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Research by Chinese scientists builds on evidence that controversial imaginary numbers are fundamental to foundations of quantum physics. Photo: Quanta Magazine

Imagine that – Chinese scientists show how unreal numbers get real-world results

  • Chinese researchers find the strongest evidence yet that imaginary numbers are fundamental to foundations of quantum physics
  • Experiments show controversial fictional numbers can play a key role in describing reality
In the mystic world of quantum physics, a team of Chinese scientists is proving that one of the field’s favourite imaginary tools might not be fanciful after all.

Through a series of intricate experiments, researchers have revealed the strongest evidence yet that imaginary numbers – invented centuries ago for the sake of pure mathematics and seemingly irrelevant to the real world – play an essential role in describing reality.


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The team, led by quantum physicist Pan Jianwei from the University of Science and Technology of China in Hefei, confirmed that such numbers are a fundamental building block of quantum theory.

The work is “significant progress for testing the foundations of quantum mechanics”, the team said in an article in the journal Physical Review Letters published last month.

Imaginary numbers result from taking the square root of a negative number. Abstract as they may seem, they are a helpful tool used by mathematicians to solve complicated equations.

In quantum mechanics, scientists rely on the concept of complex numbers – the sums of real and imaginary numbers – to predict the uncertainty of the quantum world.

However, the role of complex numbers has, for decades, remained controversial as physicists disagree on whether such numbers are actually necessary for quantum theory or simply a mathematical convenience.

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So last year, European researchers came up with an idea to put the philosophical debate to scientific tests using entangled particles.

Entangled particles share a common quantum state, but remain linked no matter how far apart they are in space. In the experiments, researchers sent the particles from two different sources to three different participants, who then took measurements.

In such an experiment, researchers predicted that measurements made with complex numbers would lead to better predictions than those made with real numbers only.

Late last year, Pan’s group became the first team of researchers to put the idea to the test.
Proximity was key to the team’s success in using entangled particles for their experiment. Photo: handout
Using entangled light particles, the scientists were able to conceptually demonstrate that a quantum theory with complex numbers works better.

But the experiment had some flaws. For instance, some stages of the experiment were conducted in close enough proximity that information could have passed between the study participants.

In their latest effort, the researchers made sure the particle sources and participants were positioned at least 89 metres apart from each other across five locations at the university’s Shanghai campus to rule out possibilities of interference.


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By ensuring the preparation of entangled particles and measurements were made independently and quickly, the team was able to show again that quantum theory using complex numbers outperformed that which used only real numbers.

“Our results ensure the indispensable role of complex numbers in quantum mechanics,” said Pan and his co-authors in the article.

The next step for the team is to remove other potential flaws from previous experiments. For instance, the team said it plans to use high-efficiency light sources and detectors to fix a potential detection loophole problem.

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The researchers did admit that “it is impossible to rule out all loopholes” due to “hidden variables”, which could have existed since the birth of the universe.

The team also included researchers from the Jinan Institute of Quantum Technology in Shandong and Tsinghua University in Beijing. Their work was supported by the National Natural Science Foundation of China, the Chinese Academy of Sciences, the Ministry of Science and Technology as well as provincial governments.