MadSci Network: Physics

Re: How do quantum leaps work and its there anything f

Date: Thu May 12 22:21:14 2005
Posted By: Guy Beadie, Staff, Optical sciences, Naval Research Lab
Area of science: Physics
ID: 1112819010.Ph

Hello, Phillip.

You’re checking what you’re learning against what you’ve already learned: great job! Develop this skill and you will find it easier and easier to assimilate new ideas.

In this case, you’ve taken your teacher’s comments that “they can’t measure how fast” an electron transfers from one level to the next and extrapolated to “I think there has to be something faster than light.” A faster-than-light conclusion seems dubious, so I suspect that’s when you wrote to MadSci. You were right to do so – I hope I can clear up some of the confusion.

The short answer is that a quantum leap does, in fact, take some time, so there’s no violation of the speed of light. Furthermore, there’s not an immediate change in special coordinate, so you’re not looking at a “teleportation” through space either. Your teacher is still largely right about our inability to measure how fast the transition occurs, but I’ll get to that near the end.

Based on your question, I suspect your picture of an electron is like a little ball whirling around a nucleus, like a planet around a sun. If the allowed states can be compared to the orbits of our actual planets, you’re wondering how the ‘earth’ can make a transition to the ‘mars’ orbit without traveling anywhere in between. Furthermore, even if it could tunnel to the mars orbit or something, how could it do it instantaneously without traveling faster than light?

If this is the root of the problem, I’ve got the answer for you: that’s the wrong picture for how an electron orbits a nucleus. The truth of the matter is that the electron doesn’t whirl around the nucleus; it just IS around the nucleus. The electron can be thought of like a thick cloud enveloping the nucleus up, down, and all around.

The shape of this cloud is important. Different states corresponding to different electron energies are represented by differently-shaped clouds. For example, some clouds are spherically-symmetric like balloons while others are dumbbell shaped. Generally, the more structure to the cloud the higher the electron energy associated with it. The bigger the cloud is the higher the energy, as well.

So, when an electron jumps from one state to another, it “morphs” the shape of its cloud. There’s always some overlap between the two clouds (or else it wouldn’t transition to the new state) so there’s never an issue of the earth-to-mars problem. And the process always takes some time, too, so you don’t need to worry about instantaneous motion.

When your teacher told you that this transition time couldn’t be measured, he or she was largely right. You certainly cannot measure the transition time for any one atom. You cannot make that kind of measurement without screwing up the very electron cloud you’re trying to measure. And when you try to measure the behavior of lots of atoms you find that you get a whole bunch of different transition times. The _average_ transition time of a collection of atoms, however, will be the same each time you measure it.

Here is the answer to an almost-identical MadSci question!
Re: How can Quantum Jumps happen instantaneously?

Two more relevant MadSci posts:
Re: How long lasts the jump of electron from one energy level to another?
Re: How long does it take for an electron to jump orbits.

If you’re interested in the Bohr model of an atom (from which most people get their view of an atom with quantized ‘orbits’, and which served as the starting point of quantum jumps for most people) you can go to this very good site:
Bohr's Atom
You’ll see the solar system picture, at first, but further reading will lead you to more-realistic models of an atom.

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