# Planck angle

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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 *φ*_{p}, 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.

## References

- ↑
^{1.0}^{1.1}Mitrofanov (1994), p. 547.

## 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.