$ ( \text{Hydrogen Ground State Energy} ) \times (\text{Age of Oldest Known Star}) = 1 \text{ Js}$

Question

While exploring connections between quantum and cosmological scales, I found an exact numerical identity that seems surprisingly physical, not just coincidental.

The ground state energy of the hydrogen atom is: ​ $$ E_H =13.605693 \text{ eV} = 2.179872361×10^{−18} \text{ J} $$

This is the energy of the simplest bound quantum system in nature.

The oldest known star HD $140283$ (the "Methuselah Star") is a well-studied, extremely metal-poor subgiant — essentially a pristine hydrogen/helium object — with an age estimated as:

$$ T_M = 14.46 \pm 0.8 \text{ billion years} $$

At the upper end of this uncertainty, we have:

$$ T = 14.46 + 0.8 \text{ by}= 14.54 \text{ by} = 4.587 \times 10^{17} \text{ seconds} $$

Multiplying these two quantities gives:

$$ E_H \cdot T = (2.179872361×10^{−18} \text{ J})\cdot(4.587 \times 10^{17} \text{ s}) = 1 \text{ Js} $$

This is exactly one joule-second — the classical unit of action.

This seems to imply:

Over the full age of the oldest known star, a hydrogen atom’s bound electron accumulates one joule-second of classical action.

This surprised me for its dimensional clarity and numerical precision — involving no tuning or approximations, only observed constants.

My Question

Has this identity:

$$E_H \cdot T = 1 \text{ Js}$$

been previously studied, interpreted, or connected to any known principle — e.g., in:

Dirac’s Large Number Hypothesis?

Quantum cosmology?

Action-based formulations of physics?

Is this just numerology, or could it represent a deeper relationship between atomic systems and cosmic timescales?

Answer 1

The ground state of hydrogen atom depends on the reference point for calculating potential. The energy you mentioned is:

$$E_H=-13.605\dots \text{ eV},$$

comes out to be the ground state energy when the potential at infinity is taken as zero. So, we can very well change this energy by taking a different reference point and the result would not hold anymore.

Over the full age of the oldest known star, a hydrogen atom’s bound electron accumulates one joule-second of classical action.

AFAIK, the ground state energy of hydrogen (taking a particular reference point) was the same all the time. If what you mentioned has to be true, it must be accumulating action in the present time too, which is simply not the case.

Hence, the result which you came at is, in simple terms, numerology .