Einstein's Theory of Special Relativity Demystified

yeah welcome to uh may may episode for introduction to astronomy for another fun field where all the all the action is so let's start with a story always like to start with stories and it's called the twins paradox so you get these twin guys Roger and Trevor they're 25 twins and Roger decides he's going to get a little bit restless so he's gonna hop at a spacecraft new technology and fly off to Barnard's star system which is that's even light years away from Earth and so heads on over there and then he realizes Hmm this is not all it's meant to be grass is one of those cases where grass is always greener on the other side of the fence but as you get older realize there's Brown on both sides so he sorry the cynical um so anyway he decides to come back but honors return he comes back to Earth and he finds you know Rogers owning age 30 he's only aged five years but his twin brother is now 73. how did that happen so that's a lovely story which we'll delve into that later in the talk but yo who can tell me who's who's science who was the scientist and who was the and that was the name of the theory behind that that that makes all that possible how we understand that yeah it's Einstein's and that's why tonight we're going to be talking about Einstein's theory of special relativity and tonight we're going to lift the hood up and have a look underneath it and demystify it and really make it is pretty straightforward it's just some fun implications so let's start off with let's give you three sticky messages I'm going to give you them at the end of the talk but I like to throw them up front as well so you're going to learn three points to take home and tell your family tonight if they'll allow you in the house so the speed of light is the same for all observers in uniform motion now there's anyone traveling in a nice steady straight line at a normal Pace without increasing or decreasing their speed constant speed the speed of light is always observed to be the same space and time that we imagine to be difference like we're in the star dome right now that's sort of our space that time we're moving here as I keep blabbering on time shifting forward but you're going to learn that space and time irreversibly entangled into one entity called space-time and the third sticky message you're going to take home is that the implications of that last statement include differing Observer perceptions of space and time so it's not fixed space and time is not fixed it's variable and it all depends on your perspective as the Observer so let's have a road map of what we're going to do so chapter one will be on the introduction we'll talk about the definition of special relativity what it's actually about we'll talk a little bit about the background what led up to Einstein to say you didn't wake up one day oh I've got this idea he you know he developed this idea and had some thought so what was the background that led to it and then we'll have some fun talking about the implications of special relativity and then I'm going to throw you your three sticky messages again so yeah yeah definition in the background well this guy obviously needs no introduction this is Albert Einstein this was picture was taken about 1905 it was a miracle year when he brought out four groundbreaking papers uh one on what special relativity another one was the uh a spin-off from that with E equals MC square very famous equation creating mass and energy together and of course the photoelectric effect and so on so this is about the era when he came up with this and what it means is that special relativity Theory yeah it regards the relationship it brings space and time together it's the formula to link the two together into that one entity and the special part of it people say why is it the special relativity ten years later he worked on the general theory of relativity which involves any sort of movement with acceleration the use of the word special because it's referring to a special setting of just uniform although it's constant motion as you see the special setting of universal in other words you'll see us who often use inertial so uniform initial all means constant motion no acceleration you're not speeding up you're not slowing down you're not changing a corner at all um so it's that special setting of constant motion you start bringing space and time together so the bit of bit of background what led up to it of course is three Giants and arguably the greatest people science has ever to walk the planet with Galileo Newton and of course Einstein so let's start with these two and uh Galileo first came up it will fizzle these two guys all their research was done really on motion observations of motion and Galileo was the first he created his law of inertia which he put forward which that says the natural state of motion of an object is a straight line at a constant speed in other words if there's no friction everything just travels in a straight line if you want to slow something down you've got to introduce a force if you want to speed something up you've got to introduce a force if you want to change direction of something you've got to introduce a force the natural tendency of everything just keep going you might say well how can you boot a football across the across the room when it comes to a bit of a halt friction is the force there the external Force going on but it's a classical example space you see an asteroid it just gets a pin throws it across the room inside the space station and it just keeps flying like that and it you've got to apply a force to slow it down or alter it in some way so that was Galileo's law of inertia and the Newton came along incidentally Newton here was um as you'll see was born on the same that date of birth he was born on the same year that Galileo died so he picked up the bat and so to speak and he expands ended on these laws of motion to create the principle of Galilean relativity so all really these scientists were thinking about relativity what do different observers see and how are they related and so Newton's principle of Galilean relativity States the laws of mechanical physics are the same for all observers in uniform motion I.E there's no preferred or special state of uniform velocity which includes at risk so what all that means is that this guy kicking a soccer ball in the middle of the park just booting it around or throwing a ball up in the air or whatever it doesn't matter whether he does it in the park or whether he does it in a plane traveling at 600 kilometers per second he's still you throw a ball up in the air or you boot it it behaves exactly the same you don't own an airplane or a train suddenly have a happy moment jump for joy and end up flat on the back of the back of the plane on the train do you on the back wall you'd only be happy once um so you know the so the laws of physics and we take that for granted don't we you know we're you know you might be on a plane trip and you want to throw a ball or something or a bit of paper at seven you know two or three rows ahead hey hey hey you know like that or whatever you don't expect it to fly back at 600 km just back you know per hour to the back wall we just take it for granted but that is a law of physics and that's really really important so the laws of mechanical physics are the same for all observers and uniformed emotion so if you did a scientific experiment in the pack or you did it in the lab or you did it in an airplane you get exactly the same results so and that includes at rest so I'm moving at a constant speed or I'm at rest The Identical laws of motions so and another thing I put here so just a little bit of food for thought so for example here's a classic one you're playing table tennis and you decide to hop up on the plane you have a game of table tennis and you're hitting the ball backwards and forwards