Something from nothing (ft. virtual particles)

Probability Level 1

In an ideal vacuum a theoretical sphere of radius r r contains a theoretical right circular cone of height h h whose vertex and edge are in complete contact with the inner surface of the sphere.

Suppose a pair of virtual bosons pops into existence arbitrarily within the sphere.

What is the probability that the pair does not end up inside the cone?

2 r h 2 − h 3 r 3 \frac{2rh^{2}-h^{3}}{r^{3}} 1 − 2 r h 2 − h 3 4 r 3 1-\frac{2rh^{2}-h^{3}}{4r^{3}} 2 r h 2 + h 3 4 r 3 \frac{2rh^{2}+h^{3}}{4r^{3}} 1 − 4 r h 2 − h 3 4 r 3 1-\frac{4rh^{2}-h^{3}}{4r^{3}} 2 r h 2 − h 3 4 r 3 \frac{2rh^{2}-h^{3}}{4r^{3}}

Kshitij Bhat by Kshitij Bhat , 28, India

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