They discover that the laws of Physics follow a mysterious mathematical pattern

«Although physical reality manifests itself in a wide range of phenomena with different levels of complexity – the scientists write in an article that can now be consulted on the arXiv prepublication server – the equations that describe them show certain regularities and statistical patterns. «

To reach this conclusion, Constantin and his colleagues were inspired by linguistics, “where Zipf’s law states that the frequency of any word in a large corpus of text is approximately inversely proportional to its rank in the frequency table.” In other words, Zipf’s law states that the most common word in a language appears twice as often as the second most common word, three times as often as the third, and so on. In English, for example, the word ‘the’ tends to make up about 7 percent of any long text, followed in frequency by ‘of’, which appears about 3.5 percent of the time. And what’s more, the same law also seems to hold true in other situations, such as the distribution of population in large cities.

In the laws of Physics, also

Therefore, the authors decided to investigate whether such patterns also arise in the distribution of the symbols used to construct the different laws of physics. For which they used three corpus of formulas totally different from each other: those used in the famous ‘Feynman Physics Lectures’; those from a list of equations with author names obtained from Wikipedia; and a set of equations that describe inflation during the first moments of the Universe’s existence.

Constantin and his team treated each symbol and each mathematical operator as if it were a word, and then analyzed their distribution and the frequency with which they appear by applying Zipf’s law.

“You might expect,” says Deaglan Bartlett, of Sorbonne University and co-author of the study, “that this distribution would differ significantly between the three different sets of equations because they come from different places.” But to his surprise, that was not the case, and the three outfits seemed to fit into a single pattern.

Researchers are not entirely clear what it means that the equations of physics, which describe the reality in which we live, follow this pattern. On the one hand, it could be that this was telling us something important about how reality works. After all, each equation separately is extraordinarily accurate in predicting real events in the Universe, so a ‘general pattern’ followed by all the equations together could very well contain valuable information about how the world is organized in that we live.

Constantin, a supporter of this idea, explains that the pattern found is very consistent, and that it occurs even in the symbols that appear more rarely: “The operators that appear less frequently (the exponential, logarithmic, hyperbolic and trigonometric functions) follow the same law. Which is surprising.”

Bartlett, for his part, points out that the result could simply be a statistical byproduct that does nothing more than reflect physicists’ attempts to express their ideas succinctly. “We create operators that we know are useful,” says the researcher. With language, what we want is to communicate the greatest amount of information possible with the fewest symbols or in the shortest time possible, and the same thing happens with equations in physics.

“Understanding the underlying reasons behind this statistical pattern,” the authors write, “can shed light on Nature’s modus operandi, but also reveal recurring patterns in physicists’ attempts to formalize Nature’s laws.”

Another interesting possibility is that the two scenarios are equally real and occur at the same time. “By being pioneers in the study of statistical regularities in the equations of physics,” the article concludes, “our results open the door to a ‘meta law’ of Nature, a law that all physical laws obey.”