and this uh and the uh um yeah aa80 what would you expect to happen just normal wouldn't you the ball go backwards and forwards backwards and forwards you're not having to compensate the fact that you're up in an airplane how about if you had your cup of tea sitting there you wanted to heat it up and put it in the microwave so you know all these laws here and you say yeah I take that for granted but here's something that wasn't around an Einstein's day but we take it for granted what would you expect to happen if you're in a microwave on that plane and you put your hot cup of tea you put your cold cup of tea rather than they wanted to heat up and push the start button for a minute or two on high is it going to stay cold are the uh the light waves gonna go from cooler get stretched out because you're traveling at 600 kilometers per hour and get stretched up to radio waves and your teeth never gets warm because you're traveling at that pace are the wavelengths of light going to get crunched up and it's going to heat up a lot quicker because high energy photons no it's exactly the same isn't it and already you're probably getting where I'm heading with this where Einstein was heading with it all what makes light different to anything else when he first created that can't be so stop and think about it and you microwave oven and near a plane it's just a classic example so let's start talking about relativity so we're going to start first of all with this other Galilean relativity principle so how does someone else observe and record events from a different inertial frame in other words a different reference of motion and here's a classical way let's look at this example here so you've got this guy sitting on the back of a truck and he's throwing a ball up and down up and down and that's how he sees and how he records that motion and here's your coordinates that he would use XYZ for your coordinates and T for time but supposing you were sitting on the side of the road and you saw this truck drive by you're not going to see what this guy here is experiencing or someone else sitting on the track you're going to see that ball Arch over in an arch and come down like that once again you take it for granted but that's what's happening you just don't even think the second nature to you so if you're trying to describe that with a set of coordinates you call what call a transformation and this is called the Galilean transformation and notice the oh only thing that's changing here time is not changing its distance is changing to allow for the velocity or the speed of that truck that's the only thing you really have to do to change the set of coordinates from this guy's thing to a set of coordinates to describe what this guy is saying you're all you're doing is changing the horizontal axis incorporating the velocity of the truck and that will disputably with time describe a nice Arch there but already I'm trying to introduce the principle that the same activity is going on a very simple activity but you get two different observers seen totally two different things and you might say big deal that's but most of us we take that for granted but we don't actually doesn't sink home what's actually going on that's a very important law of physics so that was all fine and and life was good when they thought yeah we've got the Galilean transformation that makes sense that's classical physics I think we can safely leave science there and then this cut Along Came the Scottish genius was this in the 1800s who can tell me who this guy is Maxwell yeah thanks George yeah Maxwell so this is James Clerk Maxwell and brilliant man you know when you talk about who are the greatest scientists ever to walk the planet some people will bring up this guy very very clever guy sadly he died when he's about sort of about 50 or so very sadly but um so Maxwell discovered that light was an actual fact propagation of electromagnetic waves it was something he described it what it was so let's delve a little bit deeper into that and what we mean by that is you get an electrical current or electrical field that's propagating through space and as that changes it generates a magnetic field and as the magnetic field generates electric field and it's just a series of operations of propagation so you get electric field it it propagates then that moves on to a magnetic field the magnetic field creates electrical field and so on and so on and he worked out this he called it electromagnetic radiation because it was a a propagation of self self-propelling sort of electric and magnetic fields all getting laid out heading in a Direction and the time they'll decide oh I wonder what electromagnetic radiation is and at a similar time someone actually worked out what the speed of light is Maxwell with his equations which I'll come to next slide he had already calculated what the velocity how fast these electromagnetic radiation propagated waves should be traveling through the vacuum of space and lo and behold when someone measured the speed of light it was exactly the same and they realized that's what made them realize that that's what light is it's the propagation of electric and magnetic fields in a wave like fashion so he described these very four straightforward simple sort of equations he put forward in these four equations describe everything we know about electromagnetism very very important so in these equations there's two constants of nature that he discovered which are measurable and the first one is Epsilon which is an equation here and mu so both of these are constants of nature which can be measured and what do they stand for Epsilon refers to the primitivity or those the resistance of free space to formation of electric field mu refers to the pivability or the resistance of free space to allow magnetic field lines to run you might say oh big deal yeah okay I think I get that what's this what is the significance of those two statements that's telling you the nature of this universe it's vacuum space that's out there and the resistance of space to laying down massless at Electro magnetism electric Fields getting laid down there's a certain resistance it just doesn't happen instantly a magnetic Field's got to then get laid down it doesn't happen just instantly there's a bit of resistance going on in the vacuum and that's a natural state terroristic of our universe now the universe might be a little bit different but for our universe for what we know that these are constants of Nature and this is the natural resistance in other words it slows stuff down nothing happens instantly so from these formulas you can actually work out here because it's got C and that's the speed at which these the velocity at which these electromagnetic propagations should take place and you rearrange these formulas and what do you get C the speed of light is it's the inverse of the square root of mu and Epsilon these are constants in other words characteristics of our of natural ones of our universe you can measure these and lo and behold you can actually work out what the speed of light is you always say why why is there a speed of light why doesn't light just zip through it's just it's got a resistance vacuum is something and I think as you learn in particle physics and stuff too a vacuum is a very very busy place it's teething with activity particles coming in out of existence it's a foam of activity and it's going to have some resistance like what is resistance e is resistance to light the universe the vacuum of empty space has resistance to light and through these constants here that brilliantly put all these together worked out with c um and so from here it is works out to about 3 times 10 to the 8 meters per second is the observed speed of light what's special about it C is a universal constant don't people get hung up about the whole concept the speed of light it turns out that c is a very common