# Planck angle

In physics, the Planck angle is a hypothesised limit on the smallest discernible angle. An observable example approaching this is the astronomical observation of one of the smaller astronomical bodies, a gamma ray burster, at the furthest possible observable distance. The angle subtended by such a small object, so far away, is considered to approach the Planck limit on angles.[1]

The Planck angle is denoted φp, is related to[clarification needed] the ratio of the Planck length

$\displaystyle{ \ell_\text{p} =\sqrt\frac{\hbar G}{c^3} \approx 1.616\;199 (97) \times 10^{-35} \text{ m} }$

to the classical electron radius or "electromagnetic length"

$\displaystyle{ r_\text{e} = \frac{1}{4\pi\varepsilon_0}\frac{e^2}{m_{\text{e}} c^2} = 2.817 940 3267(27) \times 10^{-15} \text{ m}, }$

so that

$\displaystyle{ \varphi_\text{P} \sim \frac{\ell_\text{P}}{r_\text{e}} \sim 5.73 \times 10^{-21}. }$[1]

It is thought this angle is the smallest angle between the world lines of free photons, which may interact with electrons or pass through the QED vacuum.

## References

1. Mitrofanov (1994), p. 547.