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What is truly surprising is that the momentum of real number theory has been stopped!
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This video was released on February 18, 2022 and has reached 58,000 views
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How much is the root number -1 equal? Anyone who has been in high school knows that it is not a real number, but an imaginary number, generally written i. Complex numbers are numbers of the form z = x + yi , where x and y are two real numbers. Are complex numbers necessary to describe the physical world? This question is surprisingly profound, and has just recently been given a definitive answer by Chinese scientists (http://news.ustc.edu.cn/info/1055/78317.htm).
Before the twentieth century, the prevailing view was that the plural was merely a mathematical construct and not necessary for physical theory. For example, complex numbers can be used to easily describe fluctuations or circuits, but this is only a mathematical trick. It is enough to describe these phenomena in real numbers, but only slightly more troublesome. Because at the end of the day, all observable physical quantities are real numbers, such as position, momentum, angular momentum, mass. In fact, the name "imaginary number" implies the meaning of "nothing to do with reality".
However, in the early twentieth century, after the advent of quantum mechanics, the situation changed dramatically. The mathematical form of describing a system in quantum mechanics is called a wave function, which is often written ψ, which is a complex function. The fundamental equation in quantum mechanics is called the Schrödinger equation, which is a complex equation. Schrödinger's tombstone is inscribed with this equation. You see, the first letter is the imaginary unit i!
So for a hundred years, everyone who has studied quantum mechanics, including me, has remembered that complex numbers are essential in quantum mechanics. Mr. Yang Zhenning commented: "Quantum mechanics is a great revolution in human history, and after its development, it was found that i = root number -1 was used in basic physics. People who have studied high school mathematics may remember this i. It has also appeared before in quantum mechanics, but it is not basic, it is just a tool. After the development of quantum mechanics, it is not just a tool, but a basic idea. Why fundamental physics must use this abstract mathematical idea: the imaginary number i, no one can explain now. ”
You may ask, aren't physical quantities in quantum mechanics real numbers? Would you be able to measure whether the position or momentum of a system is imaginary? The answer is no, and quantum mechanics still guarantees that all these quantities are real numbers,—— after a series of complex number operations. This is the subtlety of quantum mechanics. For example, the wave function of a single particle ψ a function about the particle coordinates x, y, z, ψ the square of the absolute value at (x, y, z) is the probability density of the particle at this point. The plural takes the absolute value of course is the real number, everyone understands this meaning, right?
However, some theorists have been trying to express quantum mechanics purely as real numbers. That is, they want to reduce the role of complex numbers in quantum mechanics to the level of wave theory or circuit theory, i.e. useful but not essential. In fact, for single-particle systems, such a theory is easy to construct. Since a complex number is equivalent to two real numbers, a real part plus an imaginary part, it is enough to double the number of variables. In technical terms, it is to double the dimensions of Hilbert's space so that a pure real number theory that is perfectly equivalent to standard theory can be constructed.
However, the most wonderful thing about quantum mechanics is not in the single particle, but in the quantum entanglement between multiple particles. If you look at my recently published popular science book "A Brief Introduction to Quantum Information", you can understand what quantum entanglement means and why it is so wonderful. In professional language, quantum entanglement overturns "local realism," in which the real world is either not local, or not real, or neither. So for pure real number theory, the real test is whether it can describe quantum entanglement as well as standard theory?
Counting the original single-particle system, real number theory has been broken through three levels in a row. At this point one began to speculate that perhaps it could pass all the tests, that is, for any conceivable experiment, the theory of real numbers could come to the same conclusion as standard theory. If this is the case, the role of complex numbers in quantum mechanics is not essential, and the textbook will have to be revised.
However, what is really surprising is that the momentum of real number theory has been stopped!
On December 15, 2021, Spanish, Austrian, and Swiss scientists Marc-Olivier Renou and Nicolas Gisin, among others, published an article in Nature titled "Quantum theory based on real numbers can be experimentally falsified" (https:// www.nature.com/articles/s41586-021-04160-4）。 They point out that experiments can be constructed in which two particle sources each produce a pair of entangled particles that are then sent to three detectors. Particle One produces A and B1, and Particle Two produces B2 and C. A and C enter the leftmost and rightmost detectors, respectively, while B1 and B2 enter the middle detector, where an entangled state is measured of the two particles, that is, the two particles that are not originally entangled become entangled. This process is called "entanglement swapping" because it eventually causes the A and C at both ends to also become entangled. Austrian scientists proved that this process cannot be described with real number theory. No matter how the theory of real numbers is modified, the prediction of certain values will be different from the prediction value of standard theory.
The experimental framework is proposed, and the next step is to actually do the experiment. In January 2022, two experimental groups in China achieved this measurement using two physical systems. My colleagues at the University of Science and Technology of China, Academician Pan Jianwei, Professor Lu Chaoyang, Professor Zhu Xiaobo and others, and Professor Cabello of the University of Seville in Spain, collaborated to use a superconducting system. Fan Jingyun, Yang Shengjun, Li Zhengda and others of the Southern University of Science and Technology cooperated with Wang Zizhu of the University of Electronic Science and Technology of China and scientists from Spain, Switzerland, Austria and other countries to use optical systems.
Both experiments reached the conclusion that the theory of real numbers was rejected, but the intensity of the negation was different (https://baijiahao.baidu.com/s?id=1723374973319653921). The experimental result of the University of Science and Technology of China excludes the theory of real numbers with 43 standard deviations, which is a surprisingly high degree of confidence, because the probability of statistical error at 5 standard deviations is only 3 in 10 million, and 43 standard deviations are simply the octave of the real hammer. The experimental results of SUSTech are only 4.5 standard deviations, and the confidence level is a little lower, of course, this is related to the system. But for whatever physical system, this is a very difficult experiment. Both experimental groups demonstrated superb techniques that would play a role in many areas.
These experiments show that complex numbers are still indispensable in quantum mechanics. For example, the American Physical Society's review article on this is titled "Quantum mechanics must be complex" (https://physics.aps.org/articles/v15/7). After a round of negation, we have reaffirmed the standard theory in the textbook. But why does our world need plurals? What are the underlying reasons behind this? This inspires us to think and explore more.
Finally, some media outlets have failed to understand the context of these studies, such as saying that "if complex numbers had physical significance and were no longer mathematical tools, the whole foundation of physics would change." In fact, if you have studied quantum mechanics, you will know that this change has already happened a hundred years ago!