constant that comes up time and time again in constant and equations for physics equations um that the end I think one of my last slide to talk about what is the significance of what's special about light and the answer if you find out is nothing there's nothing special about the speed of light it just happens to be the nature of our universe so so that was Maxwell did that sort of work and then who can tell me who these two famous uh sort of experimental physicists are and put it include they performed a very important experiment experiment in 1887. Michael yeah very very clever uh renewing um known for their High Precision experiments and what they did I think it's my next slide yeah so with this thing so they work out okay they suddenly understood light is a propagation of these electric alternating electric and magnetic field lines going through so they propagate in waves waves need something to propagate through waves in the ocean sound waves you know ways through the air and stuff you need a medium some sort of substance for waves to propagate that was pretty straightforward in the 1800s makes a lot of sense so they hypothesize that maybe the universe was permeated with very tenuous ether some sort of substance that was just flowing or just suspended in the universe and everything as the sun traveled around the Galaxy it went through this ether and when the Earth rotate we were Orbit's brother around the Sun it too just worked its way through the ether so a few people thought about it including Michaelson and Morley and I thought well this is so they're going to be certain times in a year we're going to be you know going perpendicular or with the ether as the Sun and the Earth moves through this way we're going to be going with the ether and light's going to be traveling with us so the speed of light might be a bit quicker repair quicker say if we're going back this way and we're going against it it might be maybe the light's going against The Ether or we're going against The Ether maybe the speed of light might be a little bit different so they set up an experiment which is very accurate total confidence in it that at the time is still to the state the highly sensitive instrument they could tell them pretty much they had it down you might say speed of light measuring an 1800s absolutely they could measure so these two guys they thought they would create this instrument that could measure the speed of light and measure it at different times of the year and so the instrument would be picking light up in at different orientations if you will to this ether that the Earth and the Sun was quietly working its way through so that in theory they should pick up a difference in the speed of light but lo and behold they found there was no difference whether it was April and they were pointing that way towards the ether October pointing that way Against The Ether whether they're going perpendicular to this hypothesized ether there was no difference in the speed of light so that caused a bit of a stir and got a lot of people thinking about that um one of the times I sort of put a big Downer on the whole idea of The Ether and well maybe these these particular light waves don't need a thing to go through because if if there was an ether there we would have picked it up so that put a big doubt on that but also it got Einstein and a few others thinking well maybe there is no ether maybe there's more to the story about light than we think and then these two guys characters so uh Lawrence and Fitzgerald they said they stated that the speed of light does differ there's an ether out there the speed of light does differ we just have not measured it that way our instruments have showed that the speed of light is the same why because they had this ad hoc hypothesis don't know where they got it from something packing accordies who knows but they've got some sort of hypothesis they picked out they said there's no and it was just ad hoc that the length of objects as they travel through the ether in motion they contract and shrink down a little bit and that's the reason why we get we show this apparent observation that the speed of light is exactly the same so that led to an equation they actually sat down and worked it out if that was so if our hypothesis is right let's work out how much shorter this thing would have to be the length would have to contract to make this so and I came up with this equation here the larynx Fitzgerald transformation for length contraction it describes how much an object contracts for a given speed so here is you've got the length of the object As You observe it after when it is traveling through the Earth and actually watch your instruments actually recording with this is what they call the resting lip length in other words if you had the instruments and they weren't traveling anywhere just sitting in a nice stationary State when you first measured them up before you set them up that's the resting length and there's there is it's over the square root of one month the V represents the velocity at which an object or the instruments are traveling through space and see the speed of light you might say who the hell did they get to that you're going to see that in a minute I suppose so they came up with this formula they just came up this ad hoc hypothesis that thing shortened and that was why the speed of light looked the same but speed of light did differ and they worked out how much so the interest now the formula works that I'm about to show you but for the wrong reasons so yeah then Along Came Mr Einstein and he three things actually he as a child he'd always had thought experiments about light he just had this real thing about light and he often you know asked people oh my God what would be like if I shot a beam of light and could run or fly in an airplane because they did probably didn't have him it was more trains in it days if I had a fast train just hypothetically if I could keep up with light what would I see if I outshone light and held up a mirror would the mirror just look black this is the sort of stuff that einsteined when he was young and even a child he was throwing around in his mind and then he sort of got inspired about my Maxwell's equations that the speed of light showed a constant speed it was actually a physical property there was nothing magical about light and as I jumped ahead a little bit of time I showed you the microwave situation on the airplane if we know now there's nothing special about light but he was one of the first guys he said look at Maxwell's constant look at those equations that tell us about the speed of light that's a property of the universe yeah what's different to that to the laws of other laws of motion and so on but also it was that Michaelson and Morley no result that said the speed of light the instruments never detected any difference despite different orientations Through The hypothesized Ether so that got him expecting thinking and inspired so he then went on to extend the Galilean relativity principle to include light that's where he came up here his theory of special relativity was based on two postulates one is which we've already seen the laws of physics are invariable and identical they're remain the same and all inertial frames of reference meaning that no matter what as long as shift doesn't involve acceleration but at a constant speed doesn't matter if you're still whether you're moving this quick or this quick or whatever the laws of physics are all the same with you boot a ball in the ear and how it comes down or whatever here's the interesting one where he threw the cat amongst the pigeons which went against everyone's intuition at the time he said the speed of light in a vacuum is an invariant grants exactly the same for all observers regardless of the motion of the light source or the Observer so what that means if I was with a torch over here and say