//------------------------------// // Interlude: Twilight's Lecture notes on Lasers. // Story: Twilight's World // by grouchopony //------------------------------// Warning: Not every reader is interested in following the technical details of Mike's exposition on how lasers produce light. For those who don't care. Just skip this. ----------------------------------------------------------------------------------- “... But how is the light produced?” She asked hopefully. Mike sighed. “Oh no.” He held up his hands. “The answer to that question lies in the domain of Quantum Physics. That's a whole new branch of physics. It’s much too large to get into tonight. Besides I'm tired, and I'm not really very knowledgeable in that subject area.” Mike had been standing in the location where he had first entered the room. Now Twilight walked up to him and put one of her hooves on his thigh. It was the first time she had ever initiated any contact in an effort to motivate him. Mikes eyes widened slightly as she looked beseechingly up at his face. “Please. Won't you try? Even if you don't know that much about it, this seems to be another area of fundamental physics which we don't have in Equestria. I would dearly like to know something about it.” Her eyes seemed to grow more luminous, as she gazed upwards at him. “Please.” Mike couldn't resist those incredible eyes, he caved. “Oh, alright. But this is the last one for tonight.” He admonished sternly. “It's starting to get late, and I'm getting tired.” Twilight grinned up at him. ---------------- Mike grinned back. “Okay, I'll start with atoms. Do you know the atomic theory of matter?” “All matter is composed of tiny indivisible particles, called atoms. Yes, that's a confirmed scientific fact.” was Twilight's reply. “That’s good. So, in the hopes of shortening this explanation, what do you know about the internal structure of atoms?” “Nothing really,” Twilight confessed. “Some scholars have postulated that atoms must, in fact, have an internal structure. And that theory is generally well accepted by most scholars, including myself. But as for any specific knowledge of or evidence for the internal structure of atoms, we have none so far.” Her ears drooped sadly. “Well then, let me start off by telling you that an atom is almost exclusively composed of empty space.” Twilight was surprised to hear that. Her ears perked forward attentively. Mike continued. “An atom is something like 99.9999% empty space. Actually, I'm pretty sure there are a lot more nines to that number, but you get the idea. It turns out that almost all of the mass of an atom is concentrated in a tiny ball of particles at its center. We call this the Nucleus. “A Nucleus is comprised of two types of particles, a positively charged Proton and a neutral particle called the Neutron. The number of Protons in the nucleus determines the atom’s 'element.' One proton makes a Hydrogen atom. Two protons make a Helium atom, three makes Lithium and so on.” Twilight instantly grasped the concept and raced ahead. “What purpose do the 'newtrons' serve?” “Well Twilight, I am not an expert in nuclear physics, but my understanding was that they play a major role in bringing all those positively charged protons together in the nucleus. Otherwise, the like charges of the protons would cause the nucleus to fly apart.” Twilight nodded her head in understanding. “That's enough for the nucleus. Our main focus, for now, will be on the Electrons, those negatively charged particles which occupy all the rest of the atom's space. “I should mention, however, that the proton and electron carry electric charges of equal size. So, for an electrically neutral atom, there are-” “Equal numbers of protons and electrons.” Twilight finished his thought. “See, so far it’s all very easy.” Mike congratulated her. “But Mike, what keeps the electron from being attracted by the nucleus. Won't it end up being snuggled right up against the protons?” “Ugh, I was hoping to avoid that question. You're too bright for my own good. You know that?” Twilight smiled at Mike's veiled compliment. “Well to answer that question I will need to digress somewhat, and introduce you a foundational concept of Quantum physics, the Heisenberg Uncertainty Principle. Abandon all hope ye who enter here.” “What?” Mike’s strange comment caused her to feel uncertain. “Sorry, just cribbing a quote from a famous piece of literature. “The Uncertainty Principal states that there is a fundamental limit to how precisely one can determine the exact position and momentum of a particle. If you know its exact position, then you must accept increased uncertainty as to that particle's momentum. Conversely, if you know its exact momentum, then its position is uncertain.” “But, that's so ridiculous! Of course, I know where something is. For example, you Mike are sitting in that chair, and you are not moving, so your momentum is zero.” “Yes Twilight, at macroscopic scales, you know those two values as precisely as you need to. However, Plank's constant, a number which expresses the fundamental scale at which the uncertainty comes into play is an extremely small number. You only start to see noticeable effects when you operate at the scale of atoms and subatomic particles.” “Okay, the effect only occurs at very small scales. But why can't I just measure both the position and momentum of an electron?” She insisted on her point of view. “In concept, you imagine you can. However, all attempts to measure a particle will involve having it interact with other particles that you have sent in to probe it.” Twilight considered his statement for a moment. “How about using rays of light to track the particle?” “A good idea except for that fact that even light