36. Special Relativity
Special Vs. Galilean Relativity
Special Vs. Galilean Relativity
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Hey, guys, in this video, we're going to start talking mawr specifically about special relativity, and we're going to compare it to something called Galilean Relativity, which is the theory of relativity in classical physics. Alright, let's get to it now. Like I said, Galilean relativity is our classical theory of relativity. It was established, as the name implies by Galileo Newton. Really, um, put it on a solid foundation and credited Galileo for really getting the theory started. Okay, In Galilean relativity, the problems were very, very simple. If you have some frame moving, let's not talk about frames just yet. Let's talk about a classic physics problem, like an airplane. Okay, so you have some sort of airplane moving with a velocity V through the wind. Okay, so the wind itself is moving with a speed. You okay? So let me call this V Prime, actually, because that's the speed of the That's the velocity of the airplane with respect to the air. Okay, When you're in an airplane, you're often measuring your air speeds are you're almost entirely measuring your airspeed unless you have a computer that can calculate ground speed because air speed is what actually matters in an airplane because how quickly the air is moving over the wings is what determines whether or not you fly. It doesn't matter how quickly you're moving over the ground. It matters how quickly you're moving through the air. So the air itself is moving with a velocity of you relative to the ground. So the moving frame in this case is going to be the air. So the velocity of the airplane with respect to the air is the velocity in the moving frame and the velocity in the lab frame, which is just the velocity of the airplane over the ground, is going to be the some off those two velocities, and you can see if you imagine it if the airplane is moving with respect to the air forward. But the air is pushing the airplane to the side. You could see that the airplane relative to the ground is actually going to be moving at an angle because in the pilot's mind, the heiress stationary right. The plane's just cutting through the air in the air stationary, but the air is actually moving with respect to the earth. So the actual medium that the plane is moving through is moving and carrying the plane sideways. Okay, This is what a lot of people just refer to this equation right here as the addition of velocities. Okay, It's simple additive. Simple addition. Ah, velocities in Galilean relativity. But this isn't true for special relativity, and we'll see the equation that replaces this. But it's important to realize right away that Galilean relativity has completely different ramifications than special relativity. The most important one occurs when you're near the speed of lights. Okay, So if this airplane, for some reason, was moving at, you know, the speed of light and the wind was pushing it forward at half the speed of light using Galilean relativity, if you measure the airplane speed going overhead, it would be moving at 1.5 times the speed of light. And this violates special relativity because nothing could move faster than the speed of light. Okay, so, Galilean relativity. Now it has one postulate. Okay, there's gonna be two for special relativity, one for Galilean relativity. And the one possible it just says that measurements in different inertial frames are what I say. What I call equivalent what it basically means is if a lot, if something is conserved in one frame. If a law is obeyed in one frame, that law has to be obeyed in all inertial frames. So momentum is conserved in one frame. It has to be conserved in all inertial frames. If energy is conserved one frame, it has to be conserved in all inertial frames. Okay, that's what it means for measurements to be equivalent. The actual measurements aren't going to be equal. They're not going to be the same. But they are effectively stating the same thing. They're effectively equivalent. Okay. Einstein kept this postulate basically the same. We'll see little differences as we talk further about special relativity, but it's basically still the same thing. Um, Einstein, however, had to add a second postulate two special relativity, and that second postulate is actually where all the weird stuff from special activity comes from. It's not the first postulate, because the first possible, it's basically the same. It's the second postulate. Okay, now, the reason why Einstein added a second postulate is because of an experiment called the Michelson Morely experiment in 18 just to give you unidentified of where we are in time. 18. 87 was the Michelson Morely experiment. By the way, the 16 nineties is where Newton Waas and Galilean relativity was done. 18 87 was the Michelson Morely experiment. 1905 was when Einstein finished special relativity. Okay, so this is roughly where we are in time now. Classically, prior to the Michelson Morely experiment, it was thought that light had to move through a medium. Right light was a wave. Hurts had shown that repeatedly, um, young showed that light had interference and diffraction. Um, there were plenty of experiments to show that light was a wave. Right up until this point, people, um in physics, introductory physics treat light entirely as a wave. Okay. And all waves were known to travel in the medium. Right sound travels in air or in water or technically, in solids. Also, mechanical waves like earthquakes have to travel through a physical medium. Water waves have to travel through water, things like that. So it was naturally assumed that light had to travel through a medium as well because all waves travel through a medium. Why wouldn't like? And that medium was called the ether. Okay, it's spelled weirdly. It's not spelled like the chemical ether, Um, but that's how it's pronounced now. Let me minimize myself really quickly. In 18 87 Michaelson and Morley or Michelson and Morley, like I had said, they wanted to measure the velocity of the ether relative to the earth. Okay, the ether was thought to permeate the entire universe. So here's some mysterious ether. They had no idea what it looked like. Here's our son. Here is us. The ether is gonna have some sort of velocity, and we're moving through the ether as we orbit the sun. So they just wanted to measure the velocity of the ether relative to the earth at some particular time in the year. And then they would basically repeat their experiment throughout the year so they could get a really good idea of exactly what the ether looks like. Um, as it permeates through the universe. So they used this set up that I show in this figure here, which is called Michaelson Morley Interferometer. And the idea is that light, which is coherent, so coherent light means that it's always going to be in phase as long as it travels the same distance in the same velocity it's emitted. One beam of light goes through a beam splitter, and a beam splitter is basically something that acts like a mirror sometimes and like a lens. Other times. So this. Some of this light is going to reflect. And some of this light is going to transmit now because this light is traveling at a different angle relative to one another. Whatever the ether is, let's say, like the ether looked like this or something. That means that the velocity of each beam of light is going to be different as it travels these distances, the distances air the same. It's going to be the