for example Andrew stood over there and I shined a light at him a hidden instrument to measure how fast the light beam and I shine my laser at him he would come up and say well it's exactly this 3 times 10 to the power of 8 meters per second what would it be if I started running towards Andrew at half the speed of light charging towards them surround that low what would his instrument show according to Einstein exactly the same yeah three times he'd say it's exactly the same how about if I ran backwards at half the speed of light and kept shining it to him your intuition tested oh it must look a lot a lot slow what does it measure exactly the same 3 times 10 to the eight it's just it's just counter-intuitive to what we're brought up with so it was Einstein and that was this was all about and he said there's this this particular second principle what makes light anything different to anything else the laws of physics should be the same um so another one a little cool little story is Bob the Sprinter so tell me the solution to this so there's this guy called Bob and he that he tries to run run faster and faster and faster and takes all these steroids and stuff and uh and then he just he gets caught and gets booted out of the running thing for it for a year or two has to go and sit on the sides so he uses that time to get really really super fit and he said I'm going to come back and prove to the world I'm going to run as fast if not outrun the speed of light a light beam I'm gonna have a competition set up a light beam in the stadium we'll shoot across and I'll run at the same time when the gun goes off and I'm going to train so hard I'll keep up with that beam of light so the day comes and the stadium packs up and the gun goes off they shine a beam of light and out of the Sprinter just out of the blocks and it just blows everyone in the stadium holy yeah he's traveling he's like being traveled at three times ten to the eight meters per second Bob traveled at 2.9 times 10 to the 8 meters per second he you know he was Keeping Up with the light he didn't quite get there but he's keeping up with pretty impressive and everyone while he Bob is a hero he's redeemed himself let's go and congratulate him so someone went down into the here and here they found him underneath the stadium just in the uh in the in the changing shower room area there and he was there crying his eyes out so just listen what are you crying for you've done amazing feat why was he crying why was he upset because as far as he as far as us was concerned the speed of light just zipped across and he was keeping up with it but as far as Bob was concerned the speed of light was continuing on it was he was observing it to keep moving away from him at the speed of light he was The Observer to all observers the speed of light is the same irrespective of the of the motion of the Observer or the emitter so far as Bob could see the light was always a certain distance ahead of him he could never ever ever catch up because that was the speed of light but to everyone else God he almost did it so it was just a neat counter-intuitive thing that's going on because of this Einstein statement so and it really has some really cool implications involving the tanglement of space and time which we'll talk about so that pretty much uh sort of covers what I rattled on about he got your Observer here this guy's traveling at 0.8 the speed of light this guy 0.9 he did with a beam of light here this guy sees the light shining at him despite them hitting towards each other you know it's their combined speed which we think of intuitively this person still sees that light is this that light at the speed of light see this guy here sees it exactly the same so everyone observes the speed of light exactly the same regardless of the motion of the Observer or the emitter so let's move on to the implications of of that statement involves time dilatation length contraction we'll talk more about that twins Roger and his twin Trevor and then we'll talk about things happening simultaneously and then we'll talk about the universal speed limit so time dilatation it's all about how time is perceived and that's one of my first statements is right at the front space and time are one entity and both are invariants they're not set and Conquer rather they both variant they're set and they're not set in concrete they can change it all comes down to the observer's perception and moving a clocks appear to go slow and I'm about to explain in this more depth but this is just what time dilatation is about so here's here's you've got a couple of twins here same time clock system twin B heads on out comes back twin uh twin B you know it's only gone the time has only gone that little part there but the twin B it's traveled proportionately so that's two three four five times as much clock twin bees clock brings slower because it was traveling relatively to Twin a and so hence aged less so we're going to go through that but that's what time the concept of time dilatation is about just like we spoke about Roger and Trevor so let's move on to that so you might think whoa and there's some big formulas coming up and head is all this quick I'm just gonna it's just it really is it's simpler than you think so here it is so time appears to to go slow due to light traveling a further distance but at the same speed because what have we just been told the speed of light is the same to all observers so let's have a look at situation A you've got this this sort of clock if you will a light clock and it's at rest whereby a source of light sends a beam of light up here this distance hits the mirror it comes back and hits the sensor and that's sort of like a light clock and it's sort of a set distance and the speed of light is exactly the same it goes up there and it comes down life is good that's all pretty easy to get how about this platform here you put this experiment on a trained platform or something like that and you had it moving quickly along and you sat on the train station platform what would you see so if you're on the train you're going to see the light go up and down up and down but you on the Observer on the platform as this moves across at velocity V the instrument's moving across the velocity V you're going to see the light go up like that hit the mirror here and come down a nice little triangle like that and what velocity are you going to see that light travel at see the same velocity but look it's traveling a lot you know Common Sense intuition what's the difference between here and here versus here and here which is the longer distance A or B B absolutely it's a much longer distance but what did we observe the speed of light was exactly the same something has to change and here it is here so light is observed to travel further and be and also we all agree upon that observed travel at the same speed that the light was observed to travel the same speed A and B the light doesn't care it travels at the same speed to you the Observer we all agree that speed velocity is distance over time you know look kilometers per hour meters per second speed is about distance over time so we all agree to that yep okay so there's our formula again so if they observed speed of light and a and b is exactly the same but so the speed remains constant but the distance increases to keep that figure the same time that figure there must must be bigger because say for example speed say it's a factor of two um and you had to figure out sort of uh four over two here so it was two suddenly if you crease that up to increase that to three you increase that up to six that's going to be three two you know the ratio has got to increase so if the speed is constant in all the situations but you're increasing the distance the time must increase so what that tells you is that to an observer that this whole process this sort of process of this happening must