Einstein's Annus Mirabilis, 1905 - Professor Raymond Flood

so thank you all very much for coming to my lecture today I hope you've had a a very good summer and for those of you for whom this is your first lecture digression were particularly warm welcome and hopefully we'll see you again well my lecture today is about one of the most iconic persons and science or indeed in world history and as images instantly recognized and he's a global impact as shown here in this cartoon but an American cartoon is called her block Herrmann block and it depicts earth is viewed from space and the salutary thing the dutiful thing about Earth is that it carries a plaque saying Albert Einstein lived here and in this lecture I want the concentrate on just one year of Einsteins life but what a year in 1905 his annus mirabilis his year of Wonders he published four papers of exceptional importance I'll discuss each of them concentrating on the last two where he developed special relativity and some of its consequences Gresham College will also be offering this year a lecture to celebrate the centenary of Einsteins announcement of his theory of general relativity in 1915 and I will give details of that later but I'll concentrate in 1905 and start by giving a brief biography of Einstein picking out some features of his life and his attitude that I and I hope you will find interesting lianna look at the 1905 papers concentrating on the letter to Einstein good Einstein was born and owned and southern Germany and the 14th of March 1879 his parents were Hermann and Pauline within a year his father's business at field and they moved to Munich where Einstein spent the next fourteen years he seems to have been shy and his school years did not demonstrate any outstanding ability in later life he describes in his autobiographical notes an experience which had a great impression on him it was it was when at a young age his father showed him a magnetic compass he was very impressed that no matter how the compass was turned the needle kept turning north pointing north the compass needle allô completely enclosed was influenced by an invisible untouchable force his first experience of a force failed and he said a wonder of this kind I experienced as a child of four or five years when my father showed me a compass that this needle behaved in such a determined way did not at all fit into the kind of occurrences that could find a place in the unconscious world of concepts I can still remember or at least believe I can remember that this experience made a deep and lasting impression upon me at age 10 he went to secondary school where he does not seem to have which he doesn't seem to have enjoyed but while there while he was 12 he had another thrilling experience when he met Euclidian geometry and I'm pecking like these two kind of things as he did in his autobiographical notes because they tend to give some insight into his way of thinking and the way that he worked during the Year 1905 and he wrote at the age of twelve I experienced the second wonder of a totally different nature and a little book dealing with Euclidean geometry which came into my hands at the beginning of the school year here were assertions as for example the intersection of the three altitudes of a triangle in one point enough from the top on the left which though by no means evident could nevertheless be proved with such certainty that any doubt appeared to be out of the question listen lucidity and certainty made an indescribable impression upon me that the first axiom had to be accepted on proved did not disturb me and we'll see how that's exactly the framework that he uses when he develops his theory of special relativity working from postulates to derive consequences I'm going below he also was told about the Pythagorean theorem and he says that he proved it himself on the basis of the similarity of triangles so that's the first part of your homework to do the second part is that much later in life he sold another school problem in Euclidean geometry this problem was reportedly posed by a fifteen-year-old schoolgirl and the problem asked her to construct a common tangent to two circle of different radii there's one circle there's the other circle and there's a common tangent and this is Einstein solution in his own hand and this is his own diagram here I'm not sure your second piece of homework it's on the handout and but again it's typical it's somewhat like so much of his work it's so clever and it's so concise in 1894 his father's business again filled and his parents and sister moved to Milan Einstein remained at school but rejoined the family after six months his next year was one of enjoyable travel inanity at 16 he applied to the prestigious ETH the Swiss Federal Polytechnic School in Zurich feeling at the first attempt he succeeded as a second attempt in 1896 began a four-year course for teachers of Science and Mathematics and here's his matriculation certificate on the right giving us results at the end of secondary school and I thought was I was delighted when I find this you obtained the highest grade the highest grade of six in history algebra geometry descriptive geometry and physics Eco create five in German Italian chemistry and natural history geography and drawing him in at four while his purrs result was a grade three in French language and literature so very respectable but not absolutely outstanding as you can see while at university he read widely including original work of kerkhof Hertz Maxwell and particularly Ernst Mach whose book on the science of mechanics proved the underlying ideas and assumptions of physics he graduated in 1902 graduation he supported himself by part-time teaching until he obtained in 1902 a probationary position in the Swiss Patent Office and burn and among his fellow students at ETH was Mileva Maric whom Einstein mired in 1903 and the 1904 his appointment at the Patent Office was confirmed in this year of wonders Albert Einstein published