1
$\begingroup$

If we allow that the energy to allow quantum tunnelling through a potential barrier has been borrowed by the Heisenberg energy-time uncertainty relation, from the vacuum energy. How is the borrowed energy paid back?

$\endgroup$
1
$\begingroup$

If we allow that the energy to allow quantum tunnelling through a potential barrier has been borrowed by the Heisenberg energy-time uncertainty relation, from the vacuum energy

... we don't. That is a simplified picture (more accurately, a lie-to-children), told at an introductory and popular-science level to explain how quantum tunnelling works without going into the full workings of quantum wave mechanics, and which does not represent the modern understanding of tunnelling at any substantial level of accuracy.

As such, any perceived inconsistencies within that picture are irrelevant - the picture is useless to begin with.

As to how which picture does hold for tunnelling, it is basically the wave mechanics of evanescent waves: wave amplitudes cannot go discontinuously from nonzero to zero, and if you try to stop a wave (via, say, total internal reflection) there will be some amount of 'leakage' of the wave amplitude into the 'forbidden' region with an exponential decay as you go into that region. If that region is finite, then that evanescent wave can couple to a propagating mode on the other side and be on its way. And if that sounds like the particle picture with energies &c kind of got lost - then welcome to the world of wave-particle duality.

$\endgroup$
  • $\begingroup$ It is realized that standard quantum theory, in terms of the appropriate wave-function description, gives the correct probabilities for quantum tunnelling, and other quantum phenomena. but represents "reality" between measurement, which does lead to paradox, as in Schrodinger's cat. So when there is a chance of a practical explanation, then it should not, in my view, simply be brushed aside. Random vacuum fluctuations may give a possible mechanism for the probabilities, in the case of quantum tunnelling. But how energy is then conserved, is not clear cut. It is this that I was questioning. $\endgroup$ – Jeff Storry Sep 1 '18 at 16:57
  • $\begingroup$ That explanation is a lie-to-children. It has no real backing in quantum mechanics, and it is basically useless in practice. It is simply not a solution to the conceptual problems posed by QM; the only reason it's still around is as an expository crutch used in pop-sci for audiences who would be lost by actual wave mechanics. Attempting to fix it is not very different from trying to get epicycles to work in detail. $\endgroup$ – Emilio Pisanty Sep 1 '18 at 17:26

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.