have had taken a lot longer that the internal clock must have slowed down but if you were sitting on that train you'd said go up and down like that now you might say well so you always that sort of it just makes sense the time is longer so that clock is ticking slower and all let's explain a little bit better so by how much do we calculate it comes down to simple geometry Pythagoras Theorem that we learned in sort of school sort of early on in school um that if you get a right triangle like that and say you put a sign this side as a this side is side B this side is a c that the square of this side plus the square of that side equals the square of this side a squared plus b squared C Square runs happy with that sort of Pythagorean's Theorem we learned in school pretty pretty straightforward you might think what's that got to do with relativity here is your situation so here remember we said that um that the formula that velocity is is distance over time which you just rearrange it distance equals velocity times time so the platform moving across at at velocity V its distance must be velocity T so you just divide it by two because we're only interested in one true we want to split it up into a nice triangle so we're just splitting off half the distance so that's the velocity at which that platform was traveling times the time recorded divide by two and that's your distance likewise the distance here is the speed of light times time divide by two and your distance here you you know your distance because you know how high your clock is but so look with your formula just like with your a square plus b square your c squared you just substitute it in so here's your a so it's V2 divided by 2 squared here's your D you throw that in squared and that must equal um the CT divided by 2 squared we know we know what what V is because we we did that we know what D is you rearrange the formula we know what c is 3 times 10 to the power it's a power of 8 meters per second so from there what's the thing you can solve you can solve it for time you know C you know D you know D you rearrange the formula and work at the time that you perceived that for happen the guy sitting on the train saw the clock go up and down up and down like that you saw it going like this and there's a simple formula just using Pythagoras Theorem to make this formula here and this is it so you can see where they're getting it I've got a little video that actually showed you briefly how you actually formed that so this is the time measured on the moving body in other words I've added these little bits in here this is the observed or perceived Time by someone sitting on the platform that time there t0 represents the time measured on the stationary body in other words the passenger power is the passions passenger's concerned on that train he's still in a science experiment his little light clocks working just fine thank you very much that's his time it's his clock and you put it over one minus the um the square of the velocity of the trainer which is moving divided by the speed of light and this here is known as the laureen's transformation where have you seen that's very similar isn't it to Lorenz Fitzgerald's formula for the uh for the transformation because once again they got the formula right but for the wrong reasons because they did the math to match the observation not the other way around they found the formula that they wanted and I think it's coming up short yeah this is it here so let's just see if I can operate this it's just about a two minute video just to talk about what we've talked about it when they were in motion the essence of his reasoning can be seen with the aid of the simplest possible clock two mirrors a fixed distance apart with a light beam bouncing back and forth between them bounce of the beam is a tick or a of the timepiece to Henry his clock is stationary and altogether ordinary but for Albert that clock is moving and between tick and talk he sees the light beam trace a diagonal path which means it's traveling a longer distance but the speed of light is the same for all Observers so the light must take a longer time to travel the longer distance therefore Albert believes the moving clock runs slow but how slow [Music] the relativity of time is derived from the right triangle formed by the distances traveled [Music] the Pythagorean theorem shows that the path of the moving light is longer than the distance between mirrors [Music] by the factor one over the square root of 1 minus B squared over c squared Factor occurs so often in relativity that it is given its own symbol the Greek letter gamma [Music] so to an observer at rest a moving like clock seems to be running too slowly by the factor gamma a ruler or anything else in motion also seems contracted by that same factor that video just sort of shows that yeah the clocks do tick differently and that form in your first look you think oh that's a big complicated formula it was actually derived very simple and if you just you didn't have to follow it with probably too much to follow that one moment time but you can see it was just a matter of shuffling the figures around from Pythagorean theory um and and there it was that's how they got the formula so that was time dilation in other words moving clocks appear to be going slower not to the person who's moving back to the Observer and so that was how the perception of time gets changed habits perception of space space gets changed too or the perception of space with uh with movement and it's called length contraction so moving objects and distances appear to shorten as you travel instead of clock slowing down like slow down but also lengths appear to shorten so space shortens essentially how much where have you seen that formula that's your length formula so this L represents the observed length when you're seeing someone travel at high speed a ruler traveling at high speed that's how what you measure or you perceive the length of that ruler to be the person who's hanging on to that ruler traveling through space at Almighty speeds that's that they will tell you no no the rule is this long it's resting left and it's just the square root of one minus V squared over C square there's no need to be afraid or phased by that equation at all it's just derived through the simple right angle triangle formula Pythagoras Theorem now just a comment here the length contraction is in the in the direction of motion that things start to shrink and get and get shortened so yep length contraction occurs in the line of Direction so that's here that's the formula there so you've seen that that was from my previous slide from the and like I said they got the right formula but for a different reason the wrong reason they looked at the results and sort of how can we make a formula to match this and they create the formula of course in Einstein went the other way around and worked out in theory what it should be and the observations matched so this is just a as in your handout here this is time dilatation so you can see the faster you get to speed of light some of the faster someone observes you to be traveling um that the your clocks get slower and slower and slower and slower until you're almost to the speed of light in your clocks coming to a complete halt length contraction is something as You observe something to go faster and faster and faster as you're approaching the speed of light it gets that length or that ruler gets shorter and shorter and shorter and shorter to the point should it reach the speed of light you've got no ruler left um so moving clocks appear to slow down Lynx appear to shorten by the factor of that equation the links the lorrentz transformation so that formula is very general and as the documentary said it's actually just labeled gamma it's used so often in physics so there's lots of things to confirm special relativity um you know atomic clocks