Special Relativity - A Level Physics

hello today we're continuing in our a level physics revision series looking at the subject of special relativity you can find more advanced videos on this subject in my playlist on special and general relativity special relativity applies to inertial reference frames which essentially means non accelerating frames that is to say that in special relativity people are either stationary or they're moving at constant velocity and relativity means that you and I have different relative perspectives on the same event let's suppose that you and I are in boxes here am i this is me and this is you and all we can do is to see each other through a little peephole we have no means of seeing anything else that might serve as a reference point what we can see is that we're traveling away from each other so this distance is getting larger I might think that I am stationary and you are moving away with a certain velocity V to the right you might think that you are stationary and I am moving away with a certain velocity to the left or it could be that we are both moving away from one another with a combined relative velocity of V but here's the thing there is nothing you can do no experiment that you can perform that can establish whether one of us is stationary and the other is moving away or maybe that both of us are moving away all the laws of physics will behave in exactly the same way if we are stationary or if we are moving at constant speed if you are juggling if you are playing snooker all of those things will work just as well in a moving frame at constant velocity as they do in a stationary frame that is not true in an accelerating frame if one of these is accelerating and you try to juggle you're the balls will fall because they won't land in your hand as you expect them to do so now the special relativity as we understand it today all derives from an experiment performed by two people called Michelson and Morley and they were trying to find the speed of earth through space they called it the ether the speed of earth through the ether they knew that the earth went around the Sun they knew that the earth that the Sun went round the galaxy but the real question was how did earth move relative to space itself and they based their experiment on this principle if you take a river that is flowing at let's say 3 miles an hour and you have a rower who can row in ordinary still water and let's say 5 miles an hour and you say to that rower I want you to row across the river and then come back again and we will time you then the rower of course will not row across because if he does the river will carry him downstream so the rower has to row in that direction at 5 miles an hour and the river will push him so that in fact his actual transit across the river is in that direction the river is flowing at 3 miles an hour he's flowing in this direction he's travelling at 5 miles an hour in that direction we all know that the 3 4 5 triangle or you can use Pythagoras to show that the actual speed across the river will be 4 miles an hour and that will be true when he comes back as well so if the river is one mile wide then the rower will have to row across and back that's a total of 2 miles at 4 miles an hour the total time to cross and come back will be half an hour now let's say the rower we want you to row one mile that is the same as the width of the river one mile downstream and then we want you to Road back again well when the rower is rowing downstream at five miles an hour the river will also carry him at a further three miles an hour because the river is flowing so he'll go downstream at eight miles an hour and that hour that sorry that mile will take him 1/8 of an hour but when he rows back at five miles an hour he's rowing against a river which is flowing at three miles an hour so his net progress will be only two miles an hour and therefore the mile that he has to travel to get back will take him half an hour and that means that the total time to travel there and back will be 5/8 of an hour and the critical thing is that that is different from the half an hour it took to row across the river and back so in other words even though in Stillwater the rower travels at five miles an hour when he's going across the river and back it takes half an hour but when he goes the same distance downstream and back it takes five eighths of an hour now if I hadn't told you that the river was traveling at three miles an hour but I had given you all the rest of this information you could have calculated that the river was flowing at three miles an hour and Michelson and Morley took that self-same principle and what they said was if we can do a same kind of idea of getting something to travel a cross and back and down and back and measure the difference in the time it takes then essentially we can measure the flow of the earth through space because that's essentially the equivalent of the river instead of using a rower Michelson Amaury used light what they did is they took one light beam and they took it to a mirror that was a beam splitter essentially it's half silvered and half allows light through so some of the light was reflected up to a mirror up here and some of the light went through the mirror and to a mirror here and these distances are about the same you can't make them exactly the same but about the same and then of course the light would be reflected from the mirror and come back again where it would hit this half silvered mirror and some of it would go straight through this beam would be reflected and that would come down to an eyepiece so you've got light that is reflected that way or goes through the mirror that way and when the light beams come back they recombine at this mirror and come down to an eyepiece now because you've got a single beam of light that's been split and then rejoins you're going to have an interference pattern which basically means you're going to see a series of fringes and those fringes will be light dark light dark caused by interference it's the same principle as ripples on a pool interfering