I learned something new today. I never realized that if you hit an electron with a photon that has more energy than it takes to push it to the next band, and the electron is freed from the atom, that the remaining energy, the difference between the bandgap and the energy of the photon, is conserved by imparting kinetic energy into the electron. That was cool to know. In hindsight it seems obvious but somewhere along the line I'd been given the impression that unless the photon's energy matches the gap the electron won't jump, or it might jump two or more bands if a photon matches the sum of the gaps. I never realized, or knew that fractional amounts were allowed in different ways as long as the energy is conserved.

What I still wonder about is what happens if you hit the electron with a photon that can't push the electron up to the next gap? I know the electron will stay in the orbit it was originally in, but does the photon have any effect on it at all? What happens to the photon? Is it absorbed and emitted immediately because it can't push the electron up far enough, does it bounce off, or does it simply pass on by because there's nothing for it to do?

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The photon can get hung up briefly, in a quantum mechanical sort of way, if its energy is close to the required electron transition energy. The additional energy is briefly "borrowed" under the terms of the Uncertainty Principle.
So for a period of time determined by the size of the energy deficit, the photon is participating in what's called the "dressed state" of the atom it's interacting with; then it continues on its way.
It's a succession of interactions of this kind which slows the transmission of light through transparent materials. Substances like glass and water have absorption bands tucked out of sight in the UV, and visible photons can therefore get caught up in the dressed state of the atoms: blue photons for longer than red photons, because the blue photons have closer to the "right" energy. So the speed of light in a transparent medium varies with wavelength.

Grant Hutchison

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This is an effect related to "refraction", and indeed does happen in glass, for example. Another type of interaction whereby a photon can interact with an electron without making the electron "jump the gap" is a scattering effect, called Rayleigh scattering, whereby the photon changes direction but not energy. That would be somewhat analogous to bouncing a rubber ball off a wall-- the ball is not thrown hard enough to knock the wall down, but it can bounce off and still conserve energy. Whether you are dealing with scattering or refraction really just relates to whether or not you have to worry about coherent interference effects in the medium as a whole.

Ok... this is way too cool... I always wondered about what happens when people say that light was slowed down. Now this makes perfect sense. The light isn't slowed down, it always travels the same speed, it just stops for an instant, then goes again, so that the total length of time to go from point a to point b is longer.

So would the "bending" be due to the fact that the electron is moving and moves so far with one frequency, a little father with another frequency, prior to releasing the photon, kind of like kids jumping off a merry-go-round after going so many degrees?

(And if anyone cares to explain the electron movie saronsong posted the link to, I'd love to hear it. I read the article twice and watched the video and I'm still scratching my head.)

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Arthur C. Clarke

The Brain Science Podcast

For that to work, it would require a curious degree of cooperation between all the electrons a beam of light encounters when it passes through a transparent medium.
I don't think there's an explanation for refraction that works when we treat a photon as a particle. The path the photon "chooses" is determined by the behaviour of its wavefunction as it propagates through the transparent material.

Grant Hutchison

You said that 99% better than wave/particle duality is normally described, but in that last 1% I'd like to point out that using a wavefunction to treat the action of a particle doesn't mean we aren't treating it like a particle, it means we are not giving the particle a trajectory. It turns out that particles don't have trajectories, they have wavefunctions, but in the limit of a short wavelength for that wavefunction, particles behave as though they have trajectories-- hence the historical error of thinking they really did. (And of course someday someone on "BAUT 3000" will comment on the "historical error" of thinking particles had wavefunctions.)

Point taken.
I was thinking of the "dressed state" as being a story that does, at least tacitly, assign a trajectory to our particle (one automatically imagines it stopping here and then here and then here ...).
So I should have written that that particular story about particles () doesn't help us imagine refraction.

Grant Hutchison

Yes, I agree with what you were saying there. And by the way, the "dressed state" picture works with the wavefunction too, in fact it has to if you want to preserve the coherence that allows refraction to work. In effect, there are additional waves sent out by the "dressed" atoms that interfere with the wavefunction of the initial photon, which both deflect and retard its progress.

I was thinking of a prism when I read this comment. It seems to me the trajectory of the light is altered by the prism, so the last few posts prior to this one have me a little confused. After reading this comment I thought I understood what was going on.

I do realize that the light in a prism is being reflected, but something is causing the spreading of the light frequencies and I always understood that to be the different "speeds" at which the light travels through the prism.

So the different frequencies are being hung up at different rates when they are absorbed by the atoms in the prism and they are released at different times... how does that cause the spreading? If the trajectory isn't changed then the prism should reflect light incoherently instead of tending toward coherent spreading.

I take it what I just said is wrong but I don't understand why.

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The only way of finding the limits of the possible is by going beyond them into the impossible.

Arthur C. Clarke

The Brain Science Podcast

This is why I said that the picture of an individual photon being caught up and then moving onwards along a specific trajectory through a transparent medium doesn't help us understand refraction.
To do that, you have to imagine the wavefunction of the photon exploring all possible trajectories, and thereby becoming concentrated in those paths which suffer the least destructive interference. It's the general interaction of the wavefunction and the medium which produces the refraction. (Which, as you say, correlates with the speed of light in the medium and therefore the wavelength of the light.)
Feynman's book QED: the strange theory of light and matter is very good on this, I think.