that you know very very accurate you play have atomic clock on the ground you put atomic clock in a soup you know in a jet flying at High Velocity the clocks will keep different times the clock traveling in the in the uh in the jet traveling High Velocity will tick slower than the atomic clock on the ground that's been well and truly proven GPS satellites they wouldn't work unless you have to factor in the fact that the high velocities they're traveling you've got to factor in relativity for their timing yeah Electronics you know your TVs your watches your mobile phones and stuff that's All Electronics that's all you know electrons and stuff zooming around at huge velocities if they ignored the laws of special relativity in designing these watches and mobile phones and television sets they wouldn't work so what more evidence do you need when you go home turn the TV on and you go home to the family say oh I see you're checking out special relativity um but I think one of the more Nature's really cool one of here has got the muon Paradox which is really cool nature actually shows us that our special relativity is so so these things got muon is a subatomic particle it's the heavy cousin of of the electron um it's very unstable it's got a very very short half-life so it doesn't hang around for long and it's high energy situations that they are created so you've got they you've got cosmic rays which are heading towards Earth and slamming into a into our atmosphere high up and cosmic rays a high velocity high energy charged particles where they come from things like Supernova explosions across the Galaxy and stuff they're up there and they slam into into particles in the upper atmosphere and for brief moment time these little subatomic particles called muons are created high up in the atmosphere these muons in travel because there's been a lot of energy imparted to them by these these charged particles cosmic rays traveling close to the speed of light and the muons that then get created up here and they head on down towards the ground at 98 the speed of light they've got a mean lifetime about 2.2 microseconds so the time to reach the ground is 15 times their mean lifetime which immediately tells you the chances of finding them on the ground are calling to Newtonian physics is pretty slim pretty negligible you're not going to find many Newtonian physics predicts negative amount of muons there's just not the most almost all of them are going to have decayed by the time they reach the ground but you put your muon detector on the ground and you wait and you start thinking aha I know that formula from stardome I know that formula that's why my TV works and it's what do they detect there are a good appreciable quantities of muons that they do detect because of special relativity time dilatation and length contraction now let's split that up you say well watch what going on here so from our perspective The Observer if we were just hypothetically thought experiment to observe that new one we would see their clocks ticking a lot slower so they're Half-Life suddenly to us our perception on the ground is a lot longer so they're living longer so they've got more opportunity to get to the ground from the muon's perspective is a thought experiment looked out instead of looking down and seeing two 20 kilometers of the ground the muen and that velocity have looked down say oh it's only about a couple of kilometers to the ground we've got plenty of time and so it's for those two reasons that yep the muons despite the the natural Half-Life have been about 2.2 microseconds they quite happily travel down 20 odd kilometers which in theory should not happen why special relativity they're traveling at very close to the speed of light so that's Nature's proof to us that special relativity but we don't need that for our you know we don't need that proof we've got a plenty of our own thanks very much but that's pretty cool Paradox now let's get back to Roger and Trevor so why the difference here so remember Roger Upton is and his ship and traveled at uh 0.9 times the velocity of light to Bernard Star seven light years away turned around came home again they were both 25 Roger gets back he's only aged five years and Trevor 73. what was going on there so let's have a look at it from Roger's perspective on the spaceship his clock was running normal time he said look I'm standing here I'm at rest my clock's at rest to me everything's running normal time but he looks out his window and he doesn't see Barnard's star seven light years out he sees the the distance because he's traveling at high velocity so first he's concerned he's stationary but he sees the rest of the universe around him is is speeding so he sees length contraction so he looks out and doesn't see seven light years he says oh it's only 2.2 light years to Barnard star that's no problem and of course that he turns and comes back again for another 2.2 light year so it's roughly 4.5 just rounded off to five years but you can see the reason that he only aged approximately five years and came back age 30 was because he perceived the difference of length contraction it was only about 2.2 light years these figures are actually that was one of those exam questions in cosmology so the figures are actually pretty close there so it's about 2.2 light years versus seven light years each way from Trevor sitting back on Earth what's his perspective he still sees the distance seven light years but he sees Roger moving along close to the speed of light this is Roger's clock running really really slow so Roger so in other words Trevor feels like Roger's clock is running slowly and Trevor just sits there and waits for another you know sort of 50 odd years for Trevor to get back but Roger it far as he's concerned it only took five years there and back Roger it took 21st 24 Earth years each way now you might say and I remember first doing this as a thought experiment I just came across the list I thought well hang on a minute what's wrong with this Roger's traveling at this fast velocity seeing this but you could argue the same bet Trevor as well so you could argue quite happily that they should remain the same but there is a subtle difference here anyone know what it is that actually makes this happen was that that acceleration the acceleration yeah George is right it's the acceleration it's a it's a situation of asymmetry the fact that um Roger had acceleration and deceleration going on in the process and that's what bring teases all this stuff out to reality um it's sort of an asymmetrical situation so Trevor was just continuing a constant velocity everything so he perceives all this to be happening but Roger was asymmetrical he evolved deceleration to get up that speed and deceleration but those figures that's what would happen that it's called the pin the twins paradox cool so how about simultaneity um simultaneous events you know we all agree if something happens on the other side of the room or whatever we all agree what happened and what order and so on but suddenly we're starting to play around with we've just told you how it's all it comes down to motion space looks different different perspectives according to emotion according to emotion time has different perspectives so it follows from there that people agree and disagree on what uh what occurred in what order and the first simple example is let's look at a train so this is from the perspective someone sitting on a train trains um it's zooming along here someone's on the train have a light beam and the light beam heads in each direction as the train travels they're in the train as far as they're concerned they're at rest with that light so they see that light in each Direction the same velocity so as far as they're concerned is they would say the lights both light beams shown at the same time from the middle hit the front and the back of the train