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.

 

[denian]

I can understand your confusion about the concept of "borrowed energy" in quantum mechanics. This term refers to a phenomenon known as quantum fluctuations, where particles can temporarily possess energy that is not their own.

In classical mechanics, energy is a constant quantity and cannot be created or destroyed. However, in the quantum world, particles can briefly acquire energy from the vacuum of space, which is filled with virtual particles constantly popping in and out of existence.

These virtual particles can interact with real particles and transfer energy to them, giving the appearance of "borrowing" or "loaning" energy. But this energy is quickly given back as the virtual particles disappear.

This phenomenon has been observed and confirmed through various experiments, and it plays a crucial role in understanding the behavior of particles at the quantum level.

I would suggest delving deeper into the principles of quantum mechanics to gain a better understanding of this concept. It may seem counterintuitive, but it is a fundamental aspect of the quantum world that has been thoroughly studied and validated by scientists.

I hope this helps clarify the concept of "borrowed energy" in quantum mechanics. Keep exploring and learning, and you will eventually grasp the intricacies of this fascinating field of science.