How do Quantum Leaps Happen?

Today in a lecture we discussed electrons, the photo-electric effect, and how incident photons excite electrons to move up energy levels. The thing that baffled me is how exactly do electrons move between the different energy levels if they can only exist at discrete radii from the nucleus of the atom, i.e. what is the process behind it? My lecturer mentioned them disappearing and reappearing at a higher energy level when excited, but wouldn't such "teleportation" mean that they are moving faster than the speed of light?
- Michal Nerek (age 18)
Sussex Uni, Brighton, England

This is a great question. The problems you are worried about arise in the Bohr model, frequently taught but not the way the quantum world actually works. 

The claim that electrons "can only exist at discrete radii from the nucleus of the atom" is simply false. Each definite-energy state of an atom's electron has a smear of different radii, all the time. The kernel of truth in what you were taught is that any bound state of an electron can be made up of a combination of states each of which has a nearly definite energy, although not a definite radius.

So let's ask how, when exposed to the right frequency of light, an electron's state can change from one (ψ₁) of low energy  to one (ψ₂) of higher energy , when there are no electron states with intermediate energies. The state at some time will be aψ₂+bψ₂ , where a and b are (complex) numbers with |a²| +|b²|=1. In the presence of the light |b²| grows. Then, if nothing else is going on,  |b²|  will shrink and the electron will oscillate between the two different definite-energy states. There are actually no discontinuous effects here, no quantum leaps, despite the gap between the energies of the two component states. You can write down how the state changes in time as a flow of fields that never travel faster than the speed of light. Quantum field theory (somewhat fancier than the description here) is the formal way to do that.

How then do we get what seem to be sudden changes? For example, if you put a photon detector near a collection of atoms in the higher-energy state, why does the collector give off a series of random clicks rather than gradually registering a flow of light? In this more complicated physical situation, the gradual oscillations are replaced by more rapid switches. That discontinuity arises because the large scale world (detectors, ears, brains,...) seems to insist on being in a rather definite state, not a mush of different possibilities. Why? That's another, less cut-and-dried discussion, for which some of the key search words are "quantum decoherence" and the dreaded "interpretation of quantum mechanics". The "measurement" process does create effects which are not describable by any local flows, at least if you think that only one version of each outcome occurs. You can search this site and elsewhere for "Bell Inequalities" for more on that topic.

So we haven't gotten rid of the mystery, but we've pushed it to a different level. The way an electron changes state in the presence of light is one of the stages that's exactly describable and continuous, unlike in the Bohr picture.

Here's some other answers that may help: . Follow-up #12 in this one is on just the same topic: .

Mike W.

(published on 10/04/2013)

On "Cosmos," Mr Dehrasse-Tyson describes quantum leaps made by electons as they orbit their nucleii. He stated that the upward, or I suppose he means outwrd, as in further from the nucleus, leaps are caused by a photon striking the nucleus. Interesting.... He further states that the downward leaps are not understood as to cause. Would it not follow that they may be caused by a particle such as an ati-photon? Also, what is the actual speed of electrons in their orbits? I am very curious as to whether they break the supposed cosmic speed limit as they perform these leaps, and therefore point the way to our own furthering of a star-drive. Thanks!
- Daniel Gorgone (age 54)
Robbinsville, NJ, United States

I've put this in a thread with similar questions, for background.

The absorbed photon does supply the energy to allow an electron to to go to a higher-energy state. The interaction of the photon with the nucleus doesn't play much of any role at all.

The downward energy transitions, in which photons are emitted rather than absorbed, don't have the sort of external cause you can point to. Their cause is, however, sitting right in the quantum theory of electromagnetism. There's no particular mystery there.

It's interesting that you wonder about "anti-photons". It turns out an anti-photon and a photon are the same thing. However, what's "anti" about the photons involved here is that they leave the atom rather than come into the atom. 

The electrons move at a range of speeds, even in the single-energy states. None of the speeds are faster than light. A typical range for small atoms is about 1% of c.  During a transition between these single-energy states, all the speeds are also less than the speed of light.

Mike W.

 

(published on 04/12/2014)