The Physics Major

Physics, in and of itself, is an extremely broad major, as it encompasses the smallest particles we've ever found to the largest stars and black holes in the universe. There could be a dozen people watching this who all go into physics and end up getting completely different careers in different fields of physics and have very little knowledge of what the others are doing. You can get into subfields or branches such as particle physics, plasma physics, astrophysics, medical physics, geophysics, quantum physics, and plenty more. For this video, we're going to slow it down and just cover the physics major. Whether you want to go into astrophysics or medical physics, most people will start as basic physics majors, gain all the foundations, and get more specialized in grad school. Many schools really only offer physics as a major for undergrad rather than those other subfields, and even if you have let's say astrophysics as an option for a major, plenty of people will say it's still better to start in physics for more breadth and flexibility than in a graduate program you can specialize once you're more knowledgeable on the foundations and your interests. As a physics major, you learn a little about various branches of physics. Typical required courses in undergrad include these, which I will be going over in this video and the next, along with some applications. But let's jump into what you can expect as a physics major. All physics majors start at the beginning with basic classical mechanics, the stuff most of you learn in the first semester of high school physics. Classical mechanics deals with things on a macroscopic scale such as projectiles, satellites, orbiting bodies, etc. One thing you'll start with is how to break down the movement of a two-dimensional projectile. Like you can represent its velocity with an x-component and a y-component. The x-component of velocity would be like if you have a tracker that's always above the object that can only move in one dimension. The speed of that tracker is considered the x-component of the velocity, as it only moves in the x-direction. The y-component of velocity would be the same concept before a vertically moving tracker. The speed of that vertically moving tracker changes because gravity acts in that direction. Since gravity does not act sideways, this x-component of velocity would be the same over the entire path. And thus you can really analyze two-dimensional motion in one dimension at a time, which you learn equations for. Then when you study forces and put like a block on an incline, even though gravity acts straight down, you'll have the tools to represent the component down the incline that will cause motion. Then one extremely important concept you learn about is energy. There are multiple forms of energy, but the two I'm going to use for demonstration are kinetic and potential energy. If you lift a ball into the air, you give it potential energy, which is a function of its height. The higher you lift it, the more potential energy it has. If you release the ball, it gains speed and in turn kinetic energy, which is a function of the velocity. Well, actually the velocity squared. The super important thing to note is that these two quantities are conserved, and we can quantify them. Imagine we have two cups, one for potential energy and the other for kinetic energy. When we lift the ball into the air, we give it potential energy, which let's just say is 10 units. Now once we release it, it starts to lose height, but in turn gains speed. That amount of potential energy lost is exactly how much kinetic energy is gained. The total amount in the cups never changes. If we freeze time and look at the system and see that the ball has lost 40% of its height let's say, that means it lost 4 units of potential energy from the initial 10, which means the kinetic energy gained 4 units, because again the total has to equal 10 always. Because kinetic energy is quantifiable, we can set it equal to velocity squared, which also actually has a one half times mass in it, and then we can solve for the velocity of the ball. The cool thing about this, at least for our scenario, is the path of the object does not matter. Had there been some weird slide at the same initial height, and the ball dropped the same distance, the velocity of the ball would be the exact same, and the equations would not change at all. That is assuming the slide was frictionless or is very very smooth. Now in high school physics you will also learn about the basics of electricity, magnetism, some thermodynamics, optics, and a few more topics depending on the class you take. But now let's look at some college level classes and what you'll encounter, the first one being classical mechanics. Yes, this is the same field we just went over, but in college you take another class on it that takes it to a whole new level of difficulty. To repeat, this field is about projectiles, spacecrafts, orbiting planets, and even galaxies. And you won't talk about the quantum world like particles, atoms, or anything like that. Two of the biggest concepts you learn in this class are Lagrange's and Hamilton's equations, which will give you a much more powerful way to represent complex systems. While these two concepts are rather advanced to understand mathematically, we can definitely grasp a