Written by AZoQuantumApr 24 2017

**Physicists have tested whether quantum mechanics needs a more complex set of mathematical rules by searching for deviations from standard quantum mechanics. To do so a team of researchers headed by Philip Walther at the University of Vienna used exotic metamaterials to design a new photonic experiment. **

These metamaterials were fabricated at the University of California Berkeley. Standard quantum mechanics is supported by their experiment, which permits the scientists to place bounds on alternative quantum theories. The results, published in "*Nature Communications*", could provide guidance in theoretical work focusing on the search for a more general version of quantum mechanics.

Quantum mechanics is supported by a set of mathematical rules, explaining the workings of the quantum world. For instance, these rules predict how electrons orbit a nucleus in an atom, and how photons, particles of light, can be absorbed by an atom. Even though these standard rules of quantum mechanics function very well, there still exist a few open questions based on the interpretation of quantum mechanics, and scientist are still not sure whether the existing rules are the final story. This has indeed motivated a few scientists to produce alternative versions of the mathematical rules, which are capable of properly explaining the results of past experiments, besides providing new insight into the fundamental structure of quantum mechanics. New effects, requiring new experimental tests, are also predicted by some of these alternative mathematical rules.

**Everyday experience of mathematical rules**

In everyday life, if individuals wall all around a park they will end up at the same place whether they choose to walk counter-clockwise or clockwise. According to physicists, these two actions commute. It is not essential that every action needs to commute. While walking around the park, if individuals walk clockwise, and first find money lying on the ground and then come across an ice cream man, individuals will leave the park with a refreshed feeling. However, if individuals instead decide to walk counter-clockwise, they will then see the ice cream man first before finding the money needed to buy the ice cream. In this situation, individuals may leave the park feeling disappointed. Physicists thus provide a mathematical description of the physical world in order to determine which actions do not commute or commute.

Complex numbers are used by these mathematical rules in standard quantum mechanics. However, an alternative version of quantum mechanics was recently proposed which uses "hyper-complex" numbers or numbers that are more complex. Hyper-complex numbers are a generalization of complex numbers. Most of the predictions of standard quantum mechanics can be replicated by physicists with the help of the new rules. However, hyper-complex rules predict that a few operations that commute in standard quantum mechanics do not in fact commute in the real world.

**Searching for hyper-complex numbers**

A research team headed by Philip Walther has presently tested for deviations from standard quantum mechanics predicted by the alternative hyper-complex quantum theory. The park was replaced with an interferometer by the scientists in their experiment. An interferometer is a device permitting a single photon to travel two paths in a simultaneous manner. The ice cream and money were replaced with a specially designed metamaterial and a normal optical material. The metamaterial slightly sped the light up as it passed through, and the normal optical material slightly slowed down light.

According to the rules of standard quantum mechanics, light behaves the same whether it first travels through a normal material and then through a metamaterial or vice versa. This also means that the action of the two materials on the light commutes. However, that may not be the case in hyper-complex quantum mechanics. The physicists observed the behavior of the measured photons and confirmed that hyper-complex rules were not required to describe the experiment. *"We were able to place very precise bounds on the need for hyper-complex numbers to describe our experiment,"* says Lorenzo Procopio, a lead author of the study. But, the authors stated that it is always very complex to unambiguously rule something out. Lee Rozema, another author of the paper, says *"we still are very interested in performing experiments under different conditions and with even higher precision, to gather more evidence supporting standard quantum mechanics."* This work has put forth rigid limitations on the requirement for a hyper-complex quantum theory, however, there are several other alternatives which need to be tested, and the ideal avenue for this is provided by the newly-developed tools.