with another set of ripples you can see this in my video on ways but here's the important thing if you now move or rotate this whole experiment take the whole thing and rotate it then it's a bit like the roller instead of rowing one mile in that direction rowing one mile in that direction or one mile in that direction or one mile in that direction or one mile in that direction and as we've seen the time taken for each of those would be a little bit different because of the effect of the river so the idea is that if the earth is traveling through space at a certain speed and if you rotate this experiment then the time taken for the light to travel to the mirror and back will be slightly different and consequently the interference pattern will be different so as you rotate the experiment these fringes will move and measuring the extent of the movement of the fringes will in a to calculate what the speed of the earth is through the ether so Michelson and Morley did this experiment but the trouble was every time they moved the equipment the fringes didn't change and that suggested that the amount of time it was taking for the light to travel there and back there and back didn't vary according to the rotation of the equipment that's rather like saying that the time it takes for the rower to go up and down or side to side is exactly the same but we showed that it wasn't and couldn't be if the river is traveling at 3 miles an hour of course it would be the same if the river wasn't flowing at all if this was just still water then of course the rowers time going a mile across the river and the mile downriver would be exactly the same so that's one possible conclusion of the Michelson and Morley experiment that the earth isn't traveling through space at all it is stationary but that's not a very likely outcome since the earth we know those around the Sun we know the Sun goes around the galaxies so it's impossible for the earth to be stationary in space the other conclusion that you have to come to therefore is that the time it takes for the light to travel this distance is irrespective of any movement by the earth through the ether that is to say that the speed of light C is constant independent of the speed of the observer or the speed of the source and that turns out to be a critical point when it comes to special relativity why is that well let's consider you on a train there you are and the train is traveling at this direction at 30 miles an hour and you have a small ball which you roll along the corridor of the train in the direction that the train is moving at 10 miles an hour what does an observe that's me standing on the platform or deserve as the train goes by I see a ball on the train traveling at ten miles an hour but the train itself is traveling at 30 miles an hour so I will observe that the speed of the ball is 10 plus 30 equals 40 miles an hour relative to me it travels at 10 miles an hour relative to you but because the train itself is traveling at 30 miles an hour I say that the balls total speed is 40 miles an hour relative to me now let's do exactly the self-same experiment here are you on the train which is traveling at 30 miles an hour and instead of having a ball you shine a torch and the speed of the light that comes out of that torch will be see I am standing on the platform and I measure the speed of that light now you would think that the light should be see the speed on the train plus 30 the speed of the train in exactly the same way as we had up here but that would be wrong because according to Michelson and Morley what I will measure is that the speed of the light is C the same speed that you measure irrespective of the speed of the train and as we shall see that has some rather intriguing consequences so let's see why let's imagine that I am once again the observer this is me and I have marked out my frame of reference that is to say I've event effectively put meter sticks along the ground and I've marked off every meter right the way on the ground and that's my measuring scale you are traveling if you like on a train here are you and you've got your own measuring system on your train along the corridor of the Train you've marked off meter and and the train is travelling at a speed V this is you this is me and just to distinguish any measurements we may make I'm going to say that all the measurements in your time frame measurements of distance will be X Prime and met measurements of time will be T Prime whereas in my frame measurements of distance will just be X and measurements of time will be T so wherever we put a prime that's what you measure wherever we don't put a prime that's what I measure and I can draw a space-time diagram that is simply time here space here I'm using X and T because those are my measurements and I can plot your velocity that will be a straight line because you're going at constant velocity special relativity requires that you're getting a constant velocity and I can measure that velocity it's simply the distance you travel X divided by the time you take to do it ki and that is the line of your velocity I could incidentally also measure the speed of light that will be C by convention we tend to draw the speed of light at an angle of 45 degrees but the point about this is that the scale has to be such that this is the speed of light so for example if this is one second then this has to be three times ten to the eighth meters because light travels at three times ten to the eighth meters per second now how do I calculate how far you have traveled well here we are this is me on my graduated scale and here is you traveling at speed V in this direction and I will say that you have traveled this distance which is X measured on my scale in time T and that means that your velocity is the distance you've traveled divided by the time he is x over t or if you like x equals V T by contrast you are standing on your scale and you are saying compared to my scale compared to the scale that's on your train you're not moving at all because you and the scale are both moving at V so compared to this scale