Question

The Heisenberg uncertainty principle applies to photons as well as matter particles. Thus, a photon confined to a very tiny box with size ∆x necessarily has a large uncertainty in momentum (and thus energy). Since energy is equivalent to mass, a confined photon will create a large gravitational field. If the equivalent mass is very large, the confined photon will correspond to a black hole. Recalling that the Schwarzschild radius of a black hole was defined as rs = 2GM c 2 , at which box size ∆x is the photon’s energy large enough to create a black hole with Schwarzschild radius rs = ∆x ? [Note: this scale is called the Planck length, the scale where quantum mechanics and gravity become inextricably mixed.]

Answer 1