I was playing around with fundamental constants and out popped 13.8 billion light years. What is going on?<p>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<p>((h / (m_e * c * 2pi)) * (h / (m_p * c * pi/2)) / (2G * m_p / c^2))
=
13.8 billion light years<p>https://www.wolframalpha.com/input/?i=%28h+%2F+%28m_e+<i>+c+</i>+2pi%29%29+<i>+%28h+%2F+%28m_p+</i>+c+<i>+pi%2F2%29%29+%2F+%282G+</i>+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
What's going on is that if you play around with enough numbers, you'll find one you like.<p>That 13.8 billion light years isn't a constant of the universe. It's a temporary condition, an accident of the particular instant in which you happen to be looking. There's nothing fundamental about it, so the fact that you got it out of an arbitrary arrangement of other values is a coincidence.
If you leave off the "to light years" conversion, you'll see that the units don't match up. A light year is a measure of distance (m). The result of this equation is 3.86×10^99 s^4/(kg^2 * m^3). How or why Wolfram decided to convert that into 13.82 billion light years is anybody's guess, but it's definitely wrong and nonsensical. You can't convert a s^4/(kg^2 * m^3) unit into just an m without more.