you are not moving so you say that in your frame of reference X prime which is the measuring your frame of reference is zero that is to say you are not moving with respect to your frame of reference because both you and the frame of reference are on the train so the frame of reference and you remain in the same place relatively so you say you're not moving I say you are now then if x equals V T then X minus VT equals 0 but X prime equals zero and so we get that X prime is equal to X minus VT all we're doing there is comparing your assessment according to your scale with my assessment according to my scale and of course for the moment we are going to assume that when we each measure time we measure the same time so the assumption that we're going to make is that the time that I measure T will be the same time that you measure which is T prime that we are gonna discover is actually not correct but it's an obvious thing so we'll assume it for the time being and how can we make that happen well what we can do is we can have a situation whereby as you this is you and this is me as you pass me traveling at V we can have an arrangement whereby they can be a very short contact between our two boxes which synchronizes the watches or the clocks on both of our relative locations and that means that at some time in the future when you have reached here I'm still here you've reached here we would say that if five seconds has passed on my watch five seconds will also have passed on your watch we can each of course also measure the speed of light in our respective frames and I will say that the speed of light is the distance traveled divided by T and you will say that the speed of light is X prime divided by T prime because we are each measuring in our own frame of reference but Michelson and Morley says that we will both get the same result so now let's just take the formula that we just derived and see what comes from them firstly we establish that X prime equals X minus VT that was simply to compare you saying that you don't move in your frame of reference and I say but you do move in my frame of reference we also established that C is x over T which means that x equals C T and we establish that C is X prime over T prime which means that X prime is C T Prime so let's feed these into this formula here X prime is CT prime so up here X prime is CT prime equals X will that CT minus VT which means that CT prime is equal to T into C minus V now if t prime equals T which is what we think is the case the clocks remain synchronized then we have that C is equal to C minus V and that obviously cannot be true unless V is 0 but V is not 0 because you are moving relative to me so we've arrived at a nonsense something has gone wrong somewhere what has gone wrong well let's go back to our starting position which is that X prime is equal to X minus VT and if that's the case I can simply reorganize that to say that x equals x prime plus VT and since we're assuming that T prime equals T I can put a prime on that so that both of these terms are measurements that you will make so this is what measurement you make compared to the measurements I make this is the measurement I make compared to the measurements you make but something's gone wrong so we are going to take these two terms and we're going to put an error term in them essentially we're going to multiply both by an error term called gamma we're going to say somewhere we've made a mistake so let's make that mistake equal to gamma and see if we can find out what gamma is to work out what gamma is what we're going to do is we're going to multiply both sides of these equations together so we're going to have X prime times X is equal to this term times this term which is X minus BT times gamma times X prime plus V T prime times gamma and that's going to come out as X prime x equals well let's first take the two gammas that's going to give you gamma squared into now we've got to multiply these two terms in brackets so x times X prime is X X prime plus X VT prime minus VT X prime minus V squared t T Prime all I've done is to multiply that bracketed term by that bracketed term now it's all beginning to look a bit horrendous but we remember that we determined that the speed of light was x over T and the speed of light is X prime of T Prime it's constant whoever is measuring and that means we can say that T is equal to X over C and T prime is equal to X prime over C substitute these values for T and T Prime into this formula here what do we get we get that X prime X is equal to gamma squared from here into X X Prime well that's that plus XV now instead of T prime I'm going to put X prime over C minus V and instead of T I'm going to put X over C times X prime minus V squared and instead of TT prime I'm going to put X over C X prime over C so I've simply in this formula replaced all the T's and T Prime's by X over C or X prime over C respectively now again that still looks awful but you'll notice that XX prime exists in every term so I can divide throughout by X X prime if I divide this by xx prime I get 1 equals gamma squared because that remains the same in 2 this becomes 1 plus if you divide that term by xx prime you get V over C if you divide that term by xx prime you get minus V over C and if you divide this term by xx prime you get minus V squared over C squared and now you'll see that these two terms cancel and so we've now got that 1 is gamma squared into 1 minus V squared over C squared or if you prefer gamma squared is equal to 1 divided by 1 minus V squared over C squared or gamma is equal to 1 over the square root of 1 minus V squared over C squared and that gamma is called the Lorentz transform so what we're saying is that whereas we originally rode that X prime equals X minus VT which was simply comparing what you think in your frame of reference to what I think in my frame of reference what we should have done is to multiply this term by gamma which is the error term and gamma is 1 over the square root of 1 minus V squared over C squared so actually that is what we should have had and that's the relativistic