Grant Hutchison

That is the most elegant explanation I've yet heard on this, Grant.

Thanks!

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Whoever says "perception is reality" is daft. It's merely an abstraction, and often not a very good one.

I'm still absorbing this. I don't really understand it yet, but I may be making some connection somewhere because I feel like I'm close to understanding it. I'll brood on it a while longer.

In the mean time, is there anyway to know what direction a photon will go when released by a stimulated atom? I would think not, but I really don't know.

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Arthur C. Clarke

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It depends on what is stimulating it. The most ideal situation is if the atom has a long-lived "ground state" that you can assume it starts out in, and then follow the quantum-mechanical process until the atom is back in that ground state. First a quantum has to excite that atom, generally a photon or an electron. The state of the photon or electron will then have some control on the state of the excited atom (energy must be conserved in order for the process to be resonant and have high probability), and the state of the excited atom will have some influence on the state of the photon emitted (both its energy and the direction it is likely to go). Usually the direction can be quite widely spread out (often in a kind of bipolar shape called a "p wave"). One exception to this is called stimulated emission, wherein the atom gets excited somehow, but instead of self-de-exciting by emitting a photon, it comes under the influence of another pre-existing photon and is coaxed into de-exciting by resonance with that pre-existing photon. When that happens, the new photon is always in exactly the same state as the pre-existing photon, so it will go off in whatever direction (to within the uncertainty principle) of the pre-existing photon. That's how you get a laser "beam".

I'm starting to think I might understand this a little. I imagine atoms on the front line of the incoming photons as being excited by whatever photons come their way, and the duration of excitement will vary according to the photon's frequency. Eventually the photon that "fits" the bandgap best will hang around longest and competing photons will be deflected by the atom. The photons that the atoms have the greatest "affinity" for will be slowed the most and since they are hung up, and neighboring available atoms have to settle for photons that match closely up or down the frequency range. Then those photons get hung up for a slightly shorter duration. This would cascade along forcing the photons that have the worst match to the bandgap to be deflected the most, and they would have the longest distance to travel, but not necessarily the longest time (this would depend on the time the atoms hold the photons they like).

I immediately saw problems with this. If it were true then something would have to force less energetic photons to move in one direction and the more energetic photons to move in the other. If the "sorting" I describe above would do that in some way like I mentioned, great, if not I have a problem.

Is there some property of the atom that would cause directional deflection?

Would photons of the same frequency stand a better chance of replacing one another in an atom, or would more energetic frequencies bully them out? Using the example of stimulated emission, it sounds like same frequencies would ease each other along better, which would fit my "model" nicely, so I hope it's true.

Another place this model breaks down is if the some of the incoming photons have the energy to cause the electron to jump two gaps. It doesn't seem the light would spread itself out according to frequency if that were the case. There would be bands of more energetic light landing close to the best single gap fitting photons.

I'm really hurting my brain with this... as I was typing the paragraph above I remembered that the photons can be split into lower frequency photons. Now I have to consider how that fits.... hmm... gap 2 emits a less energetic photon, while gap 1 emits a photon that matches the photons the atoms have an affinity for. So if I can get the less energetic photon to boing off to the right while the matching photons go straight and the more energetic photons boing off to the left, it would fit.

But then I have another problem. What if an atom is holding onto a photon that fits gap 1 nicely and a photon that fits gap 2 comes along. Would the first photon be held longer in this situation? It would be stuck until the second photon was emitted wouldn't it? (This isn't relevant but I assume the photons sort of blend into one big happy energy unit which is split up again as the atom emits chunks of it's hide as individual photons again. Is this true or are the photons held discretely?)

This is the best I can do so far. How does reality differ from what I've described?

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Arthur C. Clarke

The Brain Science Podcast

It's not the property of a single atom, it's the action of all the atoms working together to create interference. Think of the wave function like water waves coming in to shore, and the atoms as being like the supports of a pier. A single pier only makes little circular waves on top of the incoming pattern, but a bunch can alter the propagation of the whole wave pattern.
Each atom has particular frequencies it likes to resonate with, like tuning forks. The interaction is quantized, so at most one photon at a time can interact with a particular atom, but that rarely matters because most atoms will not likely be interacting with a photon at any given moment unless you have a great deal of stimulated emission happening, like in a laser.
Yes, or a more energetic photon that includes both energies 1 and 2 could be emitted. I don't follow every aspect of what you are imagining, but it seems to have some of the important features. The normal picture is that each atom spends a certain statistical fraction of its time in each of the "energy levels", and those fractions are set primarily by the brightness of the radiation at the energies of those "band gaps" (called level transitions in a single atom). To get refraction, you need to keep track not just the amplitudes of those statistical tendencies, but also a quantity called phase, so that you can get constructive and destructive interference.

I'm back to brooding on this...

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The only way of finding the limits of the possible is by going beyond them into the impossible.

Arthur C. Clarke

The Brain Science Podcast