little of how and why they're used, and I'll start with this question. An object is going to start at point A and is going to end at point B by sliding down some incline. You are to make the slide or curve that will take the object from point A to point B. And yes, the slide will be frictionless. You can make any shape you want. It could be a straight slide, one with a big drop-off to begin, or anything else that ends at point B. The question is, what curve will get the object from point A to point B in the shortest amount of time if the only force causing motion is gravity? For anyone thinking it will be a straight line, that is actually incorrect. But we'll come back to this in a minute. Now in Calculus 1, we all learn how to find the relative maximum or minimum values on a curve, ones where the y-values are smaller or larger than all points near it. So given some complicated polynomial, you can use calculus to find exactly where these points are, assuming you don't have the graph like we do here, only the equation. You can think of let's say this minimum as the point where if you move slightly in any direction along the curve, the y-value only goes up. So there's some point x you are looking for that spits out a minimum y-value associated with it, compared to other points around it. Take note of this, you're finding a coordinate x that spits out a minimum y-value, all of a single point. Now let's go back to our example. If we have some slide that connects A and B, there will be a time associated with it, the time it takes for the object to slide down. A different shaped curve or slide will have a different number or amount of time it takes to slide down. Yes, two curves can definitely have the same time, but that's not of importance here. Now there are infinitely many curves that connect points A and B, all with some time associated with it. Our goal is to find the curve that minimizes this time. It's kind of like what we learn in calculus, but instead of having a point x that yields a minimum point y, we have a curve that yields a minimum value, in this case time. Doing this involves something called calculus of variations. Nothing you need to know now, but while we can use calculus to find points of maximum values, we need something more advanced to solve for a curve that optimizes some value. To those who have taken calculus, this involves a differential equation known as the Euler Lagrange equation. If you solve the equation, which I'm not going to go over, you'll find the path that minimizes time is a cycloid, the same shape you get if you were to trace out the path that a point at the end of a bike tire travels. So take that shape, cut out all unnecessary parts, turn it upside down, and send an object down a slide of that shape, and it will be any other path every single time. And just like our calculus example of slightly moving in one direction from your minimum, if you slightly alter that optimum cycloid curve, regardless of how you do it, the time associated with it gets bigger, hence it's a minimum. Okay, now let's say you throw a ball through the air, and we look at just some portion of its path. Just for the sake of throwing in numbers, let's say it took 3 seconds to travel this distance. Why did the object take this path? Why did it not travel in a straight line, or some weird curve? Well, yes, because gravity is acting on the object, causing it to arc down and take the path that it did. That's totally true, but there's another way to look at it. There is something more special about this curve. If we break the laws of physics and think about three scenarios, each where the ball starts at point A and takes 3 seconds to get to point B, there is something minimized about this curve that it actually takes. It's not time, because we said they all take 3 seconds, and it's definitely not distance as the straight line is the shortest. It's something not remotely as obvious. If you look at any point along the path, I think we can all agree that the ball is moving, and it has some height since it's not on the ground. That means it has kinetic energy and potential energy, and at every point it has a slightly different value for each of these as it travels through the air. Now if you subtract the potential from the kinetic energy at every point, and add all those values up, that is what is minimized for the curve it actually travels. So take the kinetic minus potential here, then here, then here, and keep going, and add them up. If you did that for one of these other curves, doing the same thing at every point, you'd get a bigger value. Now this is slightly wrong still because I'm not showing the curve against time, but hopefully you get the idea. And this right here allows us to analyze complicated systems, because we can look at the entire curve something travels, and use some higher level math to say of every path it could possibly travel, I know which it will be, because it's going to minimize that sum of kinetic minus potential energy, and you'll have the tools to find those optimum curves, rather than just points like in calculus. When looking at a double pendulum, you don't have to look at how gravity affects it at every single point, which would be complicated. You can look at the path as a whole, run the math, and determine the equations that represent its motion. Straight from