correction now you'll notice something but if the velocity is very very very much less than C the speed of light that V squared over C squared becomes effectively zero and therefore you're Jeff's left with the square root of 1 which is 1 and that means that X prime equals X minus VT which is what we thought was the case all along it's only when V approaches or gets close to the value of the speed of light that this relativistic term comes into effect so what we've shown is that special relativity or the Lorentz transform term has an effect as V gets very large for ordinary speeds that we are used to for example the Train it has no effect that's why the ball rolling on the train all you had to do is to add the speed of the ball to the speed of the Train but when you get to something traveling at or near the speed of light this term becomes very important the beat the 1 minus the square root of 1 minus V squared over C squared becomes very important let's each measure a rod in your world so here you are on your world traveling at speed V and you have a rod this is you this is me in my world you have a measuring scale I have a measuring scale your measuring scale is X Prime and T Prime my measuring scale is X and T now the first thing we have to understand is that when I measure the of the rod in your frame I will have to measure both ends simultaneously in order to get the reading on my scale if I measure this end furthest and then go away and have a cup of tea and come back and measure this end you will be here and I will measure that the length of the rod is some absurd distance because I allow time to elapse between measuring attained so I've got a measure both ends simultaneously otherwise you'll move and I'll get the wrong reading so for me T must equal zero because I've got a measure both ends at once so if we take this formula here and make T equal to zero then I get that X prime is equal to X divided by the square root of 1 minus V squared over C squared because T in this formula is zero and so it just reduces to this formula here now remember X prime is the local that is that's what you are measuring in your world X is remote that is to say I am measuring the distance remotely so always remember X prime is the local measure X is the remote measure so we can rearrange this formula here to say that X is equal to X prime into the square root of 1 minus V squared over C squared and you'll notice that the square root of 1 minus V squared over C squared will always be between 0 and 1 if B is very small then the V squared over C squared term becomes vanishingly small almost zero and this term becomes 1 if V is the same as the speed of light then V squared over C squared is 1 1 minus 0 is 0 so this term becomes effectively zero and so the transform to the transform term is going to be between 0 & 1 and that means that X is always going to be less than X prime X prime is what's measured by you locally with your rod X is the distance I measure your rod to be remotely and that means that I will say that the length of your rod is shorter than you say it is and that is called length contraction a moving rod looks shorter now once again you have to realize that if you're moving at 30 miles an hour this term is going to be negligible it's going to be 1 or rather this term V squared over C squared is 0 therefore this term is going to be 1 so you won't notice any change but if you were on a train moving at near to the speed of light and you measure the length of your rod to be 1 meter I will measure it to be very much less than 1 meter as we shall see in a moment now what about time because we've always assumed up to this point that time is the same that T equals T prime now is that right well I can tell you it isn't but let's see why let's go back to our famous formula that X prime is equal to X minus VT multiplied by the Lorentz transformation which I shall say is gamma remember that gamma is equal to 1 over the square root of 1 minus V squared over C squared and we'll also remember from the speed of light that light is equal to x over T and it's also equal to X prime over T prime which means that we can take as just do it X is equal to CT and X prime is equal to CT prime so let's substitute these values into this formula so now we get that X Prime his CT prime is equal to X which is CT minus VT well T is just going to be X over C so it's minus VX over C all times gamma if we divide through by C we get that T prime is equal to CT divided by C is t minus VX over C squared all times gamma and T prime remember is the local time that is the time that you are measuring in your frame of reference and T on its own is the remote time that is to say it is the time I measure looking at something in your world and of course we could have taken the other formula which relates my value of X to your measurements the this is a formula we've showed earlier it's just the other side of the coin and again by substituting we can say that X is CT he whose X prime which is CT prime plus VT prime which is V X prime over C all times gamma and if we divide through by C we get that T is equal to T prime plus V X prime over C squared times gamma and what that shows you is that T very definitely is not the same as T prime T is my measurements it's the remote measurement t prime is the measurement you make of your clock in your system so it's the local measurement let's suppose for example that you switch a light on and off in your frame of reference in your train you switch the light on and off and you measure how long it takes between switching the light on and the time that you switch it off that will be in your system T Prime now if in your system that taught the light doesn't move because the scale and the light are in the same frame of reference so your light is fixed which means that X Prime for you is going to be zero so this formula reduces to T is equal to T prime times gamma because X prime is zero and as we've already shown that X prime that gamma is 1 over the square root of 1 minus V squared over C squared if one at one not if the square root of 1 minus