exactly the same time that's what an observer on the train would say it was simultaneous if you were sitting on the platform and that train was zipping past at some high velocity by the way all these these um these effects do happen at low velocities we just don't notice them but they are happening you hop on a plane to fly to Melbourne or Sydney or somewhere you are you actually are gaining a micro second on someone else you just don't notice it certainly not enough time to slip a cold beer down at the airport anyway though having there's a bar on the plane you could probably still slip one down I'm sure but um anyway I digress so he sees this guy sitting on the train with a light beam going either way but he also sees to him the speed of light is the same so what he sees is of course because the Train's moving in this direction here going that way so he sees the beam of light's got a shorter distance it whams into the back wall and then whams into the front wall so someone sitting on the platform of the train would say no I disagree that light beam shot out it actually hit the back wall before it hit the front wall or if they had a sensor on each wall they'd say the Bella went off here and then it went off here as opposed to this guy here would say no the little sensors went off at the same time so that's this very simple explanation of why uh the sequence of events differs according to your observation motion how about a train traveling four fifths the speed of light in this direction going that way from left to right a lightning bolt hits this tree and this tree here at the same time as far as the Observer is concerned have it this guy here sitting on the train would he say the lightning hit both trees at the same time or would he say a it hit a first and then b or B first and a or both at the same time he's going to say hit tree B first because if length contraction he says the distance between here remember the velocity he's traveling towards there is traveling towards that tree this the the length contraction see that's going to be a very much shorter distance but and just in fact he's traveling in that direction at that High Velocity but he sees the light she travels at the same velocity so if the lightning hit this tree it's got a shorter distance to travel to him here but it's got a longer distance to travel here and Ferris he's concerned the light from that tree coming towards him is exactly the same velocity as that tree so this Observer here says no the lightning hit both trees of exactly the same time because the light travels at the same time at the same pace and the distance is the same this guy here says no I see both beams of light from both trees traveling at the same velocity but this was a lot shorter so B was struck first similar situation here um the lightning this person in the spaceship he would say look it struck B first and then a this person down here says no it hit the both at the same time so I've got another little video here just to uh to highlight that point Albert and Henry [Music] just for the sake of argument at the exact place and time they pass each other they observe a flash of light a sphere of light expands outward from that point since each measure the speed of light relative to himself each believes correctly that he is always at the center of that expanding sphere even though they themselves move farther and farther apart [Music] how can two people in different places both be at the center of the same sphere to confirm his perception each sets up light detectors and equal distance apart [Music] however while Albert's detectors register the light arriving simultaneously he believes the light strikes Henry's detectors at two different times [Music] meanwhile Henry sees the same thing in reverse [Music] they agree on the speed of light but they disagree on whether events happen simultaneously or at different times this is not semantics nor a petty debate it means that time as well as distance has to be affected by motion however as a nice little illustration it was a sort of nice visualization sort of how simultaneously is another whole implication of it all so haven't the universal speed of C why can't an object travel faster than the speed of light that all comes down there's another thing we haven't mentioned yet is a concept called Mass there's two explanations behind it but it's all to do with relativity relative mass and the intuitive sort of explanation is that mass is observed so here's your resting mess if someone was traveling at high speed and first of all I should say what is mass mass doesn't necessarily mean how big you are anything like that the definition of mass is the resistance of an object to be accelerated it's inertia so if something creates a lot of force to push it along that's of a higher mass than something that's easy just to give a poke and it goes along so that's the definition of mass and so as you velocity gets higher and higher and close to the speed of light you're perceived from an observer your mass goes up and up and up according to you know according to this lorentz um transformation formula so as the mass increases to infinite levels you can see here's the velocity of light down here here's the the perceived Mass from someone observing you or you observing everyone else for that matter and as it preaches the speed of light the mass gets higher and higher to infinite levels whereby you then need infinite when you hit the speed of light you need an infinite amount of energy to keep accelerating pushing you along which of course there is no infinite amount of energy that doesn't exist so you cannot reach the speed of light because of that so that's the nice sort of intuitive way to look at it and you can delve a little bit deeper and go to the concept of relativistic mass and one of Einstein's out of all that relativity uh special relatively derived from those formulas is that equals MC square and he produced a whole paper on it proving that energy and mass is the same thing but just expressed as different entities but it is the same and as you approach the speed of light mass and energy sort of become more and more similar in property it's called relativistic mess or your resistance deceleration and it refers they start just instead of deciding it's a mass they start putting the kinetic energy of the movement into the equation to work out the relatistic mass and you can see that put it here the the energy of the the transformation equation you get m c Square so there's the energy they put m c Square in here so your relativistic mass which includes the kinetic energy gets higher and higher and higher as you approach the speed of C the total energy approaches Infinity which an object cannot possess infinite amount of energy so notice that wrist mass is invariant if in other words you're chugging along you don't think you're getting more resistant but people are observing you and you're observing everyone else relatively as well um so that that is why you can't observe anything to go faster than the speed of light it's because of relativity so here's backyard food for thought and it also means you can have your hot cup of tea at six at 30 000 feet traveling at 600 kilometers per second light doesn't get stretched out or doesn't get bunched up to higher or lower energy wavelengths you put it in the microwave you get microwaves that heat up because the Einstein was quite right there's nothing special about light it just simply follows an obeys that original Galileo relativity principle that Newton said the laws of physics are all the same for everyone at a uniform motion and they just forgot to take light onto that which Einstein came along and did thanks to Maxwell and the Michaelson Amore experiment so there's nothing special about the speed of light yeah it just happens to be the same as the universal constant C and it's the maximum speed at which a