[Music] Stanford University all right so what is particle physics about particle physics is about particles it's about the question and this is a very ancient question at least I suspect about 2500 years old is nature discreet discreet meaning to say not that it's polite but that uh that it um that matter and substances and energy they didn't think about energy but they thought about matter that matter comes in discrete units in indivisible uh units which of course the Greeks called Adam I'm told that the word Adam means indivisible despite the fact that of course we break up atoms all the time nevertheless that was the origin of the word indivisible that um all things in the universe are made up out of something discrete let's call them particles particles is a good name for something discrete something indivisible that idea is as I said extremely ancient the opposite idea is also ancient again I don't know precisely when it was first formulated I happen to remember a little more about the history the atomic idea that was it doesn't matter who it is incidentally do not trust my history not because I don't know the history but I sometimes tell the history in which um in which I organize things logically rather than rather than temporarily so don't trust uh the time sequence that I tell you it often represents what I wish the time sequence was rather than what it actually was but it's it's good for being to present the lot logic of what happened to presented in a logically compelling way rather than a uh a strict historical way in any case uh there were these characters who were the atomists and the the opposite of them the people who thought that matter material and so forth was continuously distributed continuously distributed means simply not made up out of discret elements but I don't know what the right word is uniform continuous is the right way right word a shmear as my grandmother would have said a shmear smeared out over a space in some uniform continuous kind of way and we might call that the field theory of matter Fields what are Fields fields are functions in space for example they could be the density of material uh in in a given region of space they could be the electric and magnetic fields those are good examples electric and magnetic fields that determine how charged particles move but the fields themselves the electric and magnetic fields are things that we conceive of as being uniformly distributed in space not uh not in the form of particles and so perhaps matter liquids solids and so forth are also in some sense continuous just like the electromagnetic field that was the opposite idea uh the particle idea the discrete idea had words like molecules atoms and so forth collisions um and particles the Continuum idea Continuum is the right word the Continuum idea had words like Fields attached to it uh continuous fields of properties of of various kinds which turned out to be right in some sense neither and both in some sense neither and both turned out to be right the subtleties of quantum mechanics got in the way of either of them being completely right but it also got in the way of either of them being completely wrong quantum mechanics is a subtle and difficult subject uh as are many of the preliminaries to particle physics I think I have taught all of them by now several times and they do exist on the internet the internet uh lectures that I've given they're out there and um I advise you as I said I will try to keep itself contained but I am going to assume to some extent the knowledge that I have taught previously in these classes it can be picked up off the internet very easily uh I I don't know how to do it I couldn't do it for the life of me I can never access my own lectures but everybody else can do it and uh well the real reason is I don't like looking at myself so I never I never do open my own lectures but they're out there and they're fairly complete there are at least two courses out there on quantum mechanics I think one on classical uh mechanics at least one on special theory of relativity and uh and electromagnet ISM so since I put that effort in I'm now going to try to uh draw on it not today but uh in the future and use many of the things that I have lectured about okay uh as I said the particle physics question is whether nature is discret or not let's just do a little bit of History which I will probably get wrong but uh that's at least um chronologically to my knowledge the first real evidence again it's to my knowledge the first real evidence that matter was discreete came of course from chemistry it didn't come from physics it came from chemistry uh the division between chemistry and physics is a highly artificial one chemistry is simply just the basically the physics of atoms and molecules but uh it came from the chemist uh well John John Dalton John I think John Dalton who realized that the masses of chemicals the mass of a given number of molecules a given number of molecules now how he knew that he was had to deal with a given number of molecules when he might be talking on the one hand of hydrogen the other hand of a carbon dioxide or something how he knew it was a given number of molecules is itself a story of a gad's name comes into it and so forth the word mole not the creature that lives under the ground but the the uh uh the mole is avagadro's number of molecules how they knew how many molecules they didn't know how many molecules but how they knew how to compare different substances and say both of them had the same number of molecules that itself is an interesting story but it's not the story I want to tell the story I want to tell had to do with the mass of a mole of material a mass of a given number avagadro's number of molecules that came in discrete multiples of the mass of a mole of hydrogen now not exactly but close enough to a pretty good Precision uh the mass of a mole of Goble is a integer multiple not three not three halves not Pi not the not some other silly number but some integer times the the mass of the same number of molecules of hydrogen that sort of suggested to Dalton that there were building blocks that uh carbon what is it carbon 8 carbon 12 carbon 12 had 12 units of whatever uh hydrogen one had hydrogen was one unit of stuff whatever that stuff was carbon 12 and whatever whatever the other numbers were so it seemed like things were being built up out of basic units which basically had the same mass as a hydrogen atom almost as though everything was made up out of units of hydrogen uh Dalton I think proposed something like that that there were basic units and those basic units had the mass roughly of a hydrogen atom so that was the first bit of evidence and of course this was essentially right today we understand let me just tell you why that's true from today's perspective not to make a mystery out of it uh everything is made out of atoms and atoms are made out of protons neutrons and electrons electrons are very very light compared to protons and neutrons and in counting up the mass of an atom the electrons are not very significant an electron has about a mass of 1 12,000th of no one yeah 1 1200 1 1200th of the mass of a proton or a neutron so electrons don't come into the equation they do come into the equation but only a very very small term forget about them protons and neutrons constitute most of the mass almost all of the mass of ordinary material on the other hand protons and neutrons surprisingly there's no well there is a good reason for it but uh but at the time there was certainly no known reason in fact protons and neutrons weren't known but protons and neutrons have about the same mass as each other as I said about 2,000 times the mass of an electron and so the mass of a molecule is basically the mass of protons plus neutrons they have about the same mass and therefore the mass of a molecule is an integer multiple of the mass of a proton and neutron on the other hand hydrogen is the nucleus of hydrogen is just one proton and so it did turn out that Dalton was right all materials have a mass which is approximately there's an approximation in there protons and neutrons don't have quite the same mass slightly different less than a percent incidentally a tenth of a percent or even less uh whereas electrons are so light that they don't come into it very much and so Dalton was right and there was the first to