Physicists describe nature by constructing theories, and when expressing physical theories, they use mathematical objects such as equations, integrals, derivatives, etc. In the long course of history, as physical theories continue to evolve, physicists have also used more complex mathematical concepts to describe more complex physical phenomena. At the beginning of the 20th century, in the quantum mechanics of describing microscopic particles such as molecules, atoms, and subatomic particles, a special mathematical object appeared, the imaginary number, which was a major change.
The imaginary number i is defined as the square root of -1, and it often appears in equations as a tool to make calculations easier and easier. Centuries ago, mathematicians invented the plural number consisting of imaginary and real parts, and Descartes coined the term "imaginary number" to contrast it strongly with "real numbers."
In mathematics, the plural of the "combination of virtual and real" plays an important role, and the imaginary part of it is like the unicorns and elves in the animal world—magical, interesting, but unrelated to reality, and scientists do not expect it to play an equally important role in physics.
Indeed, everything we can measure in the real world is described in real numbers, even in exotic quantum physics—even though imaginary numbers seem essential in describing the nature of matter, the results of all possible quantum measurements are still real numbers. This raises a puzzle for physicists: Are imaginary numbers essential to quantum physics?
Now, two new experiments based on the same theoretical design show that a theory that follows the laws of quantum physics does require imaginary numbers to describe the real world.
Before the birth of quantum theory, Newtonian mechanics or Maxwellian electromagnetism used real numbers to describe how objects move and how electromagnetic fields propagate. Although these theories sometimes use complex numbers to simplify computations, their axioms still use only the real parts.
The advent of quantum theory fundamentally upended this situation, because its construction assumptions were expressed in complex numbers. In the early days, complex numbers in quantum theory were seen more as a mathematical convenience than as a basic building block. The application of complex numbers to quantum theory has also upset many physicists, including Erwin Schr dinger, one of the founders of quantum mechanics. To describe electrons, Schrödinger became the first to introduce complex numbers into quantum theory equations. But he did not think that at the level of physics, the imaginary numbers in his equations were necessary.
Contains the schrödinger equation for the imaginary number i.
By 1960, swiss physicist Ernst Stueckelberg had shown that quantum theoretical predictions for all single-particle experiments could be derived equally from real numbers alone. Since then, the consensus has been that in quantum theory, complex numbers are just a tool that was introduced for convenience.
Since then, some physicists have tried to construct quantum theories using only real numbers, using so-called "real quantum mechanics" to avoid the imaginary part. But the problem is that physicists have been unable to experimentally test these "real quantum mechanics" theories. Therefore, the question of whether imaginary numbers are necessary in quantum theory remains.
In January, physicists at the Vienna Institute for Quantum Optics and Quantum Information presented a paper on the preprint website arXiv in which they proposed an experimental plan to initiate a validation of the theory of "real quantum mechanics."
The experimental plan was inspired by the Bell test, a quantum experiment that can be used to test whether quantum properties are determined by localized hidden variables (i.e., the properties of particles are determined before measurement) or by non-localized quantum entanglements (non-localized representatives can propagate faster than the speed of light). It involves a quantum source S that emits two entangled particles, such as photons, one sent to Alice and the other to Bob.
Physicists in Vienna wanted to expand this line of thinking to test "real quantum mechanics." In the new design, they set up a scenario involving two separate quantum sources (S and R) that send pairs of entangled particles to three different people — Alice, Bob, and Charlie (A, B, C). Here, "entangled particles" means that the two particles are related to each other in a way that is allowed in quantum theory (complex and real numbers coexist), but not possible in classical theory.
More specifically, the experiment required source S to send two particles (such as photons) to Alice and Bob, respectively. Alice can measure particles after receiving photons; Source R does the same thing, except that it sends two entangled photons to Bob and Charlie, who can also measure the received photons, as Alice did. A Bob that receives two photons performs a special type of measurement.
A "real quantum theory" without imaginary numbers predicts outcomes that differ from standard quantum physical theories, allowing experiments to distinguish which theory is correct. The key to the experiment was to find a suitable way to measure Alice, Bob, and Charlie's 4 photons, and the difficulty was how to implement this thought experiment with existing technology.
Now, the paper, originally submitted to arXiv, is officially published in the journal Nature. Using advanced instrumentation and experimental setups, two Chinese research teams demonstrated that if the quantum hypothesis were to abandon their imaginary part and use only real numbers, they would lead to different predictions.
One team of scientists conducted the experiment using photons, and by comparing the results of Alice, Charlie, and Bob in many of their measurements, they found that the data could only be described in terms of quantum theory with complex numbers. Another group of physicists based on the same concept, based on a quantum computer, conducted experiments and came to the same conclusion that quantum physics requires complex numbers. Both experiments will be officially published in the Physical Review Letters in the near future.
However, some physicists have pointed out that the new results do not completely exclude all real theories that bypass imaginary numbers, but only some quantum theories based on real numbers. Despite such voices, many physicists believe the new findings are compelling, and these interesting, thought-provoking studies will provide physicists with better tools to better understand quantum theory.
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#参考来源:
https://www.icfo.eu/newsroom/news/article/5232
https://www.sciencenews.org/article/quantum-physics-imaginary-numbers-math-reality
#图片来源:
Cover image: szcylu/Pixabay