in the annals of physics four papers have grown breaking important and there are very few libraries in the world that contained volume 17 of the 1905 annals of physics the first of these works does to outline them briefly to start off with was the work of introduced quanta of energy that light can be absorbed or admitted only in discrete amounts a core idea of quantum theory and he used it to explain the photoelectric effect next was a paper on Brownian motion explaining the movement of small particles suspended in a stationary liquid his third paper on the electrodynamics of moving bodies introduced a new theory linking time and distance it was consistent with electromagnetism but omitted the force of gravity this became known as the special theory of relativity and assumed it see the speed of light is constant irrespective of where you are or how you move towards the end of 1905 he published does the inertia of a body depend upon its energy content this contains one of the most famous equations of all e equals mc-squared asserting the equivalence of mass and energy and we will come back to look at these in more detail shortly these papers establishes reputation but it was only in 1909 that he obtained his first academic post a professorship at the University of Zurich but a stay in Zurich was brief moving to Prague and back to Zurich and then for a long stay in Berlin before emigrating to America in 1933 and from then on he was based at the Institute for Advanced Study in Princeton he announced his general theory of relativity in 1915 and this year marks the hundredth anniversary of his presentation of the theory of general relativity this was done at a session of the Prussian Academy of Sciences in November 2015 and this work led to a scientific revolution that has forever changed our understanding of the universe and as you'll see on this slide professor Anderson will discuss the story of brilliant physical intuition which is led to deeper insights about the universe in which we live and his lecture is here at the Museum of London at 6:00 p.m. on November the 24th Einstein was awarded the 1921 Nobel Prize for his research on the theory of the photoelectric effect one of the earliest applications of quantum theory by the early 1920s his best scientific work was done although he was still very influential and was internationally renowned as a reaction to the Nazi threat and the potential of atomic power he was involved with a letter to Professor Roosevelt warning about the possibility of atomic weapons although Einstein played no part in their development scientifically he became increasingly dissatisfied with quantum theory and hard to interpret it his other area major area of scientific concern was trying to obtain a unified field theory that would bring together gravity and electromagnetism and his work on a unified field theory is thought to be ingenious but of little lasting value he died in April 1955 from an abdominal aortic aneurysm at the age of 76 and let me finish this brief biography of Einstein with a quote two quotes in fact from a speech he made to the German League of human rights in Berlin in 1932 all his political views he wrote I am an adherent of the ideal of democracy although I well know the weaknesses of the democratic form of government social equality an economic protection of the individual appeared to me always as the important community rooms of the steel and on science he wrote the most beautiful and deepest experience a man can have is the sense of the mysterious it is the underlying principle of religion as well as all serious endeavor and art and science he's never had this experience seems to me if not dead then at least blind and there's a web reference there where you can actually hear him speak give him the speech so let's not return to 1905 this year of Wonders to experience for ourselves the sense of the mysterious so a low Brownian motion is the second of his four 1905 papers I'll consider it first briefly as the other three of a common connection involving light and Brownian motion you probably know it's named after seventeen nineteenth century Scottish botanist 1827 while examining under a microscope grains of pollen suspended in water he observed the my new particles undergoing a rowdy jig Jaggi irregular motion and here's a simulation of Brownian motion here and the yellow blob or whatever color it happens to come out as the large blob there represents the particle and the rapidly moving many gray ones the molecules and the reason was thought by many people for the irregular motion was that it the large particle was being bombarded by the smaller ones the bombardment might be equal in all sides of the particular instance so that would shift the particle and once it was shifted to a particular point it was as likely then to be shifted further away us to be shifted back again it was in the earth to speak Einstein did in his paper was to quantify this and I'll just show you if I may how he did that this is the section from towards the end of the paper on the movement of small particles and what he finds there is that the distance traveled in the X Direction is given on average by the square root of two times D D is a constant called the coefficient of diffusion and T is the time so that the straight-line distance traveled in four seconds is going to be twice the street distance that has traveled in one second and the straight-line distance traveled in nine seconds is going to be three times on average the straight-line distance traveled in one second so the distance traveled goes up with the square of the time and he was not only able to derive this but at the very end of the paper just to show you and he was able to do a calculation for a particle of a certain size in water at 17 degrees centigrade where he knew what the coefficient of diffusion was he was able to say that the average distance moved by a particle of a particular size in water at 17 degrees centigrade was six