my knowledge the first real evidence that matter came in discrete units okay now molecules weren't atoms of course took a little while longer to find out that molecules were made up out of atoms and the atoms weren't just protons and neutrons or hydrogen that atoms themselves the things we now call atoms that there were about a hundred of them 100 different kinds this was of course the great Triumph of chemistry of the 19th century and early 20th century to identify all of the elements that go into the periodic table up there incidentally the periodic table is not very periodic uh you know if you really look at it it's it's a bit of a fake the periodic table it's not very periodic uh but nevertheless identifying all those separate atoms up there the elements the elements in some things which are composed of all the same kind you know that story composed of atoms and identifying the atoms and at the end of the identification of atoms roughly about a hundred of them less than 100 uh occurring in nature uh 92 of them to be precise well more than that if you include Isotopes but of water a 100 different kinds of atoms and everything made up out of atoms so atoms at the end of the 19th century the things we call atoms or elements were the building blocks the elementary particles of nature now of course it took another 5 years after the turn of the century for Einstein to do something that nailed really really nailed the molecular theory of matter it wasn't until 1905 that Einstein explained in detail how you could prove that matter was really made out of particles but uh long before that chemists physicists understood for the most part that um that everything was made out of these 92 elements so they were the elementary particles Now sort of all hell broke loose in the beginning of the 20th century very very end of the 19th century when some discoveries were made the electron was discovered about three years I think before the turn of the century I don't I don't know exactly when it was the electron was discovered and a number of other things were discovered but in particular radioactivity was discovered radioactivity was the first real uh signal of the thing which was later to become Nuclear Physics uh and nuclear physics and particle physics and had all the things that needed to be explained sort of there in a in a sort of tiny tiny little version so let me just remind you about radioactivity just for fun uh who was it who discovered radioactivity I don't know you remember I don't think it was Marie cury who discovered radioactivity I don't think so H was it Beckel I think it was Beckel yeah was Mar cury she what she did was you know lots and lots of experiments to pin it down with great but it was it was Beckel and he had a chunk of lead don't ask me why he did this I do not know he had a chunk of lead and a little hole in the chunk of lead like that and some material down here radioactive I guess the first thing that happened was he had some radioactive material presumably radium or something like it and his labor atory and he had a photographic plate and accidentally the photographic plate happened to be near the uh uh the material not here over here material photographic plate and the photographic plate got ruined but ruined by the presence of the radioactive material the radioactive material um just ruined you know was like light shining on it and ruined the photographic plate anybody else or not anybody else probably me would have just thrown away the the the plate and said ah this is ruined let's find another plate and start the experiment over again but Beckel realized he had discovered something he had discovered that radioactive materials do something to the photographic plate as if they had been illuminated by some radiation so he decided to study that radiation a little bit better and he put the source of it deep in a block of lead how he knew to use lead I do not know but lead was a good substance because it's very dense and he put it into a hole drilled into the lead and then put his photographic plate out here and uh wanted to see whether it would illuminate a single spot over here you know everything was columnated by this hole he wanted to see whether it would uh uh create a sharp little spot as if something were coming up out of this hole and indeed it did so he got the idea that a beam of some sort was being ejected or something was being ejected by this radioactive material and being columnated along a beam that was the first particle beam that was the first beam of particles all right what was it he had no idea what it was but then I guess a second uh forious accident I think it was an accident again I'm making up the history as I go along but it's it's close to the truth uh he happened to have a magnet in the laboratory and for some reason the magnet was in a position here where a magnetic field was created near where these particles were being ejected and what happened when he put the magnetic field when he put the magnet near this is the beam split into three separate beams three separate beams one went straight ahead just as if the magnetic field was not there one of them got deviated to the left and one of them got deviated to the right left right right left whatever one deviated more than the other in fact they were not symmetric and Beckel or somebody whoever was around knew enough to realize that beams of particles trajectories of particles get bent by magnetic forces if you have a magnet and you have a Charged particle the charged particle goes through the magnetic field and either bends to the right or to the left depending on the sign of the magnetic field and the charge of the particle so if the particle was a positively charged particle it would bend one way in the magnetic field if it was a negatively charged particle it would bend the other way in the magnetic field and what Beckel had found is that there were three kinds of radiation one behaving as if it was composed of electrically neutral particles which one was electrically neutral the one that wasn't deviated at all course he didn't know they were particles all he knew is that some columnated effect happened that illuminated the uh the uh the detector the screen the the photographic plate one of them got deviated to the right as if it were a negatively charged particle he called that component of the radiation he called that component beta the component that went straight ahead he called gamma and the component that deviated in the other direction as if it were positively charged he called Alpha these became the three distinct kinds of radioactive um effects three distinct kinds of radioactivity beta radioactivity gamma radio gamma and Alpha just again I'm not interested in making suspense here let me just tell you what they were you probably know what they were many most of you well many of you know what they were beta was electrons negatively charged particles uh which were just the electrons that already been been previously discovered from cathode Ray tubes and that kind of thing these were electrons coming out the alpha particles We Now understand and at that time there was no precedent for it that they are helium nuclei two protons and two neutrons stuck together atomic number four uh Dalton would have had he had he had access to helium which he didn't he would have said helium was number four on his uh on his um integer collection of materials and Gamma are photons okay electrically neutral no electricity at all and uh these three kinds of now um I think he did again I I I don't remember the history but he might have had a sufficiently dilute source that these particles arve d one at a time at their destination in that case he would not have seen a bright spot over here he would have seen BLiP BLiP BLiP BLiP illumination occurring or spots occurring discret little spots occurring for the electrons and he might have said oh those are particles particles arriving one at a time Illuminating the screen discreetly he would have done exactly the same thing for the alpha particles he would have found that the alpha particles arrived one at a time in other words he could have used he might have used I probably did used the screen here as a counter analogous to a guer counter or something whether he did or not I don't know uh but um but it's something you can imagine that he detected the particles coming