Understanding "Borrowed Energy" in Quantum Mechanics

[leftyguitarjo]

In my readings, I keep seeing what people refer to as a particle "borrowing" or "loaning" energy, and quickly giving it back.

And I'm totally lost.

Quantum mechanics has always eluded my understanding, but just grasping this "borrowed energy" thing would help I suppose.

 

[lzkelley]

Because of the uncertainty principle, energy only effectively needs to be conserved on large time scales (large in a relative sense). This means that for a very (very very) short period of time, you can have more energy than you did previously--which is generally referred to as "borrowed energy"-- but conservation of energy requires that it be "given back" within a certain period of time.

To go into a little more detail: you're still never actually violating conservation of energy -- there are just small times scales in which the energy doesn't have a definite value, in which case small fluctuations are allowed. The smaller the time-scale, the larger the fluctuations. If you're familiar with the more common uncertainty principle for position and momentum DelX*DelP >= hBar / 2 ---> energy and time have a synonymous relation: DelE * DelT >= hBar / 2. Both of these uncertainty relations come from the generalized uncertainty principle that refers to how any 2 observables interact.