Two new studies suggest that imaginary numbers are necessary to describe reality.
When you take the square root of a negative number, you get an imaginary number, which has been used in the most important equations of quantum mechanics. Physicists can write out quantum equations in simple terms with the help of complex numbers. Whether quantum theory needs these mathematical chimeras or just uses them as a convenient shortcut has been controversial.
The implications of having complex numbers in their equations was a concern for the founding fathers of quantum mechanics. The first person to introduce complex numbers into quantum theory, with his quantum wave function, wrote a letter to his friend, saying that the use of complex numbers was unpleasant. is a real function.
The world's most beautiful equations.
Physicists have found ways to express their equations with only real numbers and an additional set of rules for how to use them. There is no hard experimental evidence to rule out the predictions of the "all real" equations, so there is a question of whether imaginary numbers are optional or not.
Two studies published in December proved that Schrdinger was wrong. If quantum mechanics is correct, imaginary numbers are a necessary part of the mathematics of our universe.
The early founders of quantum mechanics were not able to see the complex numbers in the theory, according to the lead author. There is no clear way to identify the complex numbers with an element of reality.
The authors of the first study wanted to know if complex numbers were vital. John Bell proposed the test in 1964 as a way to prove that quantumentanglement was required by quantum theory.
In their updated version of the classic Bell test, the physicists devised an experiment in which two independent sources were placed between three detectors in an elementary quantum network. The source S would emit two light particles, one sent to A and the other to B, in an entangled state. If the universe were described by a standard quantum mechanics based on complex numbers, the photons that arrived at detectors A and C wouldn't need to be entangled.
The researchers of the second study performed an experiment in which they shone laser beams onto a crystal. Some of the crystals' atoms were released as entangled photons after the laser energy was given to them. The states of the photons arriving at the three detectors were not entangled, meaning that their data could only be described by a quantum theory.
The result makes sense, since the photons need to interact to become entangled, so those arriving at detectors A and C shouldn't be. The experiment only rules out theories if the reigning conventions of quantum mechanics are correct. This is an important caveat, but most scientists are very confident that this is the case.
Renou said the result suggests that the possible ways we can describe the universe with math are more constrained than we thought.
Renou said that by observing what's coming out of some experiments, we can rule out many potential descriptions without making any assumptions about the reliability of the physical devices used in the experiment. It could take a small number of experiments to arrive at a complete quantum theory.
The researchers said that their experimental setup, which was a rudimentary quantum network, could be useful for outlining the principles on which a future quantum internet might operate.
Live Science published the original article.