one at a time that would certainly be feas visible with a Geer counter and so evidence that whatever this radiation is it's coming in discret little bundles that we could call particles what about Gamma same thing for gamma gamma's coming one at a time but at that time Beckel had no idea neither did anybody else uh what gamma was it was uncharged that was all that was known and it illuminated uh the screen just as the others did okay that was as I said in some sense the first particle physics experiment we'll come to some later particle physics experiment soon enough all let's next talk about electromagnetic radiation ordinary electromagnetic radiation oh well I said I wasn't going to make suspense gamma is photons gamma is light gamma well it's very high energy light but gamma is in some way connected to ordinary light so let's come to light gamma was the big mystery because there were no neutral particles known at that time that uh could account for the gamma radiation and so gamma was a mystery and that mystery persisted until fairly uh uh fairly late in the very early 20th century let's put it that way fairly late in the very early 20th century uh was of course plunk and Einstein really Einstein who were the first to understand understand that light comes in quanta that light comes in photons but let's go back light was sort of the strong strong case for something which was not made of particles light was something which was clearly made of fields it was made of the electromagnetic field okay the electromagnetic field electric fields and magnetic fields forming waves when you shake a charge waves get given off the wave fields are continuous wave fields at least according to classical electrodynamics and they give off waves that propagate through space completely continuously and uh Newton of course had thought that light was uh was particles but Newton by that time had been completely uh relegated to the dust bin at least as far as theory of light went there were many experiments some of them done by Newton himself that strongly said light is waves not not particles so let's just talk about light a little bit electromagnetic radiation if you take electromagnetic radiation it comes in waves so if there's a source of electromagnetic radiation here an antenna some form of antenna emitting could be radio waves it could be microwaves it could be uh infrared it could be light it could be ultraviolet an atom is a perfectly good uh antenna incidentally doesn't have to be a big macroscopic tower an atom with a charge going around in a circle is an antenna antennas emit waves and those electromagnetic waves when they also fall on a photographic plate or other device which is sensitive to light or sensitive to radiation will illuminate that uh will illuminate that and turn it white or black turn it black I guess uh and that's in the character of light now how do we know that these things are waves how can we tell that they're also not bullets shot out of uh shot out of uh the source here so one thing you might do is do very something very similar to what was done over here put an obstruction little hole and see whether the light is columnated exactly as if it were bullets being shot out of the gun here it was bullets you would illuminate a little spot over here and of course what happens is that you don't illuminate such a small spot you illuminate something which is fuzzier than that you eliminate a funny fuzzy region but that in itself did not prove that light was waves not at all you could say well just maybe when these particles go through this opening here maybe they have little forces exerted on them by the edges of the hole here or whatever which deflect them some of them get deflected and so maybe you get a more smear picture a more smearing image than you might have hoped for so it was not just that the beams got deflected the light beams got deflected that in itself was not enough to argue for uh for a particle structure to light or sorry a wave structure to light I'm sorry but you do something else which is much more sensitive to the wave character of light you here's here's the screen over here again you open up two little holes two little holes next to each other if light was simply particles what you would expect to find here is basically two smears of the same kind just superimposed on top of each other maybe a little extra dense in the center where they overlap but just two smears one the image of this hole one the image of that hole with nothing unusual okay this of course is not not what happens what happens is each hole emits waves you could do the same trick with water waves in fact it's not hard to do the same trick with water waves and the water waves interfere if this is the high point of a wave coming out of here and this is the low point of a wave places where the high points combine from the two holes re enforce each other places where a high point from one hole meets a low point from the other hole cancel each other and so the effect is to see when it hits the screen here to see bands bands of positive reinforcement where the high points add missing places with no light where the high points meet low points right that's an interference pattern interference pattern is a real signal of wav like motion of wave Behavior waves you can do this as I said with water you just to put your finger into water and Wiggle two fingers and the two waves from the two will will spread out some places they'll reinforce some places they'll cancel and so rather peculiarly but not nothing terribly unusual um places which were would have been illuminated by either of the two holes by themselves there's destructive interference they get canceled and places you get constructive interference and they add and you get extra intensity that is the kind of thing this interference property was the kind of thing that really nailed the wave theory of light okay so light was a wave in fact uh this did not occur after Newton it really occurred before Newton hyen hin was a uh 17th 17th century hin must have been 17th century but previous to newon 1808 who what Thomas Young yeah the physicist demonstrated the interference yeah yeah but but Hans already had the basic ideas of wave propagation and that's from the 1600s sometime so this debate went back and Newton had done many experiments himself which should have been interpreted as uh as interfer as interference wave interference but he didn't in any case after these experiments Young's experiment others it was definitely confirmed that light is made of waves okay what kind of waves Well that took Maxwell Maxwell realized that they were waves of electric and magnetic field you know what an electric and magnetic field is an electric field well I look it up if you don't know electric and magnetic fields and light is a wavy motion of electric and magnetic fields first of all light is a wave and here's a wave moving down the axis what is that wave a wave in well it's a wave of electric field here the electric field is pointing down here the way electric field is pointing up here the electric field is pointing down let's just draw a line through there alternating electric field up down up down and the whole thing moves off with the speed of light the whole thing moves off with a speed of light electric field incidentally there's also a magnetic field attached to the thing it's a complicated uh object it has magnetic field also the magnetic field is perpendicular to the the electric field and soort of sticks out this way and that's what a light wave would look like if you could see if you could sample its electric and magnetic field as it went past you of course as it passes you it will constantly alternate very rapidly if it's uh if it's a ordinary light wave much too rapidly for you'd be able to see but if it were an extremely long radio wave very very long radio wave you might be able to see the field oscillating in front of you and uh this is this is as I said what it would look like it's a wave being a wave it will exhibit interference patterns and uh Maxwell had absolutely nailed the wave and the electromagnetic theory of light so let's talk about waves a little bit before we uh before we talk about about particles let's talk a little more about waves and the properties of waves the first property of a wave that I want to come to is the wavelength wavelength