 Hi. Well, I'm Stephen Nesheva, and I want to share some ideas about this concept of electromagnetic radiation as it relates to Einstein resonance. So the starting point for this, as we're thinking about it, is an array of light, let's say, and I have it moving from left to right here. And I've shown the electric part of that light, and its positive and negative phase. Another part of this, if you want to think about it, is that there's a wavelength associated with that light, which goes from peak to peak there. And do you think about that, how often the peaks pass by a certain point that would have some frequency? And it's all related, that is to say, if that wavelength were smaller, since the light is going at some constant speed of light, that would mean that the peaks would come by faster and faster, and that's expressed here with this inverse relationship, really the smaller lambda, the wavelength, the frequency would have to be, and so on. So frequency is kind of an important thing to think about here when we're thinking about how the light interacts with matter. So one example might be something like this. We have a molecule with some delocalized electrons. So those electrons can move up and then maybe move down and move up and down again. Light, in order to interact and deliver energy to those electrons as they're going up and down that delocalized molecule, needs to have a frequency of about 10 to the 15th cycles per second in order to be in resonance with the natural frequency that electrons typically like to move up and down molecules. So this matching is what's called Einstein resonance. It's basically the continuous idea that light, in order to drive motions of the atoms, electrons or molecules, has to have more or less the same frequency, that is the frequency of the light has to match the frequency of the natural motion. So when we have Einstein resonance between the light and electronic motion, then we can, the light can drive electrons to higher orbitals, and ultimately that's generally what we associate with color. There's another way that this could happen, and I've drawn this light now with a bigger wavelength, so the wavelength is something like that, because the wavelength is longer, according to this, the wavelength is longer, that means the frequency must be slower, and indeed it's about, in this case, 10 to the 14th cycles per second. That kind of light can be in Einstein resonance with a different type of motion. It's vibrational excitation. How does that work? Well, we've got a kind of a partial negative charge on those oxygens, and a partial positive charge on that carbon. So when the positive phase of this light is washing over this molecule, it's going to tend to drive the negative parts of the molecule down, and the positive parts up, in other words, bend it. And now, when the negative phase of that light washes over it, it's going to have the opposite, and so it's going to tend to do this, but you're only going to really get a sustained delivery of energy from the light to the molecule if there's Einstein resonance, that is to say, the same kind of frequency of light that's driving it to the natural frequency at which molecules like to vibrate, or in this case, bend. You notice that it's a lot slower than electronic excitation, and that's just because molecules, it's harder to move atoms and also they're just a lot slower to move than electrons whizzing up and down. Third example would be something like this. It's even a smaller frequency, 10 to the 13th cycles per second. Here the idea is something like this. I've got the positive phase of this light washing over this molecule, and since there's positive charges on the hydrogens and kind of negative on that oxygen, this positive phase of the light is going to tend to send that down, it's going to tend to send the hydrogens up, which you can kind of see is now a rotational motion. If it happens that by the time that gets around to the other side, then the negative phase of the light is washing over it, then that would kind of complete the cycle and start to drive rotations. So we have Einstein resonance between light on the order of frequency of 10 to the 13th second when it's trying to drive rotational excitations in a molecule.