nowfound

Life & fun · September 17, 2021

IW

I was playing with fundamental constants and 13.8 b years popped out

I was playing around with fundamental constants and out popped 13.8 billion light years. What is going on? the wavelength of an electron mass photon / (2pi) * the charge radius of a proton / the black hole radius of a proton = 13.8 billion light years ((h / (m_e * c * 2pi)) * (h / (m_p * c * pi/2)) / (2G * m_p / c^2)) = 13.8 billion light years…

Alternatives

In plain words

This is an exploration of a mathematical coincidence discovered by combining fundamental physical constants—the Compton wavelength of an electron, the charge radius of a proton, and the Schwarzschild radius of a proton—which when calculated together yield approximately 13.8 billion light years, matching the observable universe's age. The project documents this curious numerical relationship for physics enthusiasts and those interested in fundamental constants and their unexpected connections.

written from the facts on this page · September 2026

From the sources

In the maker’s words, at launch

I was playing around with fundamental constants and out popped 13.8 billion light years. What is going on? the wavelength of an electron mass photon / (2pi) * the charge radius of a proton / the black hole radius of a proton = 13.8 billion light years ((h / (m_e * c * 2pi)) * (h / (m_p * c * pi/2)) / (2G * m_p / c^2)) = 13.8 billion light years https://www.wolframalpha.com/input/?i=%28h+%2F+%28m_e++c++2pi%29%29++%28h+%2F+%28m_p++c++pi%2F2%29%29+%2F+%282G++m_p+%2F+c%5E2%29+to+light+years&assumption=%22UnitClash%22+-%3E+%7B%22G%22%2C+%7B%22GravitationalConstant%22%7D%7D&assumption=%22UnitClash%22+-%3E+%7B%22m_e%22%2C+%7B%22ElectronMass%22%7D%7D&assumption=%22UnitClash%22+-%3E+%7B%22c%22%2C+%7B%22SpeedOfLight%22%7D%7D&assumption=%22UnitClash%22+-%3E+%7B%22h%22%2C+%7B%22PlanckConstant%22%7D%7D

Does a similar job

all alternatives →
  • LN
    Large Numbers Hypothesis Revisited2021 · ▲64

    I was reviewing Dirac's Large Numbers Hypothesis (https://en.wikipedia.org/wiki/Dirac_large_numbers_hypothesis) and decided to give it a second go, now with measurements of fundamental constants more precise than 100 years ago. And I stumbled upon a value for Hubble's constant that's uncannily close. Here are the full calculations. https://colab.research.google.com/drive/1K1qoUFvqZp1fWbpcKJWq63nflgwS0ZHh?usp=sharing Meaningless, or meaningful coincidence?

  • DH
    Deriving Hubble's constant from fundamental constants2021 · colab.research.google.com · ▲62
  • PA
    Physically accurate black hole you can put in your roomJul 2026 · blackhole.plav.in · ▲477

    We have a black hole at home — with actual relativistic physics, live in your browser. I'm Sasha (Alexander) Plavin, an astrophysicist at Harvard's Black Hole Initiative studying quasars and black hole environments. I work with raytracing/radiative transfer simulations professionally, and wanted to make one anyone can play with — so I built this app. Put the black hole onto your screen (any browser), or directly into your room with AR or VR (requires WebXR, for example Chrome on Android, or any VR headset). When looking around, pay attention to unintuitive relativistic effects: rays…

  • HB
    Hydrogen Brings Light Table to Atom2015 · atom.io · ▲190
  • AP
    A physically-based GPU ray tracer written in JuliaFeb 2026 · makie.org · ▲198

    We ported pbrt-v4 to Julia and built it into a Makie backend. Any Makie plot can now be rendered with physically-based path tracing. Julia compiles user-defined physics directly into GPU kernels, so anyone can extend the ray tracer with new materials and media - a black hole with gravitational lensing is ~200 lines of Julia. Runs on AMD, NVIDIA, and CPU via KernelAbstractions.jl, with Metal coming soon. Demo scenes: github.com/SimonDanisch/RayDemo

  • IR
    I rebuilt the Flash app “Scale of the Universe” in WebGL2021 · htwins.net · ▲276

More life & fun this month

the category →

Launched alongside, September 2021

the whole month →