is simply the distance along the wave before you return through before you return one full cycle to the next wave all right so you start here and you go and you come back back to the same exact kind of thing as over here that's one cycle or one full wavelength and the wavelength for symbol for wavelength is Lambda Greek Lambda okay Lambda for length that's the wavelength and it's measured in uh units of distance it's measured in meters or it's measured in centimeters whatever your choice of units are uh okay so Lambda equals wav length wavelength let's just call it wavelength another property is if you were to stand still and just watch the wave go past you you go head we go up and down and up and down and up and down it would have some frequency how many cycles per second this is not the length of the wave in space it's kind of the number of cycles per second or perhaps even something simpler the time that it takes to go through one cycle as it passes you that could be called the period of the wave period it's a time it's measured in seconds so a very and a light wave has a very very short period up and down and up and down extremely fast 10 Theus 15th seconds or something whatever the longer the wavelength the slower the period the shorter the wavelength the uh the faster the the shorter the shorter the wavelength the shorter the period okay what's the connection between wavelength and period okay yeah right so think about the wave moving past you one wavelength how long how far does it moved it's moved distance Lambda how long has it taken it's taken the period the distance that it moves divided by the time that it takes to move that distance is the velocity of the wave for light that would be the speed of light if it's not a light wave it might be moving with different speed if it's a water wave it would be much smaller speed if it's a sound wave if it's a smaller speed but for a light wave the wavelength divided by the period is always equal to the speed of light whatever the wavelength is the period is given in terms of the wavelength or the wavelength is given in terms of the period so that's a fundamental relation it's usually expressed a different way the inverse of the period one over the period is called the frequency it's the number of waves it's the number of oscillations per second the number of oscillations per unit time is called the frequency and that's equal to 1 over the period faster the period the shorter the frequency and so you can also write this as the wavelength times the frequency is equal to the speed of light so if I give you the wavelength you can tell me the frequency if I give you the frequency you can tell me the wavelength by solving this equation and that's the fundamental connection between wavelength and frequency now since one of the things that I really do want to teach you a little bit is the terminology that physicists use for things and they tend not to use the terminology of cycles per second for frequency they use something else it's radians per second what does that mean imagine a thing going around in a circle it's going around in a circle with a frequency F that means F times around the circle per second physicists tend to use physicists and mathematicians tend to use not the number of times you go around in a second but the number of radians radian is about 57° it's an angle about that big how many radians per second and the relationship between the frequency in terms of cycles per second and the frequency in terms of radians per second is very simple in terms of radians per second we call it Omega ome and they they're closely connected to each other Omega is just 2 pi times the frequency why 2 pi because there are 2 pi radians in a circle so frequency can be measured in either either way physicists tend to use Omega except when they're writing Elementary physics books for undergraduate premid majors in which case they use f okay uh we're all physicists we're all grownup we're all uh you know so we can use Omega like uh the world of physics does Omega is the frequency of the light measured not in cycles per second but in radians per second you say where is the angle for a light wave going don't worry about where the angle is just divide frequency or just multiply frequency by 2 pi and that defines Omega right they're proportional to each other right so we can also write this then as uh let's write it this way frequency I'm going to write it frequency is equal to C divided by Lambda and now I'm going to substitute for frequency Omega / by 2 pi and what do we get we get Omega is equal to 2 pi C over Lambda fundamental equation of wave motion that the frequency measured in radians and the wavelength are related by 2 pi times the speed of light this of course is true for any wave if you plug in the right velocity okay we will use that equation from time to time so get it down now as I said light comes in different wavelengths and those different wavelengths characterize the different kinds of radiation radio waves are very long wavelengths meters are certainly more than uh certainly more than uh uh microscopic lengths radio waves can be anything from what a few cenm to uh 10 cm something I don't remember exactly where the radio spectrum begins hm no it can go up to anything arbitrarily long wavelengths are called still radio waves even though no radio could work on the basis of waves that had a wavelength of a billion light years but still they're still call radio waves um and where where's the smaller what's the smallest radio wave I think about 10 cm I all right small and it's a highly arbitrary division of course completely arbitrary what's smaller than radio waves smaller wavelength microwaves microwaves go from a few centimeters down to what the micro micrometer or something like that Micron uh smaller wavelength than microwaves infrared infrared waves and then from infrared waves you have light waves visible light visible light is a rather narrow range of frequencies or wavelengths and then comes uh ultraviolet shorter wavelengths X-rays and gamma rays gamma rays are just exactly these objects here very very short wavelength extremely short wavelength uh radiation and that's what the Beckel had discovered coming out of there the only trouble is that Beckel discovered discret bumps you know discret blips one at a time and not nice continuous waves okay that then brings us to the puzzle of quantum mechanics now we're not going to go into it in any great depth certainly not tonight but let's just recount the history a little bit Einstein and plank realized for a variety of reasons mostly thermodynamic properties of light that Einstein that light had to be thought of as being made up out of discret indivisible elements uh he might have it might have been an experimental Discovery in fact in some sense beckel's Discovery was an experimental Discovery it's just he didn't realize the thing he was seeing was electromagnetic radiation so I won't go through the actual history but let's make up a imaginary history of how the discreetness of light might have been discovered it could have been discovered this way you again shine your light on a you shine your light on a screen and you illuminate the screen and of course what you see is a nice continuous blob of light it could either be an interference pattern or it could just be a single hole in which case it would just be a blob on the screen okay but now you do the experiment differently here's your source of light you put an obstruction in the way the obstruction is a is a filter the obstruction is a not a filter but a um a semi-transparent uh semi-opaque thing which blocks out a certain percentage of the light what happens over here well the blob gets dimmer okay it's not as intense you make it thicker it's even less intense you see less light AR ding per unit of time and you make it even a little bit thicker and at some point all of a sudden the character of what's here changes and instead of seeing the blob you see the screet events little blips now if you wait a long time these little blips build up and they build up to something which has exactly the same pattern as the blob had so the blob in this case then is some sort of effect that has to do with lots of little blips so many little blips that you can't recognize them as being individual that's the blob but if you attenuate the light and