massless entity such as light has no mass or information causation that travels across the empty space empty space has a natural resistance and that just makes sense empty space is a busy busy place it's foaming with activity so here's your three sticky messages you're going to take home the speed of light is the same for all observers in uniform motion everyone no matter where someone's a light source coming towards you away from you or you're traveling away from it everyone agrees the speed of light is the same they detect it the same space and time are irreversibly entangled into one entity space time you can't separate the two and the implications include differing Observer perceptions of space and time length contraction Alters the perception of space and at high these high speeds time dotation process Alters the perception of time that's what's going on so yeah Einstein's theory of special relativity tonight demystified thank you for your attention I hope you've enjoyed it thank you [Applause] as for the equations I regret nothing any quiz that's like I think all my three cats look like that sometimes in any yes yes yes yes yes because your time yep gets complicated bringing the two together the time is the person who appears to be stationed when they're looking at someone else their clocks appear slower as opposed to that person traveling length so you've got to calculate them separately but then you bring them together like that the twin paradox I brought them together there um and that's very easy to do but you TR you don't get messed up treat the two equations separately but be be mindful in your mind who's seeing what so Roger I saw Trevor rather on the earth he was looking at Roger he was seeing Roger's clock go go slower now but Roger doesn't see the same because you've got the acceleration process but in theory Roger would see the clock Trevor's clock going slow but and then there's the length contraction that Roger when he was traveling there he looks out the window and looks like 2.2 um leads but his clock was running normal but he saw the length contraction so you do treat them separately but you bring them together and for example uh one of the questions an exam actually was prove that in actual fact that both observers the clock was running exactly the same if you had a telescope and Roger and Trevor could look at Roger's clock and with Roger you could actually calculate and show that they they all agree on on the the whole principle that things are unfolding are compensating for each other at the same rate yeah but you treat the equation separately but it comes out in the wash um those times are fat yeah yes yeah um lightwaves to say yeah for a year for them we're talking no acceleration here for a uniform velocity oh yeah red shifts your gravitational redshift you know trying to accelerate ever gravitational well but also with your redshifting there's the Doppler effect and and that's because of light is coming towards you that's a it's accelerating yeah that's a different scenario yeah that's the Doppler effect yes [Music] we were traveling towards the source you would measure a higher frequency yeah so this is the Doppler effect yeah the wavelength yeah that's the Doppler effect different again and your uh and your red shift that you get with gravitational because that's involving acceleration trying to get out of the graph once again as Bill said the reason you gravitational root shifting is because the speed of light is not changing but it's losing energy as it pulls away from a heavy body so the wavelength gets weaker and weaker and longer and longer John yeah [Music] um [Music] you know that the Michelson Mall experiment didn't just totally dismiss it it did a lot of points but it took some years John was saying in the 1930s there were still people talking about The Ether that's that's out there um yeah so things didn't change quickly and I think that also highlights Einstein's Brilliance how ahead of his time he was you know 1905 he picked up on because there they were Lawrence and and Fitzgerald they still believed in The Ether they said no no it's just that the speed of light is different there's an ether out there guys we've got to find some other reason it was Einstein who came along and said no no you guys have got it all wrong so but yeah so it was 1930s there was still a lot of people talking about either yep so the highlights how clever the guy Einstein was yeah because some members I think have been to the uh Large Hadron Collider a lot of Tourism I think the new government yes yes [Music] they were accelerating tinier subatomic particles protons how to do that to power the magnets to get those protons go so fast if you actually got an almost dedicated Power Station to do it because of the massive aircraft was talking about as a particles accelerate and it gets harder and harder to make them go any faster more and more engines but some Curious thing is I think what is the um it's about seven trillion electron volts as a measure of energy they've put into those protons here but some cosmic rays that come from outer space protons have got media orders of magnitude higher energy than that so petitioners how does the universe doing it two or three years ago some of the newspaper said ah some experiment the found particles traveling faster than the speed of C you know light in a vacuum and I think most people looked at me shook their heads and said someone needs to recheck their data again and sure enough it was a data area now another actually little um little antidotal thing to bring up here often people get confused about the speed of light and a vacuum they say Einstein said nothing can travel faster than speed of light nothing can travel faster than the speed of light that light travels in a vacuum light slows down another medium it travels slower in water in different chemicals and different medium and stuff so there are other circumstances where something can travel faster than the speed of light in that particular medium so there's nothing stopping something from traveling faster than light in a particular medium it's just you can't travel faster than that sort of rounding up three times ten to the 8 meters per second you can't travel than that figure don't try and compare light in another medium with with another particle in that same medium it's not comparing apples with apples and another people think a little bit confused if they say haven't these far away galaxies that are receding from us faster than the speed of light and it's nothing to travel fast and the speed of light okay nothing can travel faster than the speed of light in a vacuum that says within our universe that's saying nothing about space-time the reason those galaxies those galaxies aren't traveling you know aren't traveling faster than you know through zipping through face to space far far away from us it's a speed of light space time is expanding so the galaxies are sitting here just getting driven apart from each other faster than the speed of light that's what's going on so Ironside said nothing about the expansion of space-time dark energy which Jonathan spoke to about a couple of months ago he just said in our universe and our vacuum within our space-time there's a natural resistance to the height the rate at which you can lay down electrical field and then some magnetic field lines and so on and so on there's just natural resistance space-time can do its own thing quite happily thank you very much so that's a little I mentioned that little antidotal little thing in there too that people often raise so I think we've you know you've all had some fun go home and turn the TV on and enjoy some special relativity drive home safely guys thank you [Music]

Channel: Chris Benton Astronomy

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Id: 0nQplJO98ug

Length: 67min 42sec (4062 seconds)

Published: Mon Jun 05 2023