times the width of the particle but then he turns that on its head at the very end at the bottom of the paper and this formula here we don't have a chance to go into details calculates a particular number from which you're able to derive an estimate for the size of an atom or the size of a molecule of water and this was at a time when many people many physicists weren't convinced of the existence of atoms and molecules and it was due to this paper of Einstein that they were converted and the fact it still remains one of his most cited papers so let me go on to the second law is the first one that was published and to set the scene for it let me say a little bit about why quantum theory was needed because towards the end of the nineteenth century there was an increasing belief that the basic goals of physics have been achieved Newton's laws of gravity and motion have been exceptionally successful Maxwell had unified electricity magnetism and light and the discovery of radio waves confirmed his predictions all that was essentially left was to account for the interaction between mother and radiation radiation such as light the interaction between matter atoms molecules and light radiation however the newly-discovered invented electric light bulb caused problems because of the given temperature it obviously shown with a characteristic mix of different wavelengths of light giving it a particular color but classical physics was unable to explain why this should be so and by early 1900 experimental results differed from theoretical predictions essentially what classical physics did was to predict the wrong amount of radiation at the different wavelengths or frequencies in particular too much at very high frequencies so classical physics was unable to explain the electric light and it was Max Planck who got effects he realized about 1900 that the difficulty could be avoided if radiation can only be admitted in packets or quanta and what he was saying was that the energy could only be a multiple of an elementary unit this elementary unit was a constant times the frequency H times nu well if that's the case then there wouldn't be enough energy to make the high frequency packets or quanta and the color of the radiation would be modified or we'd know I agree with experiment and Planck seemed to think that these packets of energy were the mechanism by which the atoms released energy a bit like the way if you have a string a violin string a new clock it will in emit a note of a multiple of a certain frequency the crucial thing was that it was Einstein he realized that the quanta were not a characteristic of the atoms the quanta were a characteristic of light itself so it wasn't that the atom could only release light and this particular way is that light comprised of something that only consisted of quanta and he used this insight to explain another phenomenon the photoelectric effect and he did this in a paper received March 18 and published June 9 and its title was on a heuristic point of view about the creation and conversion of light so let me describe briefly the photoelectric effect and then tell you how Einstein resolved it solar panels have shown us that sunlight falling on certain materials and there's a schematic of a diner at the bottom right can object electrons and cause a current to flow but solar panels were a byte but there were two puzzles increasing the frequency of the light increase the energy of the ejected electrons but not their number so increasing the frequency increase the energy but not the number and indeed if the frequency of the light drop too low new electrons were added the second puzzle was that increasing the intensity of the alight the may amount of light increased the number of ejected electrons but not their energy very strange behavior if you look at light from a wave point of view this should not happen Einstein's resolution was revolutionary he broke with a whole century more in the century of experimental evidence that suggested that light consisted of waves he said that one thought of light as consisting of energy quanta or photons with energy proportional to their frequency then we could explain the two puzzles and here we have here we've got a material which ejects electrons of light of a certain frequency will fall upon it potassium the electrons need two units of energy to escape the photons of red light don't have enough energy so no electrons are released with green light electrons are released with a certain amount of energy with blue light the same number of electrons are released but with a higher energy that result the first problem of thinking of light consisting of photons each of the photon having a particular energy the next question increasing the intensity of the light that's the increasing the number of photons coming down increases the number of electrons but not their energy and you can see for yourself that that's the case that if you have one coming down it ejects one electron if you have two coming down and ejects two electrons but those electrons are going to have the same energy so once you move to that quanta base the photon base the particle based idea of light it explains these people of course thought that Einsteins approach that like Planck's was just a mathematical device without physical reality but then a series of experiments showed that we had to think of light as both waves and particles and this weird particle duality lies at the core of the day and the new quantum mechanics that was developed in the 1920s and we slice at the heart of our understanding of the atomic and the subatomic world so another Island after finishing his papers on the photoelectric effect and Brownian motion Einsteins submitted what was arguably his most important paper of 1905 so the rest of what I want to say would be based around this so fasten your seat belts it was called the electrodynamics of moving bodies introduced the special theory of relativity it was 30 pages long some 30 