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.

The Planck angle is denoted φ_p, is related to the ratio of the Planck length

${\ell }_{\text{p}}=\sqrt{\frac{\hslash G}{c^3}}\approx 1.616199(97)\times 10^{-35}\text{ m}$

to the classical electron radius or "electromagnetic length"

$r_{\text{e}}=\frac{1}{4\pi {\epsilon }_0}\frac{e^2}{m_{\text{e}}{c}^2}=2.8179403267(27)\times 10^{-15}\text{ m},$

so that

${\phi }_{\text{P}}\sim \frac{{\ell }_{\text{P}}}{r_{\text{e}}}\sim 5.73\times 10^{-21}.$

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.

Bibliography

• Mitrofanov, Igor G. (April 1994). "Cosmic gamma-ray burst sources: The phenomenon with the smallest angular size in the observable universe". Astrophysical Journal, Part 1 424 (2): 546–549. doi:10.1086/173913. ISSN 0004-637X. Bibcode: 1994ApJ...424..546M.