an MIT homework assignment, you'll be able to analyze how a pendulum attached to a movable sled will move over time, and you can also see they had to do that slide problem for homework like I talked about before. Or you could be asked how long it takes for a pendulum to oscillate back and forth when placed on an accelerating train. You could even analyze what the laws of physics will appear like for someone on a rotating carousel. These are all actual problems from a classical mechanics class. Then orbiting bodies, coupled oscillators, motion of rigid bodies, fluid dynamics, and more are all things you gain insight in from learning classical mechanics. Not all of them involve what we just talked about, but they are topics of interest. For those looking into astrophysics or astronomy, there's a question that's been around since Isaac Newton on the stability of the solar system. The sun makes up a little more than 99.8% of the mass of the solar system, yet all planets still exert a force on others. For example, Earth is being affected by Jupiter just a little bit. And a very complicated question is over millions of orbits, do these small periodic forces from Jupiter have a drastic effect on Earth's orbit, or will it be more of small periodic changes where the orbit as a whole stays more or less the same? Another area of interest in classical mechanics is fluid flow. It's actually surprising how much we don't know about this. In fact, under a list of unsolved problems in physics, turbulence is something that shows up. A topic you may never have heard of in fluid dynamics is magnetohydrodynamics, which has to do with magnetic properties of electrically conducting fluids. This can apply to geophysics and modeling the Earth's magnetic field. Or in astrophysics, high electrical conductivity is all over the place when it comes to astrophysical objects. So things like the sun and solar wind are areas of interest within this field. Yes, I'm getting off track from what you'll see in undergrad, but I want to show some applications as well. The next class I'm going to go over is quantum mechanics. Now for those who don't know anything about this field, quantum mechanics is weird. Watch any video on the subject and you'll likely leave with more questions than you started with, which is probably going to happen here too. In quantum mechanics, you investigate things on a much smaller scale, including atoms, subatomic particles, and even light. Now in quantum mechanics, things are less deterministic and are more probabilistic. In classical mechanics, given some initial height of a block or velocity of a projectile, you can predict how the object will move over time. Parameters of interest in a first level physics class typically are the position and velocity of an object at some time, which you get plenty of equations to solve for. In quantum physics, instead of equations to represent where an object will be, you'll use equations to determine where a particle will likely be, also known as a wave function. And that's because in quantum physics, we cannot predict exactly where a particle will be. If we have a particle that can move in one dimension, the probability of where it is might be high in some places and low in others, and that distribution can look, well, like a wave, hence the wave function, and we can analyze how that develops over time. This might not be satisfying, that we can only determine where things likely are, and to make matters worse, you'll learn how we can think of particles as in a superposition of multiple states, like they kind of exist in multiple places at once. That is, until you observe where the particle is, which causes it to then be in that place. In quantum mechanics, yes, it'd be nice if we could always determine the exact velocity and position of an electron, but guess what? Something called the Heisenberg Uncertainty Principle that you'll learn about in this class says the more you know about one of these, the less you know about the other, which doesn't seem to be the case in everyday moving objects, but in the quantum world, it's true. Another topic you'll learn in this class is the particle in a box, which tells us something interesting about the quantum world. If a particle is in a box, we know there's a 0% chance of it being outside the box, and also at the very ends of the box. And because the probability must be 0 on the ends, then the probability of where you find the particle in the middle will have these discrete frequencies. Sometimes it's more likely to find the particle here than anywhere else, and other times it has a 0% chance of being in the middle, but high probability at other places. You'll derive the equations for these probability functions in class. These discrete frequencies reveal that particles have discrete energies. In classical physics, you can throw a ball at any speed, or a satellite can orbit Earth at really any radius. However, electrons can only jump between and assume certain energies. If we just look at some quantum physics homework problems, you'll see how probabilistic it is. Like, what is the probability of measuring some energy? Sketch the probability distribution. What's the probability you'll find the particle in the left half of the well? And so on. I mean, not all problems are like this, I just picked these specific ones, but you get