pages long and I'm going to discuss what n Stein achieved by first introducing Galileo's principle of relativity and then how it was modified by Einstein so Galileo's principle relativity states that new mechanical experiment can distinguish between two uniformly moving frames of reference let me give you first of all Galileo's explanation of what that means these of course weren't Galileo's terms that's why they're put in modern terms but he gave a beautiful and compelling description of it in his dialogue concerning two chief world-systems the Ptolemaic on the Copernican sun-centered an earth-centered universe on the dialogue was Galileo's powerful advocacy of a sun-centered universe but to pursue his advocacy he had to consider the question of why we do not feel any effects from the rotation of the earth and its revolution from the Sun you're all thinking you're sitting still at the moment why do you think that the book is presented as a series of discussions and I want to show you the one that discusses with Michel Galileo's principle of relativity introduced by as one of the characters salviati's and I'm giving this a little bit of detail because it's just so beautiful it's such an example of hard to write science and to help it be understood all right Sal Biaggi says shut yourself up with some friend in the main cabin below decks of some large ship and half with either some flies butterflies and other small flying animals of a large bowl of water with some fish in it hang up a bottle that empties drop by drop into a wide vessel beneath it with the ship standing still observe carefully how the little animals fly with equal speed to all sides of the cabin the fish swim indifferently in all directions the drops fall into the vessel beneath and throwing something to your friend you need throw it no more strongly in one direction than another the distances being equal jumping with your feet together you pass equal spaces in every direction when you've observed all these things carefully although there's no doubt that when the ship is standing still everything must happen in this way how the ship proceed with any speed you like so long as the motion is uniform and not fluctuating this way or not enough emphasized that thing there now there will be water and butterflies and flies available for you to try this on the tube after the lecture but do make sure to introduce yourself to all the your fellow travelers and now we come to it you will discover not the least change in the effects deemed nor could you tell from any of them whether the ship was moving or standing still no mechanical experiment can distinguish a state of absolute rest he then goes on to reiterate in the rest of the quote which I've put up and slide because I wanted to have at the notes so you could read it and you'll see how how nice it is how everything happens exactly the same way when the ship is moving uniformly as where it was standing still no mechanical experiment is going to distinguish between two uniformly moving States or a state of absolute rest okay that's that's the rest of it so you could have to look forward to this beautiful example of scientific writing well what did Einstein do here we have Galileo's principle of relativity you've seen that before now this is true genius what does Einstein do he rubs out the word mechanical no experiment can distinguish between two uniformly moving frames of reference not only can do the chemical experiment distinguish between them but no optical experiment can distinguish between them and there's a particular consequence of that there's Einstein's principle of relativity that because he argued that Maxwell's equation describing electromagnetic radiation and lightest just a form of electromagnetic radiation apply as they stand to any uniformly moving frame of reference for example on the ship or on the shore or whatever so in particular from theoretical grinds the speed of light is related to the ratio between the electric and the strength of the electric field the strength of the magnetic field you and the ship we'll find it when it's moving I on shore will find the same values will both of the same value for the speed of light so in particular a consequence of Einstein's principle relativity is that the speed of light in a vacuum has the same value into uniformly moving frames of reference so first of all he said no experiment can distinguish a state above the rest and in particular the speed of light is the same any two and this is what I mean this is why I introduced the quotes I had earlier on these are the foundations on which is going to build it and it goes very quickly so I just try set the scene first of all and I say here it's stunning it's not mathematically difficult but it's totally counterintuitive for example we are used to having and subtracting speeds and what seems an obvious way this doesn't work with light if you and I are standing and I shine a torch eacher then you will measure the speed of light a certain value let's call it C it's usually called see if I start walking towards you this is why it's still shining the torch you'll measure the speed of the light reaching you I see this in value speed of light is independent of the motion of its source if I stop and you walk towards me then you will still measure the speed of light to see the speed of light is independent of the motion of ass observer that's very different from the results you would obtain if I were instead of shining a torch eg were throwing snowballs at you given they were coming into winter so the fact that the speed of light is independent of the motion of the source aunt of the observer means that our usual ways of adding and subtracting speeds is wrong but if our conception of speed has something wrong with it then because speed is just distance divided by time distance divided by time it implies there's something wrong with our concepts of distance or time or both let me show you one consequence of the constancy