cut it down so that the intensity coming through here is really really small what you see is blips this experiment can actually be done it was not done in those early days but you can imagine and this is what Einstein had suggested really does happen in his photoelectric paper that light comes through as absolutely discret things the motivation for it was was uh thermodynamics and other things but this might have been the form of Discovery discovering these individual blips on the screen and this is what really would happen so something very very confusing going on light is a wave that had already been proved in fact if we put a screen over here with two little holes in it two little holes in it we will again see light coming through bit by bit one at a time and if we leave it up there a long time the blips will sort of fill in and what they will form is an interference pattern so it became clear that there clear but still very confusing that light is made up out of indivisible elements called photons and that the wave character of of the light really represents or the wave pattern really represents the probability that the photon appears at different places in other words it's randomly arriving blips but they arrive with a probability in different locations which follows the pattern that was established by the wave theory the wave theory gives you a wave theory of probabilities that's quantum mechanics we made have to talk about we will have to talk about quantum mechanics a great deal more um but this kind of experiment this kind of observation about light was the first example of a connection which is really in a sense what this course is all about it's a connection first of all between waves of any kind and particles they are not two different things somehow waves and particles are two manifestations of the same thing we'll have to come back to that and we'll try to explain it perhaps again later now I'm just filling in some early early facts uh mostly just to set the stage w aves some particles at least when it came to light were Were Somehow intimately connected and it didn't make sense to say light is a particle or it didn't make sense to say light is a wave uh but has manifestations of both all right the situation only got more complicated when electrons was studied electrons are clearly particles everybody knows electrons are particles there was no ambiguity about that no more ambiguity than there was about whether light was a wave or not it was but yet something funny well something funny also happened with electrons you could do exactly the same kind of experiment with electrons you can today this experiment can really be done uh at the time it was a bit of a thought experiment but equivalent experiments You' have to put the holes you have to make a screen you put the holes much closer to each other if you want do it with electrons for one reason or another and you send electrons through of course they come through one at a time everybody knew electrons were little particles that came through one at a time but was totally unexpected is or would have been unexpected was that the electrons when you open two holes form an interference pattern so it wasn't just that light was funny particles were funny in general uh electrons exhibited wave properties light ex exhibited particle properties in fact had we taken the alpha particles which are much heavier than electrons much much heavier than electrons 8,000 times heavier than an electron much harder to do these kind of experiments with but send them through two little holes like that we also would see interference patterns this has been done with objects which are much much bigger than helium nuclei namely Bucky Balls Bucky Balls have been sent through uh uh interference experiments like this and seen to form the same kind of interference pattern so everybody know what a bucky ball is 60 carbon 60 uh in the shape of a soccer ball in shape of a a generalized soccer ball yeah right uh is it is it a regular is is a regular soccer ball got six yeah like a soccer ball no it's not it's not really a soccer ball but uh so and is widely believe that if you did it with bowling balls well you can't really do it with bowling balls much much much too hard I understand that people who did it with Bucky Balls are going to try to do it with living cells viruses to prove the viruses are quantum mechanical and then they're going to ask the virus what the virus felt it anyway good the waves and particles are somehow the same thing and if you want to penetrate that more deeply you got to learn some quantum mechanics and the place to do it is um in my lectures which don't cost anything they're on the internet okay that's uh now let's talk about the properties of photons a little bit photons are these discrete indivisible elements of light light has energy if you absorb the sunlight it Heats things obviously has energy so therefore photons have energy what do we know about the en of a photon photons being indivisible we know the energy must come in very discret packets now what is a photon characterized by or a light wave imagine a light wave coming in composed out of these discrete photons don't try to picture it it's impossible to picture when the light wave actually falls on a screen it forms these little dots so it's particles made of particles but we see some some sort of wave phenomena associated with it the wave phenomena is associated with a wavelength and therefore a frequency an angular frequency we discover that that light wave is made up out of discrete units each with an indivisible bit of energy cannot be subdivided and the energy of one Photon the energy of every single Photon in this light beam with a given wavelength and a given frequency is given by a number called H bar Plank's constant one of Plank's many one of one of plunks constants H Bar times Omega in other words Omega is large when the wavelength is short the shorter the wavelength the larger the frequency the larger the frequency or the shorter the wavelength the larger the energy in every Photon so first lesson short wavelength photons have lots of energy long wavelength individual photons have very low energy now of course a radio wave can carry a huge amount of energy there's no question you can make radio waves with lots and lots of energy how do you make way radio waves with lots of energy you pile lots of photons up many many photons all with the same wavelength and the same frequency but there is something nevertheless some remnant of the discreetness namely the energy of such a wave is always an integer multiple this is the energy of a photon the energy of a light Ray let's just call it a ray or a light wave is some inte number as an integer multiple of H Omega right so the light rays come in indivisible units every light Ray Every Light W every pulse of light with a given frequency and uh wave wave wavelength has an integer multiple of energy in units of H bar Omega all right so this is an important equation here this equation is of of absolute Central importance to understanding why particle physics is the way it is in particular it's very very Central to the question of why we have to build big giant machines to see smaller and smaller objects uh my grandson my grandson's not a kid he's 26 years old but he asked me one day how come you have to build bigger and bigger machines to see smaller and smaller things why don't you build small machines to see all right we're going to try to answer that question but this is the central fact that the energy is proportional to the frequency of a phot of a given of a single Photon um all right we've been through waves and particles photons being carrying discrete units of energy I want to come to another set of Concepts now this is we're not we're certainly not abandoning this line of thought here but there's another line of thought that I want to remind you of mostly remind you of not quantum mechanics but the special theory of relativity special theory of relativity plays a very important role in particle physics particle physics is in a sense relativistic quantum mechanics the combination of Relativity and quantum mechanics and so let me just remind you of one particular simple fact and then be clear about what that fact means most famous equation of physics eal mc^2 this equation also plays a very important role in the reason