the idea. And for anyone in high school who has seen some probability, well, the equations for this class are a bit tougher. But no, it's nothing you need to know now. Now quantum mechanics has huge applications and has made possible many technologies that we really take for granted today. As a lab for this class, you might look at the emission spectrum of certain gases, where you run a voltage across a gas and excite the electrons. When this happens, electrons can jump down one or more of those discrete energy levels, and in turn emit a photon or light. Since those energy levels are distinct, the photon released will have a distinct energy, which means a specific color, assuming it's visible. Since different gases contain different energy levels, they all emit distinct colors. Just by looking at the color coming off, we can determine the element, which as an example helps us determine what stars are made of that are millions of light years away. Then a ton of modern electronic equipment is designed using quantum physics. The laser, MRI, or magnetic resonance imaging, the transistor, and more are all a product of the study of quantum mechanics. Which means basically the entire field of electronics, your computer, lots of communication devices and more, wouldn't be here without it. Even electrical and computer engineers at most schools I've seen have to take one quantum physics class for this very reason, to prepare for their first electronics class so they can understand what's going on under the hood of a transistor, which there are hundreds of millions to billions of in the device you're currently watching this video on. If the physics behind electronics appeals to you, something to look into is solid state physics, which is all about analyzing solids, the arrangement of atoms, some material science, and more using methods such as quantum mechanics. This has direct applications to electronics and semiconductors from a physics perspective more than an engineering perspective. For those interested in applying physics to health or the medical field, there's research being done to make it so particles can take images of a cell from inside your body in order to detect for disease. Or quantum sensors are being developed to make precise measurements which can in turn improve the MRI machine itself. For all of you future theoretical physicists out there, you may like this one. Quantum mechanics predicts something called quantum entanglement. Before my quick explanation, I'll let Walter Lewin, a physicist from MIT, summarize it. The most bizarre, the most absurd, the most crazy, the most ridiculous prediction that quantum mechanics makes is entanglement. So here's what it is. Basically when two particles get close, they can become entangled, in which their properties are linked to one another. Separate those two particles thousands or millions of miles, and their properties are still linked, which means by observing or measuring one particle, you affect the state of the other. Imagine flipping a coin here on Earth and seeing it lands heads, which in turn would guarantee that another coin on the moon that it's entangled with would land tails after being flipped. By observing one, you affect the other. If you don't like this analogy, that's okay, because neither did Einstein. He said entanglement is possible, but that's not how it works. But regardless of the analogy, quantum entanglement is a mathematical prediction of quantum mechanics, and some physicists think this is our best shot at teleportation. It would not happen like in Star Trek, but rather particles in one location, like Los Angeles, would be entangled with particles elsewhere, like Japan. The quantum state of your particles would then be scanned and sent to the other location for reconstruction of the same quantum state of all your particles. Nothing teleported or was actually sent from one place to another. Entanglement just allowed the transfer of information. What's even more interesting is the particles that make you up would be destroyed. Again, they aren't sent anywhere. So if there's another you in the world made up of different particles, is that really you? And some say that the particles that make you up aren't really what makes you you. It's the information within your particles. And using entanglement, maybe we can transmit that information one day. Now I've gone way beyond what you'll see in undergrad, but I'll end this quantum physics portion with this. Even Einstein did not like a lot of these theories within quantum physics. He did not like that the particles and atoms that make up everything in the universe are all based in probability and where things might be. When normal objects made up of those particles seem to have some definite state and a position and velocity that can be calculated. To this, Einstein famously said, God does not play dice with the universe. He thought things are much more deterministic. And with that said, I'm going to continue in the part two video where I'll cover these topics. I apologize for the length of these physics major videos, but so many of the topics interested me that I had to put them in. I'll talk more about the major itself and all that in the next one though. If you enjoyed, of course, leave a like and subscribe. Leave any comments you have below, and I'll see you all in part two.