Neutrons and protons can momentarily “violate” conservation of energy by emitting and then quickly reabsorbing particles such as the neural pion (rest energy 135 mev).
a) considering p → p + π , how long can the pion exist, according to the uncertainty principle? (ignoring kinetic energy, use the pion rest energy as the “borrowed” energy, hence the uncertainty)
b) if the pion travels at approximately the speed of light, roughly how far from the proton could it get before it must be absorbed? this isn’t just a hypothetical exercise: the strong nuclear force can be understood as being mediated by the exchange of pions, and this calculation provides a reason why it is a shortrange force.