that for in explaining why particle physics is the way it is energy is mc^ squ let's just be very clear about what it means um in the early days of Relativity people spoke of the rest mass of a object and the moving mass of an object the moving mass and the rest Mass were different mass of an object was minimum when it was standing still but when it moved the mass increases you still read that in elementary physics textbooks but you never read it in any uh in any um work of modern physics you never read that the mass of an object depends on its state of motion it's largely a change in language the change in language is such that what we now call mass is what used to be called rest Mass period whenever I refer to a mass of an object I'm talking about its rest Mass all electrons have exactly the same rest Mass all electrons have exactly the same mass period if you look up the masses of particles in a uh in a you know in a table of masses and so forth you will not find them called rest Mass you will just call find them called Mass so from now on we will never speak about the rest Mass we will speak about the mass of the electron as a number that experimental physicists measure in great detail every electron has exactly the same mass as every other electron and the mass is not something which depends on the state of motion but of course the energy is something which depends on the state of motion the faster an electron moves the more kinetic energy it has so there's something wrong with this equation yes there's something wrong with this equation this equation is no longer even though it's the most famous equation in physics it's not the right equation at least with modern terminology energy is only equal to mass time c^ 2 for an object at rest the right way to say it is the energy of an object at rest if the object has no nit motion now it could be a complicated object with all sorts of internal motions but but it could be a box of gas all the molecules flying around like mad but as long as the box of gas is itself stationary then we speak of its rest mass and we can speak of its rest energy the energy of that box of gas when it's standing still and Einstein's equation says that the rest energy of an object is the rest mass or just the mass times the speed of light squared now what exactly let me imagine two experiments that you might do to confirm this just to understand precisely what it means you take a pot of not a pot a box with molecules in it and you put it on a scale to measure its weight or its mass draw a scale the molecules are cold you begin with the box of gas very very cold and you measure the mass sorry you measure yes you measure the mass you get some number now you feed some energy into the box you heat it up you heat up the molecules in here you increase their energy the box is still at rest the molecules are not the molecules are moving around but the boxes at rest and we can ask what is the rest mass of the box of gas the answer is if you increase the energy by adding thermal energy you add a certain number of calories or a certain number of jewels jewel is a unit of energy to the Box you will discover that the box is mass the box of gas its mass increases its weight increases okay now the amount that it would increase is so tiny if you increase the temperature by 1,000° or something it's so tiny that it would be quite unmeasurable but in principle this is the meaning of eal mc^2 an object at rest if you add energy to it its mass increases its weight increases also its inertia increases harder to move it okay another example now this is the this example is not something that you can really do but the other example is something that is you know real experimental physics observational physics you start not you start with an electron and a positron we haven't talked about antiparticles let's just uh ignore the fact that we haven't talked about them for a moment two kinds of particles electrons which have negative charge positrons which have positive charge they have exactly the same mass precisely the same mass they are in every respect similar except for the fact that they have oppos opposite electric charge because they have opposite electric charge they can combine and disappear they have plus charge and a minus charge the net charge is zero nothing prevents them from disappearing while something does prevent them from disappearing they have energy each one has an energy let's suppose these two particles are at rest we bring them together each one has an energy equal to mc^ 2 so the total energy is twice mc squ mc squ for each particle we bring them together that energy can't disappear energy is conserved what happens to that energy that energy becomes photons photons go out you bring an electron next to a positron and you let them annihilate poof out go photons the photons in some sense are energy they can be absorbed by a material and heat the material they they can be converted to all forms of energy and how much energy do you get by annihilating an electron and a positron the answer is twice the mass of an electron times the speed of light squared it's a tiny amount of energy I mean if you just had one electron and positron you couldn't do much with it you need uh you know huge numbers of them to to heat a cup of coffee but uh but still in principle that's what happens and of course this is this is an observational fact that's the meaning ofal mc^2 and another way to really say it which I think is the right way to say it is to say energy and mass at least for an object at rest are the same thing why do we have to have an equation really it's just a conversion of units from what we call mass units to what we call Energy units and this tells you the conversion roughly like a conversion from meters to uh to centimeters or whatever this is the conversion between energy units and mass units right but any case if you know the mass of an object and you want to know how much energy you would get if it disappeared you multiply by the square of the speed of light so you get a lot of energy for a small amount of mass what is a speed of light and what is pl's constant let's write down the numerical values of the speed of light and pl's constant we need them one for here and one for for here Photon energy underc squ is does the mass have to have a mechanism for the energy to be released or well does it have yes it has to have a mechanism and we haven't talked about that mechanism but just let's let's stand on the outside and say look this thing happens an electron and a positron when you put them together will just disappear let's not ask what the mechanism is the one thing we know is independent of the mechanism energy should be conserved if E equals mc^2 for the electrons that energy has to show up somewhere so there are some things you say without knowing what the mechanism is conservation laws where you know that certain things are conserved you can often say important things about a system without knowing detailed mechanisms okay let's talk about uh numbers the speed of light is a very big number Plank's constant is a very small number how do I know it's a small number well the energy of a photon is a tiny amount of energy the frequency of a light wave is very large so it better be that H bar is a small number let's write them down okay so C the speed of light that is equal to 2997 62 458 I I'm not kidding you this is true plus or minus something in the last digit over here time 10 8 m per second units units are important it's not just 2.99 762 458 * 10 8 it's that number of meters per second that's a speed of light how about Plank's constant I I everybody of course will memorize this number because it's important to this class that you know that number one point same thing here memorize this one 1.05 455 571 1628 * 10- 34 very small number and what are the units anybody know what the units are I worked out the units but I I think I erased them H energy times time right but what are the units of energy mass time velocity squared right MC squ better be MC squ mass time velocity mass kilog time length squar over time squar that's energy and plun constant has another unit of uh length in it another unit of time okay so Plank's constant is measured in what's the unit of mass kilograms kilogram me squared divided by seconds so why are these numbers so crazy why are they so big why