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Ch 37: Special RelativityWorksheetSee all chapters
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Ch 37: Special Relativity
Ch 38: Particle-Wave Duality
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Ch 40: Nuclear Physics
Ch 41: Quantum Mechanics

Concept #1: 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 applies by Galileo Newton really put it on solid foundation and credited Galileo for really getting the theory started. In Galilean relativity the problems are 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.

So you have some sort of airplane moving with a velocity V through the wind so the wind itself is moving with the speed U 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 when you're in an airplane you're often measuring your airspeed sorry 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 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 in the lab frame which is just the velocity of the airplane over the ground is going to be the sum of those two velocitys 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 can see that the airplane relative to the ground is actually going to be moving at an angle because in the pilot's mind the air is stationary right the plane 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 this is what a lot of people just refer to this equation right here as the addition of velocities its simple additive 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 a completely different ramifications than special relativity the most important one occurs when you're near the speed of light. 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 one and a half times the speed of light and this violates special relativity because nothing can move faster than the speed of light.

Galilean relativity now it has one postulate there's going to be two for special relativity one for Galilean relativity and the one postulate just says that measurements in different inertial frames are what I say what I call equivalence 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 frams so momentum is conserved one frame has to be conserved in all inertial frames if energy is conserved in one frame it has to be conserved in all inertial frames 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 are effectively equivalent. 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 from special relativity comes from it's not the first postulate because the first postulate is basically the same it's the second postulate. The reason why Einstein added a second postulate is because of an experiment called the Mickelson Morley experiment in 1887 just to give you an idea of where we are in time 1887 was the Mickelson Morley experiment by the way the 1690 is where Newton was and Galilean relativity was done 1887 was Mickelson Morley experiment 1905 was when Einstein finished special relativity so this is roughly where we are in time. Now classically prior to the Mickelson 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 with physics treat entirely as a wave and all waves are 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 aether it's spelled weirdly it's not spelled like the chemical aether but that's how it's pronounced now let me minimize myself really quickly in 1887 Michelson and Morley or Michelson and Morley like I had said they wanted to measure the velocity of the aether relative to the earth the aether was thought to permeate the entire universe so here is some mysterious aether they had no idea what it looked like here's our sun here is us. The aether is going to have some sort of velocity and we are moving through the aether as we orbit the sun. So they just wanted to measure the velocity of the aether relative to the Earth at some particular time in the year and then they would basically repeat their experiment throughout the year so they can get a really good idea of exactly what the aether looks like as it permeates through the universe so they used to this set up that I show in this figure here which is called Michelson Morley interferometer and the idea is that light which is coherence 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 bean 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 aether is let's say like the aether 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 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 aether at a different angle what that would mean is when they arrive they should be out of phase based on their relative velocities, 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 aether the problem is that their experiment showed absolutely no evidence of the aethers existence they showed no evidence whatsoever that the light traveled at different velocities as expected based on their being the existence of an aether and they tried it over and over and over a lot of other people tried it they tried it 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 an aether 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 aether so at some point on the Earth the aether is moving like this but if you move to another point on the earth maybe the aether 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 aether just didn't exist that light 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 relitivity 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 going to be a common theme in modern physics that light is special 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 going to be no change in the velocity of light that the speed of light is always going to be the same regardless of the reference frame that you measure it in because there is no medium in which the light passes through.

Einstein second postulate as you see on the third line at the top is simply this the speed of light is independent I sure hope I pelled that correctly I think do I always get messed up on this value right here. The speed of light is independent of your choice of inertial frame you can measure it in a rest frame you can 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 minimise myself here.These are two different frams one is a frame moving with the car so the car is at rest in its frame and what we would call the proper frame right what we are 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. 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 a 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 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 truth for light 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 C just the speed of light right 3 times 10 to the 8. 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 times 10 to the 8 the exact same number now this is not an 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 meters per second. So if you were to take this number there would be 1,2,3,4,5,6,7,8 zero's 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 inertial frame does not change the measured speed of light. 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 and then length contraction which is that different reference frames are going to measure different distances as well 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. That wraps up this sort of specific introduction to what speciality is and mainly what the second postulate of special relativity 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. Alright guys thanks so much for watching and I'll see you guys in the next video.