of the speed of light I'm on the spacecraft up above moving uniformly along above the earth you're on earth we both have identical clocks I'm going to carry out a simple experiment it's the fire a pulse of light from the floor to a target on the ceiling the floor the ceiling the pulse travels directly upwards at right angles to the direction of motion of the spacecraft spacecrafts going from right to left I think it is we'll see it's going at right angles to that how long is it going to tick it has to travel a distance of 4 meters the speed of light is C so the time it takes is distance over the speed 4 over C so that's how long the speed of light sorry that's how long it's going to take for me on the spacecraft between the event of the pulse leaving the floor and arriving at the target know you're observing this from Earth not you don't honor the travel well or do i from your perspective as the craft passes overhead during the time taken for the pulse to move from the floor to the target the spacecraft has moved forward and you're going to see the path of the pulse a sloped not vertical and therefore longer than it is from my viewpoint on the spacecraft let's suppose that the spacecraft moves forward a distance of 3 meters while the pulse of light travels from the floor to the target on the ceiling then good old Pythagoras or the Pythagorean theorem tells us that you see you being on earth the path of the light pulse is going to be the square root of 3 squared plus 4 squared is going to be 5 all right this is the sentence you need to wake up for how long do you say it takes the pulse to travel from the floor to the target it's just the distance Phi divided by the speed but the speed of light for you is safe the speed of light is the same and uniformly moving friends so you measure the time from the pulse leaving the source to arriving the target as 5 over C and I measure it as 4 over C this is the famous time dilation effect I have my time in the spacecraft and you of your time on earth it's very quick it's very easy it's very kind to intuitive and it's got to do the constancy of the speed of light lights not like snowballs the snowball is not picking up any extra speed due to the motion of the latest not like a snowball which would pick up extra speed due to the motion of the spacecraft now I've used the numbers 3 4 & 5 just to make it so bare and shocking but unless I'll forget in the way but you can do it algebraically as well if we have the speed of the craft is very relative to the earth then all I've done is to put in the appropriate distances here you know it's the same triangle that I had with the numbers 3 4 and 5 but instead with the velocity V then what you find is that the time for the pulse to get from the floor to the ceiling viewed from the spacecraft is this factor square root of 1 minus V squared over C squared time for the pulse to get from the floor to the ceiling viewed from the earth so between two events my clock will say it takes so long which is less time than what your clock says is it's going to take okay and the factor between the two is this factor square root one minus V squared over C squared that's the factor relating the two of them and C is a very big number on the next slide I show you what it is it's nearly 300,000 kilometers per second that's moving and here's a graph of 1 minus V squared over C squared square root of it and you can see that for velocity as a small percentage of the speed of light that the factor is very close to 1 so it's going to have very little noticeable behavior sorry observable behavior and at low speeds although it does have an effect at all velocities at all speeds and the red line is just the example that I took were it moved forward 3 meters so it was moving at 60 percent of the speed of light now the time dilation has been experimentally confirmed for example using subatomic particles not going into those those are kind of things that be able to follow up on if you wish would see the references I'm going to give you at the end I just want to help help you see the forest for the trees right this factor square root of 1 minus V squared over C squared also occurs and another effect predicted by special relativity which is at you an earth a me and the spacecraft must measure differences differently distances differently suppose my spacecraft is traveling from earth to the moon we both agree on the relative speed between us we both measure that as V but because of time dilation we will have different measurements of the time it takes to get to the moon so we must have different measurements of its distance away harder our measurements of distance different it must be in the same ratio as our times different the square root of 1 minus V squared over C squared so this is another phenomena predicted by special relativity it's known as length contraction the spacecraft measures the distance between the Earth and the moon as the square root of 1 minus V squared over C squared times the distance that the person on earth measures that you measured so for me my clock is running slow but that doesn't matter I will still arrive at the moon at the appropriate time because I measure myself as having less because I have less distance to travel the factor is the same in both it so what's happening is that we're each measuring the time between two events differently I'm measuring the distances between the two events differently so is there anything we can agree on well there is Anna let me introduce it by way of an analogy if I hold a pencil up or a pan up like so perhaps yeah like so you're all going to see something different because you're all looking at it from different positions in the room some of you are looking at at nearly and on down bottom left here so you're seeing it has been very short some of the you are looking at it broadside on so you're seeing it is nearly having its its four lengths and we know the reason for this this is because each of you seeing