are they so small why are they so odd I mean couldn't was nature playing some awful joke on us to put these that to make these numbers so awkward uh or are people just being foolish in using peculiar units for example the speed of light is something which depends on your choice of units if you measure it instead of measuring it in me/ second you measure it in feet per hours you will get a different answer so there's nothing sacred about this number it depends on your choice of units length units in this case and time units you could certainly work with units in which the speed of light was a more convenient number you could work with units in which the speed of light was one the units would be light years per year for example the speed of light is one lightyear per year or one light second per second so it's not hard to choose the speed of light to be one you just use different units of space and time same is true of Plank's constant you can use units in which Plank's constant is equal to one but why is it that we actually use such peculiar units why don't how come the people who invented units Mr metric or whoever he was the the British are worse in the metric system of course they were really perverse 5,280 feet in a mile how many um how many Stone how many pounds in a stone 16 I don't know where they got these units from H I don't know was a St own 16 lb I can't 14 lb even worse 16 is at least divisible by two four times but okay 14 14 pound high is yourse H how many hands high is your horse that's another good one how about horsepower yeah I mean just bizarre units metric units are better but they're also very very arbitrary for example the meter had to do with how far a man's hand is from his nose why CU he was using measuring length of rope or something uh so these are highly arbitrary units and have more to do with Biology than they have to do with physics they have to do with Biology in the sense that the real question is not why uh a meter is what it is why why a meter is what it is it's a question of why why an arm has to have X number of molec ules in it and there's nothing special about these numbers all right given that you can ask are there units are there better choices of units of the three units what do we need we have we need three units we need a length the three things that need the three kinds of units we need are length meters or feet or whatever time seconds or years or hours or something else and mass all of the other units in physics can be reexpressed in terms of these this is a complete set of uh of units there are three of them and we can choose them in various ways for example instead of using the kilogram we could use the mass of a proton as the basic unit of mass or the mass of a of the Sun or and so forth use different units of mass um certain things in astrophysics are a lot easier not easier but a lot the small the equations are simpler they involve less constants fewer constants if you use units in which the mass of the Sun is one okay uh equations in nuclear physics are simpler only simpler in the sense that they don't involve as many arbitrary constants if you use units in which the mass of a proton is one so you can make your equation simpler and get rid of these weird numbers and how many numbers can you get rid of how many numbers can you get rid of this well you have a choice of three units Mass length and time and that means you can simplify three of the constants of nature or three of the of these type of constants here uh and set them equal to one if you like so in astrophysics or in cosmology you might want to use the Lightyear that's a much better unit than the centimeter and if you use the Lighty year and also the year Lighty year for distance year for time speed of light comes out one of course so we can simplify three numbers usually and what do we so the question of which numbers we simplify might depend on what kind of physics we're doing if we're doing astrophysics we might want to simplify certain numbers if we're doing Atomic physics we might want to simplify other numbers um and in particle physics in particle physics there are basically these two constants which we can set equal to one by appropriate choices of units appropriate choices of units can set c equal to 1 that's easy you just use units in which time is measured uh in such a way that time and distance are measured in such a way that the distance something moves in one unit of time is one unit of distance you can also set H bar equal to one and you have your choice about one other unit what's a good unit to set equal to one what's a good unit to a mass unit to set equal to one in particle physics well you could use what about the proton why not the proton or why not the higs BOS on or why not the uh why not the the uh the me particle or well the answer is obvious that there isn't the best there is no particularly good unit of Mass which will simplify particle physics so that the at best you could at best you can set one arbitrary particle to have a mass of one and uh that would be foolish because there would be no particular reason to focus on any one particle what about the why do we pick the speed of light and plunk constant as equations they appear in so many equations well they do appear in so many equations but so does the mass of the proton or the or the size of the proton why uh okay I'll tell you why uh there are two very very fundamental facts about plunk constant and the speed of light and the way that I'll say it is just to say the words no object in nature moves faster than the speed of light it doesn't matter what it is no matter how you try to accelerate it you can get it up closer and closer to the speed of light but you can't pass the speed of light right for any object in nature any right so there's something Universal about the speed of light it's a universal bound Universal for all forms of matter for anything that we can make it has a certain universality all objects are constrained by the speed of light so it has some uh it has some reason to be thought of as something Universal what about Plank's constant does plun constant come into anything where you would want to say everything in the world necessarily has precisely this property it's the uncertainty principle we haven't discussed the uncertainty principle but all objects in nature the Precision with which you can measure their positions and velocities and momenta are constrained by exactly the same constant the uncertainty in position times the uncertainty in momentum are always constrained to be as big or bigger than Plank's constant again everything all particles not just particles but objects of all kind are constrained by the same number so it's for that reason the specialness of these two constants that it makes a lot of sense to set them equal to one the size of the proton for example or not the size of the pro well let's say the size of the proton or the mass of the proton there's nothing nothing very special about the proton the proton is one of hundreds of elementary elementary one of hundreds of objects uh why didn't we set the mass of um uh give me some weird element from up there um rubidium why didn't we set the mass of a rubidium atom to one because you say rubidium is not in any way more special than um fonum okay you're learning about my uh chemistry knowledge okay there's nothing special about ridium it's just one of many same thing is true of the proton it's just one of many the electron is one of many so there's nothing Universal about it is there a third Universal quantity which is so special that we might want to set it equal to one something which everything is constrained by yeah the trouble is electric charge is a dimensionless quantity but yes we could uh the the electric charge is a fundamental constant like that gravity gravity right what can we say we can say all objects in nature attract each other with a force which is equal to the product of the mass divided by the square of the distance between them times Newton's constant we don't make any exceptions it's not that there are some objects which do that and other objects St incidentally in the case of the electric charge of course there are neutral particles so not all objects interact in the same way electrically but everything in the world interacts exactly the same way product of the masses divided by the square of