Planck angle

From HandWiki

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

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

to the classical electron radius or "electromagnetic length"

[math]\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}, }[/math]

so that

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


  1. 1.0 1.1 Mitrofanov (1994), p. 547.