is composed of particles. We call them Photons. If you hit an electron with a photon, that will definitely affect the electron's momentum.” “Light is composed of particles?” She asked incredulously. "A few minutes ago you were talking about the rays of light from the laser and their wave behaviors.” “One of the most confusing things about Quantum Physics is the fact that it demands an acceptance of the fact that all particles are simultaneously both particles and waves.” “But they can't be both. How is that even possible? The two concepts are mutually incompatible.” Mike sighed. “I don't know Twilight. All I can do is repeat for you one school of thought. The Heisenberg Uncertainty Principle is more than just a statement about the limits of observability; it is a statement about the nature of the universe. “Do not think that of the particle as having some 'true' position and momentum which you are simply unable to measure. Think instead, that the particle actually does simultaneously occupy all positions and possesses all possible momentums as defined by the limiting uncertainty. “In effect, the particle lives a ghost-like smeared out existence, occupying all locations, and traveling all possible paths, that it is possible for it to have. The aggregate effect of the probability of all possible interactions with any other particle at some localized point can be characterized as a wave function.” “But, but, this is simply too fantastical to believe.” “Believe me Twilight, this is incredibly non-intuitive. I don't think our minds are built to comprehend it fully. And the math can be especially obtuse. There are famous experiments, which always show the same results; A single particle, demonstrably alone, still manages to have interference patterns with itself, as though it were a wave.” Twilight did not reply. She merely sat still, thinking furiously. “I want to see that experiment!” She practically hissed her demand at Mike. “You've got it Twilight. But enough thinking about wave-particle dualities. Let’s return to your question about the electron. “You see, between the protons in the nucleus trying to constrain the electron to an almost infinitesimal location, and the uncertainty principle, the electron ends up resonating between the confines of the nucleus and the relaxed freedom of the outer parts of the atom. It ends up in one of several, well, you could think of them as resonance zones, within the body of the atom. We call these resonance zones, orbitals; others might call them electron shells.” Twilight nodded slowly, overwhelmed, trying to picture what such an atom would look like. “Why call them shells?” “I'm not sure. But to my mind, it forms a simplified mental picture if you imagine the electrons being arranged on successively larger shells inside the atom, kind of like a Matryoshka doll.” “A what now?” “Uh, you know, like a doll within a doll within a doll. Um, maybe you don't have those...” “Oh, now I know what you mean, Stalliongrad nesting dolls!” Twilight smiled as she recalled some fond memory. “Right. Stalliongrad nesting dolls.” Mike shook his head as he briefly wondered at the confluence of names between their two universes. “Anyway, the electrons and their positioning within the outermost electron shells are what determine the chemical characteristics of the atom.” Twilight's face lit up in pleasure at that revelation. “Back to lasers. After a whole lot of research into the internal structure of atoms, our scientists realized that an electron could absorb a packet, or quanta, of energy and jump up to one of the higher energy electron shells. Conversely, the electron can release, or emit, the same size quanta of energy and drop back down to the lower electron shell. Such jumps are characterized by specific quantity of energy. No more and no less.” Twilight frowned. “Assuming everything else you told me holds true. I can sort of see that.” “Now, suppose you take a large population of atoms, and hit them with a sudden burst of energy, such as a very bright flash of white light or perhaps an electrical discharge. If done correctly, what you end up with is a substantial population of atoms which have just absorbed the required quanta of energy to jump an electron into a higher shell. Such atoms are said to be in an excited energy state. Very soon, some of those excited atoms will emit their absorbed quanta of energy. It will appear as a photon. One of those light particles I told you about." Twilight nodded her understanding. “Now here's another mystery of Quantum Physics. When a photon, which has the exact energy as that retained in an excited atom, strikes that excited atom, it stimulates the atom into releasing its absorbed quanta of energy as a second photon. The new photon emitted by the atom is in all measures exactly identical to the first one. It will have the same energy, the same phase, and will be traveling in exactly the same direction. “Imagine those two photon's encountering more and ever more excited atoms. What started with a single photon has now swelled into a mighty tsunami, forming a bright burst of light with some decidedly unique properties.” ---------------- Twilight's jaw dropped. “That's it? That's the deep dark secret? If a photon strikes an atom in an excited energy state, the atom will give up its excitation energy as an identical photon.” “Well, you glossed over quite a few details, but that's basically it. That's the core concept of the laser.” Twilight just sat there on the couch, reveling in the satisfaction and excitement of new knowledge learned. Slowly a smile crept onto her face as she considered the deeper mysteries of the universe that had always been there, lying at her hooves, simply waiting to be unlocked.