Can we use an approximation of a "quantum tunneling" process to resolve the "dilemma"?
Tunneling is the weird and wonderful process by which a quantum particle passes through a potential barrier that a classical particle could not traverse. It comes about because of the Heisenberg uncertainty principle which gives a finite probability for a quantum particle to cross a barrier of specific height and thickness.
In recent years, physicists have explored the possibility of a second type of tunneling which happens in an entirely different way. This relies on the idea that a quantum particle can change into another quantum particle and back again with a certain probability. The tunnelling occurs when the particle changes from one that interacts strongly with a barrier and so cannot pass though it, into a particle that does not interact with the barrier and so passes through with ease.