Special Vs. Galilean Relativity: Study with Video Lessons, Practice Problems & Examples

Special relativity, introduced by Einstein, differs significantly from Galilean relativity. While Galilean relativity allows for simple addition of velocities, special relativity asserts that the speed of light remains constant across all inertial frames, independent of motion. This leads to phenomena such as time dilation and length contraction, where measurements of time and distance vary based on the observer's frame. The Michelson-Morley experiment demonstrated the non-existence of the ether, reinforcing that light behaves uniquely, traveling through a vacuum without a medium.

Special Vs. Galilean Relativity

Hey, guys. In this video, we're going to start talking more 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. Galileo and Newton really put it on a solid foundation and credited Galileo for getting the theory started. Okay. In Galilean relativity, the problems are 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 u. Okay, so let me call this v' actually because that's the speed of the airplane with respect to the air. Okay. When you're in an airplane you're often measuring your air speed. You're almost entirely measuring your air speed unless you have 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 u 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 the lab frame, which is just the velocity of the airplane over the ground, is going to be the sum of 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 in the pilot's mind, the air is stationary. Right? The plane is just cutting through the air and the air is 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 addition, of 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 light. 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 and a half times the speed of light. And this violates special relativity because nothing can move faster than the speed of light. Okay? So, There's gonna be There's gonna be 2 for special relativity, 1 for Galilean relativity. And the one postulate just says that measurements in different inertial frames are what I say what I call equivalent. What it basically means is if a law 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 in 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. Einstein however had to add a second postulate to special relativity and that second postulate is actually where all the weird stuff relativity and that second postulate is actually where all the weird stuff from special relativity comes from. It's not the first postulate because the first postulate'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 Morley experiment in 1887. Just to give you an idea of where we are in time, 1887 was the Michelson Morley experiment. By the way, the 1690s is where Newton was, and Galilean relativity was done. 1887 was the Michelson Morley experiment. 1905 was when Einstein finished special relativity. Okay? So this is roughly where we are in time. Now classically prior to the Michelson Morley experiment, it was thought that light had to move through a medium. Right? Light was a wave. Hertz had shown that repeatedly. Young showed that light had interference and diffraction. There were plenty of experiments to show that light was a wave. Right? Up until this point, people in physics introductory physics treat light entirely as a wave. Okay? And all waves were known to travel in a 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 light? And that medium was called the ether. Okay? It's spelled weirdly. It's not spelled like the chemical ether, but that's how it's pronounced. Now let me minimize myself really quickly. In 1887, Michelson and Morley or Mickelson 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 sun. Here is us. The ether is gonna have some sort of velocity and we are 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, as it permeates through the universe. So they used this setup that I show in this figure here, which is called, Michelson 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 gonna 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 are the same, it's going to be the velocities that are different. So then the light is reflected off of a mirror and travels back through the beam splitter, so some of it is WPARAM: HK12CPD<|vq_8268|>" /> through. This light also returns to the beam splitter. Some of it reflects, and then it's gonna arrive at the detector. Now the light traveled the same distance but it traveled a 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 experiment showed absolutely no evidence of the ether's 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 it 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 an ether 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 was the first instance of a wave that does not travel through a medium that it can travel through a vacuum. And this is where the second postulate of 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 since 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 gonna be the same regardless of the reference ring that you measure it in because there is no medium in which the light passes through. Okay? Einstein's second postulate, as I say on the 3rd line at the top, is simply this. The speed of light is independent of your choice of inertial frame. You can measure it in a rest frame. You can measure it in a moving frame. No matter what, you're always gonna get the same number. Okay? 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 are 2 different frames. 1 is a frame moving with the car. So the car is at rest in its, frame in 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 u in the lab frame. So the proper frame needs to be moving at a speed u 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 miles per hour, right, let's say this was 20 miles per hour, 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 miles per hour. 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 result 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 light, 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 c. Just the speed of light. Right? 3×108. Now the expected speed, if an outside observer were to measure light coming off the same moving flashlight, so that moving flashlight, right, emits the same light, this observer right here in the lab frame would expect to measure the light at a speed c, 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, 3×108, the exact same number. Now this is not an experimental error. This has been done over and over and over and over. It 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 meters per second. So if you were to take this number, there would be 1, 2, 3, 4, 5, 6, 7, 8. Right? Zeros, meters per second, this is where you would add that one to it if you were to add 10 meters per second. So it's a very, very, very unnoticeable difference when you actually do this sum, 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 light. Now there are two consequences of 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 inertial frame. Different inertial frames are 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 postulate of relativity, the one that says that the speed of light is the same in all inertial frames. Okay? That wraps up this sort of specific introduction to what special relativity is and mainly what the second partial of special relativity is. Now we're going to move on to these actual consequences, time dilation and length contraction, and we're gonna start doing actual problems. Alright, guys. Thanks so much for watching and I'll see you guys in the next video.

Here’s what students ask on this topic:

What is the main difference between Galilean relativity and special relativity?

The main difference between Galilean relativity and special relativity lies in how they treat the addition of velocities and the speed of light. In Galilean relativity, velocities simply add up, which works well for everyday speeds. For example, if a car moves at 20 mph and a ball is thrown forward at 10 mph, an observer would see the ball moving at 30 mph. However, special relativity, introduced by Einstein, asserts that the speed of light is constant in all inertial frames, regardless of the observer's motion. This leads to phenomena like time dilation and length contraction, where measurements of time and distance vary based on the observer's frame. This difference becomes significant at speeds close to the speed of light.

What was the Michelson-Morley experiment and why is it important?

The Michelson-Morley experiment, conducted in 1887, aimed to detect the presence of the 'ether,' a medium through which light was thought to travel. Using an interferometer, they measured the speed of light in different directions, expecting to find variations due to the Earth's motion through the ether. However, the experiment found no such variations, providing strong evidence that the ether does not exist. This was crucial because it supported the idea that light can travel through a vacuum without a medium, leading to Einstein's second postulate of special relativity: the speed of light is constant in all inertial frames. This experiment fundamentally changed our understanding of light and motion.

What are the two postulates of special relativity?

The two postulates of special relativity, introduced by Einstein, are: 1) The laws of physics are the same in all inertial frames. This means that if a physical law holds true in one inertial frame, it must hold true in all others. 2) The speed of light in a vacuum is constant and independent of the motion of the light source or observer. This implies that no matter how fast an observer is moving relative to the light source, they will always measure the speed of light to be approximately 3 × 10⁸ meters per second. These postulates lead to the phenomena of time dilation and length contraction.

What is time dilation in special relativity?

Time dilation is a phenomenon predicted by special relativity, where time is observed to pass at different rates in different inertial frames. According to special relativity, a clock moving relative to an observer will tick slower compared to a clock at rest with respect to that observer. This effect becomes significant at speeds close to the speed of light. The mathematical expression for time dilation is given by the equation:

$t_0=t/\sqrt{1-{v/c}^2}$

where $t_0$ is the proper time (time interval measured by a stationary observer), $t$ is the time interval measured by a moving observer, $v$ is the relative velocity, and $c$ is the speed of light.

What is length contraction in special relativity?

Length contraction is a phenomenon predicted by special relativity, where the length of an object moving relative to an observer is measured to be shorter than its length at rest. This effect becomes significant at speeds close to the speed of light. The mathematical expression for length contraction is given by the equation:

$L_0=L\sqrt{1-{v/c}^2}$

where $L_0$ is the proper length (length measured by a stationary observer), $L$ is the length measured by a moving observer, $v$ is the relative velocity, and $c$ is the speed of light. This means that as an object's speed increases, its length in the direction of motion appears to decrease.