a projection of the pencil into two dimensions perpendicular to your line of sight from your eyes to the pencil if you're looking at it you if you're looking at it and dawn you're going to see it is quite short and if you're looking at this broadside you're going to see it's closer to your your normal length and the reason we see a different you're seeing different and lengths when you look at it is because the pencil has got an extension into a third dimension along the line of sight and when we take a current of this we will all arrive at the same length for the pencil it's length in three dimensions so the correct length and this is what's observing this is what you observe which is perpendicular to your line of sight so let me use this analogy to help with thinking about our different perceptions of time and space in special relativity and this way of thinking about is did you do to one of Einstein's teachers Hermann Minkowski and he announced that the year before he died and 90 announced at 1908 the year before he died and I think it's the most productive and least confusing way to think of relativity when cough ski said henceforth space by itself and time by itself are doomed to fear away into mere shadows and only a kind of union of the two will preserve an independent reality so in the cough skis view we shouldn't think of space and time as separate from each other we should think of them as a kind of Union that knowing on a space and time so space and time are no longer separate as Newton thought of them but are intermixed now we're looking at this pencil the length you saw depended upon your position it depended upon your seat and the rib people in different seats are seeing this pencil as having different lens because you're all saying its projection onto your two-dimensional plane and perpendicular to your line of sight different people in the room in different positions are seeing different lens but you all know that you can recover the true length because you all know that the pencil has got a projection into the third dimension in space-time changing your view point corresponds to a change in speed not just position observers and relative motion of different viewpoints and so get different results our projections when they measure distances are times that's why they get they get different projections different distances different times but there is something that's going to be the same for for anybody moving in relative motion to each other there's a true way of measuring sorry I'm an invariant way of measuring the distance between two events and space-time so what is it let me see I've introduced it here by going up the dimensions from two three four so let's do it in two dimensions the distance between points and B can be written in terms of the projections x and y along two axes at right angles and then the square of the distance is just x squared plus y squared in three dimensions we introduce another axis at right angles to the first two if the projection along this third axis is Zed then L squared is x squared plus y squared plus Z squared knowing for space-time we want to introduce another dimension at the time dimension a point in space-time will consist of three space numbers and one time number and if you want this to be the same for all and of course I had to fly over how you get this there done enough time to to do that but again little reference I'll give you you'll be able to read it nine Stein's own words then the separation is between two events and space-time incorporates a fourth term coming from the time and for it to be the same for all observers the space and time terms have to appear with different signs so the way to measure the difference between two events and space-time is to calculate the quantity S which is the square root of C squared T squared minus x squared minus y squared minus say it squared so that if I'm open the spacecraft and you were an earth we will each of our own time we'll each of our own measure of distance but if we've got two events and we each calculate this quantity for the two events will both end up with the same answer in a very productive way undoing any further thinking about this and you need some help in thinking about it to get some sense is space-time diagrams and here are the space-time diagram which is only in two dimensions so it's only got one spatial dimension it's like a spatial dimension going along the floor here from left to right and I'm at the origin offered here and I fire off a simultaneously a pulse of light to the right and a pulse of light to the left and in the space-time diagram that's the one going off to the right that's the one going off to the left and that's the here and now when I do it and then these are the events comprising of my future and that's me just wandering up and down this line on the floor and if you can do that and when you hard to picture it of course but in three dimensions as well and you've got the distance for each point the origin space-time is given by this in the two-dimensional and as I've tried to stress relatively moving uniformly moving relative observers will come up with the same number between two events so let's now give you something to do with soot but I think it's quite amazing how you can just go from this constancy of the speed of light force yourself to remember it and then you come up so quickly with the fact that you are you and I you and Aerith me and the spacecraft that's the way around it was will come up with different measurements of time so let me finish with this last amazing world-changing result and this one is certainly not just a theoretical interest it was his last paper in 1905 and it's one where he establishes the equivalence of energy and mass and I should just say that although Einstein found the space-time approach initially wasn't very enthusiastic about it it's what he used as the foundation of the bedrock in order to develop his theory of general relativity when he tried