V squared over C squared is between 0 and 1 which is what we showed before then 1 over this term is going to vary between sorry gamma is going to vary between 1 when the denominator is 1 and infinity when the denominator is 0 so in other words gamma is going to be 1 or greater than 1 which means that T is going to be greater than T Prime so if you measure a certain time interval after that light is on I will say using my clock that my time is longer in other words I will accuse you of having a clock that is running slow and this is called time dilation it says a moving clock appears to run slowly once again you're not going to notice that if you're traveling in a train at 30 miles an hour but you would notice it if the train was traveling at speeds approaching the speed of light so let's look at some examples of length of contraction and time dilation first we'll do length contraction here is Alice on board a train traveling at naught point 9 times the speed of light and she is going to measure the length of a rod and we'll say that she measures it as 3 meters on the platform his Bob and he is going to measure the length according to his own meter scale and we know because we've shown that the Bob's measurement the remote measurement X is equal to Alice's measurement the local measurement times the square root of 1 minus V squared over C squared we showed that earlier X prime is Alice's measurement X is Bob's measurement Alice measured 3 so X is equal to 3 into the square root of 1 minus well V is not point 9 times C so we've effectively got - naught point 9 squared here which is months naught point 8 1 and that is 3 into the square root of naught point 1 9 and that is very roughly equal to 1 point 3 meters so what we've said is that Alice measures the Lord to be 3 meters long but Bob will measure it to be 1 point 3 meters significantly shorter and that is because Alice is traveling at nought point 9 times the speed of light and so there's a significant length contraction what about time dilation well once again here is Alice on the train moving at naught point nine times the speed of light and she's going to switch a light on and off and time the the time interval between the light being on and going off and that's two seconds it's actually the light was on for two seconds here is Bob on the platform and he is going to measure that time using his own clock and as we showed before the time that Bob will measure the remote time is equal to the time that Alice will measure which we call t prime plus VX prime over C squared all to the gamma now X prime is 0 because in alice's frame of reference the light is not moving the scale and the light and thus are on the train so the light is stationary in alice's frame of reference so X prime is zero and all we now get is that T is equal to T prime times gamma which of course is T prime divided by the square root of 1 minus V squared over C squared and now we can do the same as before we can say that T is equal to T Prime well Alice we said measured that to be 2 seconds so T prime is 2 divided by the same as we had before V squared over C squared well that's going to be null point 9 squared which is not point P 1 1 - naught point 8 1 is the square root of Noor point 1 9 and that comes out to approximately four point five nine seconds so what we're saying is that Alice measures the light as taking two seconds but Bob measures the light to be on for four point five nine seconds Bob says obviously my watch is right so four point five nine seconds is correct if you Alice only measure two seconds it must be because your watch is running slow so he accuses Alice of having a watch that he's running slowly of course that's not true this is just the consequence of special relativity now one intriguing consequence of this is that if a moving clock runs slow and that means that every clock runs slow including your body clock that if you are traveling at speed you will age less than someone who is stationary so you could envisage the following experiment here is the earth and here is a space traveler who travels in this kind of orbit and maybe takes 40 years now if that traveling is close to the speed of light then what we're saying is that their clock because they're the moving part their clock will run slow now this is truly not special relativity because of course in order to go around in a circle like this you have to accelerate and once you accelerate you get into general relativity but I'm just trying to make a point here that if you travel at close to the speed of light for a period of 40 years you will come back to the earth tens of thousands of years into the future so you age by only 40 years but you will return to the earth as it will be in 10,000 years time however there's one big drawback you can never go back you can only ever go forwards in time this way but that might be an intriguing piece of space travel for the future now an experiment has actually been done to demonstrate the reality of time dilation and is all to do with particles called muons and muon decay muons tend to be created in the upper atmosphere as a consequence of interaction of rays and particles that come from the Sun and then they fall down to earth but as they fall to earth they decay the important thing is that the half-life that is the time for the number of muons - harv is 1.5 microseconds and they travel at almost the speed of light about Noor point 99 times the speed of light so an experiment was done on top of a mountain where the number of muons were measured per minute at the top of the mountain and also at the bottom of the mountain and what they found was that at the top of the mountain they were about 500 per minute recorded and at the bottom of the mountain about 290 per minute were recorded and the height of a mountain the distance between reading 1 and 2 was about 2,000 meters now we can do a simple calculation to find out how long it takes to fall 2,000 meters well the time is simply going to be the distance divided by the velocity in this case the distance is 2,000 meters and the velocity is naught 0.99 