in a certified, scientific way.”
He speculates that certified randomness may find its way into other areas of life. For example, research funding bodies could allocate a certain proportion of their budget to applicants at random.
“In the long run the only way of getting some original ideas through may be by the old Greek idea of drawing lots,” he adds.
Thanks to funding from the EU’s Marie Skłodowska-Curie actions programme, Svozil’s reflections on randomness, as elaborated by the RANPHYS project, will be published in a free-to-download book.