velocities that are different. So then the light is reflected off of the mirror and travels back through the beam splitter so some of it is going to pass through. This light also returns to the beam splitter. Some of it reflects, and then it's going to arrive at the detector Now. The light traveled the same distance, but it traveled to different speed at a different speed. Sorry, because they each traveled through the ether at a different angle. What that would mean is when they arrive, they should be out of phase based on their relative velocities. Okay, So if here they were both like this, let's say completely in phase over here. Maybe they look like this slightly out of phase. So you're going to get interference between the light and that's going to show up as an interference pattern. And based on the interference pattern, you can measure the velocity of the ether. The problem is that their experiments showed absolutely no evidence of the ethers existence. Okay? They showed no evidence whatsoever that the light traveled at different velocities, as expected, based on there being the existence of an ether. Okay. And they tried it over and over and over. A lot of other people tried it. They tried at different times of the year when the Earth was at a different position relative to the sun. But nothing. Nobody could find any evidence of a neither, no matter where on the earth they tried it, remember? So changing your position on the earth is going to change the orientation of your tabletop experiment relative to the ether. So, at some point on the earth, maybe the ether is moving like this. But if you move to another point on the earth, maybe the ether is moving like this. They couldn't find any difference, no matter where on the earth they measured it, no matter what time of the year, no matter what time of the day. So they had to conclude that the ether just didn't exist. That light was the first instance of a wave that does that does not travel through a medium, that it can travel through a vacuum. And this is where the second postulate special relativity comes from. And this is where all the weirdness of relativity comes from. And it's actually the first thing that shows that light is somehow unique in the world of physics. That light is not like anything else that we had encountered up to this point. And this is gonna be a common theme in modern physics. That light is special. Okay, so what is the second postulate? The second postulate basically says that sense light doesn't travel through any particular medium. As you change reference frames, there's gonna be no change in the velocity of light that the speed of light is always going to be the same regardless off the reference ring that you measure it in because there is no medium in which the light passes through. Okay, Einstein second, partial it, as they say on the third line at the top is simply this. The speed of light is independent in deep pin. Didn't I Sure hope I spelled that correctly. I think ideo I always get messed up on this valuable right here. The speed of light is independent of your choice of inertial frame. You can measure it in a rest frame. You could measure in a moving frame, no matter what. You're always going to get the same number. Now, this doesn't necessarily sound super weird. When you first think about it, it's kind of like Well, yeah, if it's not moving in a medium, then it should always be in the same the same speed no matter where you measure it. But it's actually extremely weird when you think about it. In this particular case, let me minimize myself here. These air two different frames. One is a frame moving with the car so the car is at rest in its, um, frame and what we would call the proper frame right. What we're interested in is the car in this case. So the proper frame is the one where the car is at rest. And then this is our lab frame, the one at rest with respect to the surface of the earth. And the car is moving at a speed. You in the lab frame so the proper frame needs to be moving at a speed. You as well. Okay, now, just think about it. If this car was moving at 20 miles an hour and a guy threw a ball forward at 10 MPH, right, let's say this was 20 MPH. How fast would an observer on the sidewalk see that ball moving forward? Well, if relative to the guy in the car, it was moving at 10 miles an hour and the car is moving at 20 miles an hour, then this guy should see the ball moving at 30 MPH, right? The speed of the ball relative to the guy, plus the speed that the ball was already moving at because the car was carrying it at 20 miles an hour. Okay, that makes perfect sense. And this is exactly how Galilean relativity works. And if you were to actually do an experiment, you would get that results over and over and over and over. The problem is that the result does not hold true for light. Okay, if you had a flashlight in this car and it emitted lights right like this, you would measure in the car right in the proper frame. In the moving frame, you would measure the speed of light to be see just the speed of light, right? Three times 10 to the eight. Now the expected speed if an outside observer were to measure light coming off the same moving flashlight so that moving flashlight right, and it's the same light. This observer right here in the lab frame would expect to measure the light at a speed. See the speed of light, plus the speed of the moving frame. That is not what you get, though it turns out that it's still just the speed of light three times 10 to the eight, the exact same number. Now, this is not a new experimental error. This has been done over and over and over and over has nothing to do with accuracy It's not that because the speed of light is so much faster than the car is moving. You just don't notice it right. For instance, I talked about 20 miles an hour. 20 miles an hour is about 10. It's about 10 m per second. So if you were to take this number, there would be right, 0 m per second. This is where you would add that one to it if you were to add 10 m per second. So it's a very, very, very unnoticeable difference when you actually do this some. But that is not what's happening here. This has nothing to do with experimental error. This has nothing to do with not being able to measure the light properly. This is actually just a fact of physics that the speed of light in any reference frame is always going to be the same. It's always going to be that speed of light that the change in inertial frame does not change the measured speed of lights. Now there are two consequences off the second postulate that differ dramatically very, very dramatically from what we've come to expect as people. And those are time dilation, which says that a measurement of time is actually relative. It's based on your initial frame. Different inertial frames. They're going to measure different amounts of time. Okay. And then length contraction, Which is that different reference frames are going to measure different distances as well. Okay, Both of these are direct consequences of the second postulates of relativity, the one that says that the speed of light is the same in all inertial frames. Okay, um, that wraps up this sort of specific introduction to what special relativity is, and mainly what the second possible of special activity is. Now, we're going to move on to these actual consequences time dilation and length contraction, and we're going to start doing actual problems. All right, guys, thanks so much for watching. And I'll see you guys in the next video.