to include his theory we extended this theory to include gravity so the last paper is this one here does the inertia of a body depend upon its energy content no it's only three pages long this is it it's not even three pages I'm innocent translation but when you look at in the original it's quite remarkable and here we have a top and the will a out of this translation anyway there and what that is saying is that if a body gives off the energy ale in the form of radiation its mass diminishes by L over C squared if it gives off the energy L in the form of radiation its mass diminishes by L over C squared the factor connecting mass and energy is C squared and of course the result is usually now written as e equals MC squared now when you read the rest of it the approach is very similar to what I was doing with the spacecraft and a pulse of light what did i do there I had something that happened and I observed it from two frames of reference and I used the fact that the speed of light is constant those were the steps of my argument if you think back to them what does Einstein do he has a body which emits two pulses of light that's what the left-hand side is telling you about in opposite directions the middle page is viewing this process from one frame of reference which is stationary with respect to the body until from another frame of reference which is moving at speed V reference various speed the relative to the body and taking the speed of light to be the same in both frames ending up at the top of page three that e equals mc-squared so I've given you the kind of approach in the thing about the spacecraft that he takes in this thing so just this roller amuses me anyway you're thinking wrong lecture what's Newton doing here I've heard of reusing slides but this is a bit ridiculous it's just that I find it amusing because Einstein in the paper back here back we go down here how's our factor one squirt one over the square root of one minus V squared over C squared and he approximates that and the approximate start using something called the general binomial theorem and the general binomial theorem was discovered by Newton and his annus mirabilis of 1665 1666 when he returned to wills Thorpe Manor and during the plague years one of the section of plague years at Cambridge so I just thought it would be quite nice to connect the two of them in this way so I've done it there you are so the end of the Einstein article so here we have here so this is just the last little bit on the here I love the way those calculations the way did with the Brownian motion paper so he finishes here saying the mass of a body is the it's a measure of its energy content if the energy changes by L the mass changes in the same census by L over 9 multiplied by 10 to the power of 20 he's taking the speed of light as 3 times 10 to the 10 because he's measuring it in centimeters per second and he says it's not impossible sorry then that's what the energy is going to be it's not a possible that was bodies whose energy content is variable to a high degree ug with radium salts that the theory may be successfully put to the test and if the theory corresponds to the facts radiation involves inertia conveys inertia between the emitting and absorbing bodies so this equivalence of energy and mass is the energy that feels the Sun and nuclear weapons and Einstein's calculation of the energy equivalent of a mass of 1 gram that's what he's calculating there is approximately enough energy to power the daily domestic use of a city of a million people that is the effect of multiplying by C squared well this has been a quick tour through relativity and another time to pick up many an introduced many important features such as Lorentz transformation and so on but try to pick up the crucial ones that I would hope would help you who want to discover more about it and to show something about Einsteins amazing output in 1905 and he didn't only produce these four papers he produced about 20 other reviews of articles during the year and I think he had a one-year-old son at the same time so let me give you a couple of references that I find particularly useful the first one on the left is my copy of a book written by Einstein I got it when I was at school and I I read it once a year every year and I'm hoping to finish it this year and he says in his preface sir on the other hand I've purposely treated the empirical physical foundations of the theory and a stet motherly fashion so that readers unfamiliar with physics may not feel like the wanderer who was unable to see the forest for trees may the book bring someone a few happy hours of suggestive thought and I said it's very good and and I looked up one of those online stores which I shall not advertise on earth is available for ninety-nine pets imagine getting something like that for 99 pounds and then the other one that I find very helpful is Russell Stan ARDS contribution to that excellent oxford university press very short introductions and that's very good so even if you're and I hope not going away not imbued with a sense that you can approach special relativity at least you've got your Christmas present list and so my next lecture is November 17th on Hamilton boo and there are algebras and I will show her the work of these two mathematicians freed algebra from the constraints of arithmetic so thank you and don't forget your free butterflies on the way item you

Channel: Gresham College

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Keywords: gresham, gresham lecture, gresham college, gresham talk, gresham college lecture, gresham college talk, gresham professor, gresham geometry, professor of geometry, profoessor of mathematics, Mathematics, maths, math, mathematic, set theory, Geometry, pure maths, infinities, maths lecture, higher maths, Further Maths, Physics, Einstein, relativity, photoelectric, Brownian motion, albert einstein

Id: a9uQY2V_99g

Length: 49min 59sec (2999 seconds)

Published: Wed Oct 28 2015