times the speed of light and that comes out to approximately six point seven three microseconds and since the half-life is 1.5 microseconds this is more than four half lives so if there were five hundred at the top then you would expect that after one half-life that would have fallen to two hundred and fifty after a second half-life you'd be down to 125 after a third half-life you would be down to 62 and after a fourth half-life you'd be down to only 31 counts per minute but in fact there were 290 counts per minute which suggests that for the muon the time has slowed and we can now see why we can apply the same self formula that we did before T prime which is the remote time that's the time we measure is equal to the time that the muon measures divided by the square root of 1 minus V squared over C squared well the time we measured was six point seven three microseconds and that's going to be equal to the time that the muon measures divided by - essentially not 0.99 squared because the velocity of the muon is about naught point 9 knowing that of the speed of light and this is the square root of of course and that means that T is equal to be six point seven three times the square root of 1 minus a naught 0.99 squared and that comes out to be naught point nine four microseconds which isn't even one half-life because the half-life is one point five microseconds so what does that to say we say it took six point seven three microseconds for the muons to fall this distance and they should have gone through four half-lives which means that if the reading at the top is 500 then by the time we've got down at the bottom there should only be a reading of 31 the muon says no no no no it actually only took me nor point nine four microseconds to fall because that's the relativistic correction and naught point nine four microseconds isn't even one half-life which is why we haven't even halved the reading by the time we get to the bottom and that experiment has actually been done and is a demonstration of the effect of the relativistic effect of muons traveling at close to the speed of light and the fact that you get time dilation finally it can also be shown that mass is relativistic and that the remoter mass if you like is equal to the local mass that is the end prime divided by the self-same correction factor 1 minus square root of 1 minus V squared over C squared so that as V approaches the speed of light then you will see that this term becomes infinite sorry this term becomes zero and that means that the overall term the mass will become sorry mass will become infinite if you just say that again has V tends to C then V squared over C squared is 1 1 minus 1 in CLO and M prime divided by 0 is infinite so M becomes infinite and that is why massive objects can never get to let alone surpass the speed of light because as they get faster and faster they get heavier and heavier and as they approach the speed of light their mass becomes infinite which means you need an infinite force to accelerate them because force is mass times acceleration and if the mass is going to be infinite you're going to need an infinite force to accelerate them to go a little bit faster to reach the speed of light so any massive particle or indeed massive anything can never get to the speed of light and they also means that things that do travel at the speed of light like photons obviously have no mass because if you've got no mess to start with then you don't get an infinite mass as you travel faster so massless particles travel at the speed of light anything with mass is incapable of getting to the speed of light now we can take this term here and we can subject it to what's called a binomial expansion now what binomial expansions basically say is that if you've got a term 1 plus X to the power n that will equal 1 plus NX plus some other terms which under certain circumstances you can largely ignore because they are very small if we take this approach and we subjected to this here this formula reduces to M equals M prime into 1 minus V squared over C squared to the minus 1/2 minus 1/2 essentially means 1 over the square root of this term and now if we use here we get that M equals M Prime into well this term expands into 1 plus n is minus 1/2 X is minus V squared over C squared so you've got minus 1/2 times minus B squared over C squared is plus B squared over 2 C squared and that's a Bible adage essentially a binomial expansion of this term using this approach there are of course some other terms but they get progressively smaller particularly if B is very much less than C well that means that M is equal to M prime plus M prime V squared over 2 C squared and now let's multiply all the way through by C squared M C squared equals M prime C squared plus M prime V squared over 2 you might recognize this MV squared over 2 haven't we met that before isn't that kinetic energy so this must be an energy term MC squared must be an energy term so we've got energy is equal to M prime C squared plus 1/2 M prime V squared that's kinetic energy that is what is often called rest mass energy and it's the way in which essentially Einstein developed the formula everybody knows e equals MC squared so finally let me just remind you of the formula the relativistic formula that governs special relativity in terms of distance we have length contraction we say that the remote measurement is equal to the local measurement times the square root of the correction factor 1 minus V squared over C squared as far as time is concerned the remote time is equal to the local time divided by the correction factor one minus V squared over C squared and as far as mass is concerned the mass that we measure is equal to the local mass M prime divided by one minus V squared over C squared and those are the three formula associated with special relativity

Channel: DrPhysicsA

Views: 127,688

Rating: 4.8903012 out of 5

Keywords: Special relativity, Einstein, Length contraction, Time dilation, E=mc^2, Lorentz Transform, Physics, A level

Id: 6Tts3gxs_cM

Length: 51min 30sec (3090 seconds)

Published: Mon Feb 25 2013