1. Oct 20, 2011

### elegysix

I had a curious thought today, here is my logic: Charged particles have E fields. Moving charged particles create B fields. Electrons are moving charged particles, oscillating in an atom. Therefore, I concluded that an atom must be creating an oscillating EM wave, even in the ground state.

But, I've never heard of such a thing. I know all about emissions from electron transitions, but I can't break my own logic here. Its too simple of an argument for me to refute. I assume that means I am probably missing something.

I worked out a simple equation using the static E field equation and some logic from classical mechanics, and it gave me an oscillating E field where the amplitude dropped off as 1/r^2. I know this is wrong, I should have used schrodinger's eqn, probabilities, and relativistic corrections, but I wasn't trying to go that far with it.

I just want to know why they don't have this, and whats wrong with my logic.

thanks
austin

2. Oct 20, 2011

### bbbeard

Nothing wrong with your logic per se -- this paradox was well-known prior to the development of quantum mechanics. A classical electron orbiting a classical nucleus would indeed radiate down to zero energy and induce atomic collapse. Some of the things we learned when we developed quantum mechanics: (1) there is not a continuum of bound energy states available to electrons, instead only energy states for which the action is a multiple of Planck's constant are allowed, and (2) bound systems always have a ground state below which radiative transitions do not occur. I'm not sure this resolves the tension between the classical picture and the quantum mechanical picture, but then, I doubt anything does.

BBB

3. Oct 20, 2011

### alxm

Electrons in a ground-state atom move. But not in a way that gives rise to any time-dependent change in the electronic density.

4. Oct 20, 2011

### elegysix

Thanks for posting! did not know about the history of this. pretty cool.

So what I gather is that there is still no answer to this paradox?

Keyword you wrote above was "transitions" that you said do not occur. agreed. But that is not the question. close though lol.

Has anyone tried to test this? an experiment perhaps?

5. Oct 20, 2011

### bbbeard

Quantum mechanics is our answer to the paradox. We've done a lot of experiments to confirm it in the last 100 years.

BBB

6. Oct 20, 2011

### bbbeard

There is no probability current for s-shell electrons, since the time-independent part of the wave functions are purely real.

In classical electrodynamics, the electron density does not have to change in order for there to be a current that generates a magnetic field. A steady density just implies div J = 0. Consider a coil with a constant current flowing though it. The charge density doesn't change with time, in fact the net charge density is zero. But there is certainly a magnetic field.

BBB

7. Oct 21, 2011

### fizzle

As bbbeard noted, the problem of atomic collapse due to the continual emission of em energy was well known (iirc, the collapse time was less than a nanosecond). Physicists back then assumed there was some sort of continual "banging about" of the atoms to prevent collapse. Cole gives a more modern "banging about" semiclassical explanation via Stochastic Electrodynamics/zero-point radiation:

http://www.bu.edu/simulation/publications/dcole/PDF/DCColePhysicsLettA.pdf

The results are encouraging but I don't know if it actually represents the real world.

There are so many unknowns in classical em theory when it comes to atomic systems. For example, what is an electron? Why are they all the same (charge, mass, etc)? It doesn't make any sense classically ... there's no explanation other than "that's the way Nature is". QM offers a way to solve interactions without worrying about all the low-level details.

8. Oct 21, 2011

### elegysix

interesting. I remember in freshman physics asking why moving electrons created magnetic fields, and I was told "because they do. that's just how it is". That bothered me for a long time, because it was the only thing I had seen at that point which did not have an explanation.