New research has found that describing reality may require imaginary numbers
As long as standard quantum theory holds water, imaginary numbers are crucial.
(Illustration: The Bell experiment is based on quantum entanglement, and to test the importance of imaginary numbers in describing reality, the researchers adopted an upgraded version of the Bell experiment.) Source: Yuric Pitt)
Two recent studies have shown that imaginary numbers are indispensable for accurately describing reality.
Square negative numbers to get imaginary numbers. Quantum mechanics is a branch of physics that describes small worlds, and imaginary numbers have long been used in the most important formulas of quantum mechanics. The addition of imaginary and real numbers produces complex numbers, and with complex numbers, physicists can write quantum equations concisely and clearly. Does quantum theory have to use this mathematical chimerism? Or is the latter just a shortcut to studying the former? This has been controversial.
In fact, even the creators of quantum mechanics find formulas that contain complex numbers disturbing. Physicist Erwin Schr dinger, the first person to propose the wave function of quantum mechanics ψ (Psy), and introduced complex numbers into quantum theory, wrote in a letter to his friend Hendrik Lorentz: "The use of complex numbers is unpleasant and should be directly opposed to this practice." ψ (Psai) is essentially a function of real numbers. ”
(Source: Fedorov Oleksi)
Schrödinger did find a way to express its equations only in real numbers, supplemented by a series of additional conditions that describe the usage of equations. Later physicists have also realized other parts of quantum theory. But in the absence of conclusive experimental evidence, it is difficult for physicists to tell whether the predictions of these "all-real" equations are correct or not, leaving the question behind: Are imaginary numbers merely a simplified option? Can't quantum theory describe reality without it?
Two December 15 studies published in Nature and the Physical Review Letters confirmed that Schrödinger was wrong on this point. They showed through a relatively simple experiment that if quantum mechanics is correct, imaginary numbers are an indispensable part of the mathematics of our universe.
(Illustration: Schrödinger equation describes the quantum mechanical behavior of atoms and subatomic objects.) Source: James Tuttle Keane/Caltech)
"The early founders of quantum mechanics failed to find any way to describe the complex numbers that appear in the theory," Marc-Olivier Renou, first author of the paper from the Spanish Institute of Photonic Science, wrote in an email to Live Science. ”
(Source: Anton Belitsky/Getty)
To test whether complex numbers are really crucial, the authors of the first article modified the Bell test for classical quantum experiments. The test was first devised by physicist John Bell in 1964 to show that quantum entanglement—the strange correlation between two distant particles that Einstein called "ghostly hyperactivity"—was necessary for quantum theory.
In the modified test, physicists designed an experiment in which two independent sources (S and R) were placed between three detectors (A, B, and C) in a primary quantum network. Source S will emit two entangled light particles, or light quanta, destined for Detector A and Detector B, respectively. Source R also emits two entangled photons, which are sent to Node B and Node C. If the universe can be described by standard quantum mechanics based on complex numbers, then the photons arriving at detectors A and C are not necessarily entangled; conversely, if a real number-based quantum theory is adopted, they should be entangled.
(Illustration: Quantum entanglement Source: University of Glasgow)
The researchers of the second study conducted another experiment in which they irradiated a laser beam onto the crystal, and the energy of some of the atoms transmitted by the laser to the crystal was then released in the form of entangled photons. By observing the state of the photons that arrive at the three monitors, the researchers found that the photons that arrive at monitors A and C are not entangled, meaning that experimental data can only be described by quantum theory that employs complex numbers.
The results are intuitive: photons need to interact on a physical level to become entangled, so when different physical sources produce photons that arrive at detector A and detector C, they should not be entangled. The researchers emphasize that even so, it is only when mainstream quantum mechanics conventions are correct that their experiments can overturn the theory of deprecating complex numbers. Most scientists are convinced of the correctness of mainstream quantum mechanics conventions, but it's still an important caveat.
(Source: Shutterstock)
Renault argues that the results suggest that describing the universe mathematically may be much more rigorous than we think.
"By looking at the results of some experiments alone, we can rule out many potential descriptions without having to consider the reliability of the physical equipment used in the experiments." Renault said. This means that in the future physicists may be able to obtain a complete set of quantum theories by completing a small set of experiments based on basic principles.
In addition, the researchers say their experimental setup is a fundamental quantum network that may help outline the principles on which future quantum networks will operate.
BY: Ben Turner
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