Special Relativity and E=mc² - Part 1 of 5

hello in this series of videos we are going to look at the special relativity theory and we are going to derive the famous equation perhaps the most famous equation of all e equals MC squared before starting though I need to remind you that special relativity applies only to what are called inertial reference frames and an inertial reference frame is quite simply a frame which is not accelerating it is either stationary or it is moving at constant velocity but it is not accelerating neither is it going around a curve or going round in a circle even if it is going at constant speed around a circle it is accelerating because it will have a century people acceleration so it must be traveling in a straight line at a constant velocity in order for it to be an inertial reference frame if it is accelerating then you have to move on to the general theory of relativity let us consider an inertial frame called s if you like you can imagine this as a spaceship in outer space and there is a second frame of reference called s Prime all we can tell is that s prime is moving relative to s at a velocity V there is no experiment that you can do to demonstrate whether s Prime is moving to the right at velocity V or s is moving to the left at velocity V or maybe s prime is moving to the right and s is moving to the left left at a combined velocity of V all physics works exactly the same if you are moving at constant velocity as if you were standing still what we're going to do is to put an Ariel on top of the s for and a dangling wire underneath the s prime frame such that when s prime passes s the dangling wire touches the aerial contact is made and two clocks one on board each frame is synchronized they both start from T equals zero and we might imagine that they will forevermore be synchronized but as we shall discover that is not true after short time there is a light flash some distance away people on both frames of reference are able to use their frames of reference to gauge the distance that that light flash is away from them s says that the light flashed when it was X away and when the T time on the clock marked a measured T S Prime on the other hand says that the light flashed when it was ex-prime away and when the time on the clock measured T Prime now I think you can see fairly easily that x equals x prime plus this distance which represents the separation of s and s prime but what is that distance well the relative speed is speed V and the time that has elapsed is depending on whether you're measuring it on one clock or the other T or T prime so the distance will be the velocity times the time VT or VT prime so now we can say that X is X prime plus VT prime or if you prefer X prime is X minus V T all of that sounds fairly straightforward now I need to introduce you to an experiment that was conducted by Michelson and Morley in the late 1800s that caused all of the understanding of Newtonian physics to be stood on its head I shan't describe precisely how Michelson and Morley did their experiment I'm going to give it to you in a way that I think is more easy to understand before we look at their experiment I want you to imagine that there is a train traveling along in a straight line at 30 miles an hour you are standing on that train and you have a ball in your hand you roll the ball along the corridor of the train in the direction in which the train is traveling and the ball goes at 20 miles an hour relative to you there is a person standing on the platform who can see the ball on the train and you ask him to measure the speed of the ball he will say that the speed is 50 miles an hour that's the 30 miles an hour of the Train plus the 20 miles an hour of the ball now you turn round and face the other way and again you roll the ball at 20 miles an hour along the corridor of the train but this time in the opposite direction to the way the train is moving now you say to the person on the platform what speed is the ball traveling and he will say it is still traveling at 10 miles an hour in the direction of the Train because if the Train is going at 30 miles an hour the ball is going backwards at 20 miles an hour and the net effect is 30 minus 20 which is 10 miles an hour in the direction of the Train so far so good but now let's imagine that instead of rolling a ball we shine a torch and that in essence is what Michelson and Morley did obviously they didn't do it on board a train because that would not have been very practical but in principle this is what they did they took a torch and shown it in the direction of the Train and they know that the speed of light relative to them is C which is actually approximately 3 times 10 to the 8 meters per second then they said to the man on the platform what speed do you measure for light and of course they're expecting him to say it is C plus 30 miles an hour but the man on the platform simply responded I also measure the speed of light as C 3 times 10 to the 8 meters per second and then they turned around and pointed the torch the other way and said to the man on the platform what speed do you get and he responded I get C 3 times 10 to the 8 meters per second surely you should get C minus 30 know the speed of light Michelson and Morley concluded is the same irrespective of the speed of the source of the light or the speed of the observer of the light and that clearly is counter intuitive it's completely different to the situation when the ball was rolled along the surface of the Train somehow we have to explain why that happened well one of the things that you could do is to say that the people measuring the speed have measured it incorrectly you could for example say that since speed is distance divided by time that the people measuring that speed either are using an incorrect ruler to measure the distance or an incorrect clock to measure the time or maybe a bit of both so let's go back to our two frames and what we're going to do is we're going to arrange that when s Prime passes s not only will this cause the clocks to synchronize but it will also send a signal to a far distant light and switch it on of course when the light actually appears s and s prime will be in this position both of them are fully entitled to say see that they are stationary and that the other one is moving so s will say well the light travelled a distance X in time T measured on my clock and therefore C is X divided by T s prime is entitled to say the light traveled a distance X primed in a time T primed and therefore the speed of light is X prime divided by T Prime but we know from Michelson and Morley that C is constant no matter who is measuring it since X and X prime are different that suggests that T and T prime cannot be the same

Channel: DrPhysicsA

Views: 194,729

Rating: 4.9321575 out of 5

Keywords: E=mc², special, relativity, Einstein, physics

Id: U685DR19XyY

Length: 9min 41sec (581 seconds)

Published: Sat Jan 21 2012