More "miscellany": imaginary numbers explain reality (General)

by David Turell @, Thursday, July 14, 2022, 17:05 (623 days ago) @ David Turell

Another review of the issue:

https://aeon.co/essays/how-imaginary-numbers-describe-the-fundamental-shape-of-nature?u...

"Sometimes, however, as in the case of imaginary numbers – that is, numbers with negative square values – mathematics manages to stay ahead of experiments for a long time. Though imaginary numbers have been integral to quantum theory since its very beginnings in the 1920s, scientists have only recently been able to find their physical signatures in experiments and empirically prove their necessity.

"In December of 2021 and January of 2022, two teams of physicists, one an international collaboration including researchers from the Institute for Quantum Optics and Quantum Information in Vienna and the Southern University of Science and Technology in China, and the other led by scientists at the University of Science and Technology of China (USTC), showed that a version of quantum mechanics devoid of imaginary numbers leads to a faulty description of nature. A month earlier, researchers at the University of California, Santa Barbara reconstructed a quantum wave function, another quantity that cannot be fully described by real numbers, from experimental data. In either case, physicists cajoled the very real world they study to reveal properties once so invisible as to be dubbed imaginary.

***

"In their simplest mathematical formulation, imaginary numbers are square roots of negative numbers. This definition immediately leads to questioning their physical relevance: if it takes us an extra step to work out what negative numbers mean in the real world, how could we possibly visualise something that stays negative when multiplied by itself? Consider, for example, the number +4. It can be obtained by squaring either 2 or its negative counterpart -2. How could -4 ever be a square when 2 and -2 were both already determined to produce 4 when squared? Imaginary numbers offer a resolution by introducing the so-called imaginary unit i, which is the square root of -1. Now, -4 is the square of 2i or -2i, emulating the properties of +4. In this way, imaginary numbers are like a mirror image of real numbers: attaching i to any real number allows it to produce a square exactly the opposite of the one it was generating before.

***

"Quantum theory predicts the physical behaviour of objects that are either very small, such as electrons that make up electric currents in every wire in your home, or millions of times colder than the insides of your fridge. And it is chock-full of complex and imaginary numbers.

***

"The discovery and development of quantum mechanics upgraded imaginary numbers from a problem seeking a solution to a solution that had just been matched with its problem. As the physicist and Nobel laureate Roger Penrose noted in the documentary series Why Are We Here? (2017): ‘[Imaginary numbers] were there all the time. They’ve been there since the beginning of time. These numbers are embedded in the way the world works at the smallest and, if you like, most basic level.’

***

"Historically, real quantum mechanics has had not only proponents but also some successes in the realm of mathematical proofs and investigations. Theorists have been able to show that certain properties of quantum-mechanical systems can indeed be captured without resorting to imaginarity. Within the last year, however, a new crop of proofs and experiments proved that this line of reasoning can only go so far. Laboratory experiments involving quantum computers and quantised light now strongly indicate that imaginary and complex numbers are an indispensable part of the quantum, and therefore our own, world.

***

"In his book The Road to Reality (2004), Penrose writes that: ‘In the development of mathematical ideas, one important initial driving force has always been to find mathematical structures that accurately mirror the behaviour of the physical world.’ In this way, he summarises the trajectory of theoretical physics overall. Notably, he adds that ‘in many instances, this drive for mathematical consistency and elegance takes us to mathematical structures and concepts which turn out to mirror the physical world in a much deeper and more broad-ranging way than those that we started with.’ Imaginary numbers have transcended their original place as mere placeholders, transforming our grasp of reality and illuminating this grand idea.

***

"Now quantum physics has revealed that we’ve misunderstood imaginary numbers all along. They may have, for a time, seemed to be just a mental device inhabiting the minds of physicists and mathematicians, but since the real world that we inhabit is indeed quantum, it’s no surprise that imaginary numbers can be found, quite clearly, within it."

Comment: quantum mechanics is the basis of reality, and note imaginary numbers are a mental concept. To me this means there is a mind that created our reality, because when we reach down to a possible starting point it is all conceptual.


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