Physical constants sometimes show unexpectedly simple mathematical relationships that may signal deeper theoretical connections. According to Amir, Lemeshko and Tokieda, the ratio of proton mass to electron mass (1836.15267245) matches 6π⁵ (1836.1181) to five significant figures[1]. The researchers developed a probability model to determine whether such matches are coincidental or meaningful, finding that for 5-digit numbers like 1836.1, there is only a 1.2% chance of a random match with simple mathematical expressions[1:1].
The study also highlights proven cases where numerical coincidences revealed real physics, such as the Stefan-Boltzmann law’s “funny prefactor” of 40.802624638, which exactly equals 2π⁵/15 and emerges from Planck’s theory[1:2]. The researchers created a framework for evaluating these potential connections by analyzing expressions built from common mathematical constants (π, e, γ, φ) using basic operations like addition, multiplication and exponents[1:3].
1.2% chance is not significant enough in physics. You can find a lot of such coincidences if you go looking for them. Like people claiming that Pi was relevant in the construction of the pyramids.
I saw a physicist “prove” that Pi was used to construct a random bicycle frame. You just have to juggle the numbers around a bit.
Yes, if something exactly matches 2π⁵/15 there might be significance to it. But something being similar to some fraction or factor of Pi or so says absolutely nothing.
I think xkcd has a chart of crazy coincidences like this. I can’t be bothered to look it up.
I could be bothered:
circle circle circle
There are so many numerical expressions and many physical constants. The number of possible combinations is huge. It’s fun but not surprising to see some expressions approximately match a physical constant due to chance alone.