the distance between them times Newton's constant so Newton's constant is one of these very Universal things G I don't know what is it 6.74 9 8 3 1 54 I assure you it's not known to anything like that kind of precision I think it's 6.7 * 10us 11th in some units or other it's another thing that it makes a lot of sense to set equal to one why don't we do it in particle physics the reason is that partical physics is totally insensitive to gravity the gravity gravitational force between objects and particle physics is absolutely negligible so gravity would be a stupid thing to set equal to one because gravity just doesn't come into the equations of particle physics particles are too light to experience significant amounts of gravity particles that we know about today are just too light to experience any significant gravity and so it uh there's no particular value since none of the equations in particle physics involve G it better to leave it alone just go away and not fix one of the units just leave it free isn't it even fair to say that uh making the assumtion that you're dismissing it in fact what's that isn't it fair to say that uh part physics dismisses it all the time because it would be insignificant you actually don't even it's not even fair to assume that g is dismissible that in fact you're examining that these high energies may not be subject to gravity in the classical way we know well of course we know that they are subject to gravity if you take enough particles they form the Earth and you take another enough particle apart yeah so that's that's right we don't really really know what uh how Elementary particles well no we do well we can certainly take one elementary particle and see how it behaves in the field of the earth see whether it falls and they do single particles do fall in the field of the Earth but uh how single particles would influence each other gravitationally that of course has never been measured and so yeah it's uh it's possible to question whether the universal law of gravitation applies to particles uh I don't think many physicists do question it but the main point is a point a practical point there's no benefit gotten by setting G equal to 1 in particle physics because G just doesn't come into particle physics at least uh in current uh versions of particle physics there are other attractions such as attractions of two electrons or the other forces wouldn't it make sense the you're talking about gravitational attraction to set those to one instead of G attraction two electrons for example electrons don't attract they repel but yeah um but yeah you could do that but that doesn't go into your partical physics either it does go into your partical physics right it does it does um yes you you could use units and we often do in which the electric charge is equal to one and the attraction uh the repulsion yeah is the third constant you could for you could you could you could you could traditionally we haven't yeah traditionally we haven't uh there's a reason that we haven't and I'll we'll we'll eventually get to it wasn't that your point about electric charge being dimensionless once once you set c h to be dimensionless the charge is also Dimension uh yeah the charge the charge is equal to one over 100 the square of the charge is equal to 1 over 100 137 is a dimensionless measure of the charge uh and it's it's a completely dimensionless number and um we'll come to it we'll come to what it means it uh you could colum's constant is one you're saying did that be the third one if you didn't col well you can't set one over 137 you one there's an obstruction to because col con actually when I took physics that's what they did the third one they said colum's constant who constant yeah you could you could for whatever reason historically we haven't done that and there's probably no particular benefit in it um in any case we will use units in which C and H bar are equal to one quite often not always but sometimes only when want to illustrate the size of numbers will I put C and H bar back into equations so we uh oh some equations come out very simpler yeah if we set c equal to 1 then e is equal to M that's it energy and energy and mass are just the same thing we had another equation over here here e of a energy for a photon this is the energy of a massive particle which has some rest mass energy of a photon is equal to H Omega well equation simplifies if we set H H bar equal to one energy is just equal to frequency so that uh that's just an illustration of the use of what's that frequency M no well yes yes yes yes yes but not for a photon photons have no Mass don't forget this is okay there's a difference between these two the meaning of e in these equations in this equation it's rest mass and rest energy but photons can never be brought to rest nevertheless they do have energy but it's not rest energy it's the it's basically kinetic energy photons have kinetic energy uh energy of motion so this is just plain energy whatever the energy is and it's equal to their frequency so they're two different uh yeah well mass and rest mass and rest energy are relistic because what is zero what is rest it has to be relative to something yeah yeah no no no just just forget the word rest now forget the word rest you just use it to differentiate them but you know what is mass at rest in the universe where would it be not in the universe it's in the laboratory we're talking about yeah and then then it becomes relative to the relative to the laboratory energies are measured relative to the laboratory energies are different depending on the state of motion of the Observer if you have a photon or anything else and two different observers observing it they see two different energies obviously even even in Newtonian physics that's true if I have an object here and I see it I say it has no kinetic energy you're running by at 100 miles an hour you look at it and you see that it has kinetic energy so energy is something both side yeah energy is something that depends on the state of motion of an object it makes sense to ask what the energy of this cup of coffee is when it's at rest then it's just the internal motion of the molecule and so forth and um no no overall kinetic energy that's the thing which is the m when you write energy is equal to mass right but all I'm saying is the the counter that it's sitting on is not atress what's that in the universe the counter sitting on okay I me if it's at rest then it's rest relative to something else yes and the point is is that energy is measured relative to a given frame of reference energy is not a universal thing that everybody will agree on it's relative to a particular frame of reference so relative to my frame of reference the energy of this cup of coffee when it's standing still relative to me is equal to its mass okay earlier this evening again on this whole subject of uh of of naming things in constant yeah you didn't like frequency cycles per second you said physicist use Omega 2 pi to some extent that's a historical fact my question is it seems to me uh 2 pi using radi 57 whatever 2 pi times that is more complicated than a complete cycle I agree with you why why would one use something that appears to be more complex than the single side good question good question engineering math get simpler if you do that engineering math yeah yeah I mean there's some mathematical Simplicity to radians that the this uh I I think the answer is you look at all the equations you write down you write them in both terms of frequencies and you write them in terms of omegas and you see in which form do you encounter fewer factors of 2 pi I'm not sure what the answer to that is uh Omega Omega for sure it's simpler you think so oh yeah yeah you do a lot of things with e to the ey something practically speaking is it possible to accelerate two particles fast enough with energy that they will interact gravitation in principle certainly practically speaking large very far from it very very far from it no of course it depends on what you mean by a particle I don't think you'd want to call the earth a particle but uh no well what's Elementary yeah yeah what is the source of positron what say a source of positron what is a source of positrons high energy collisions that's the only way to do it you need yeah you need a you need a collision to uh to create positrons nuclear yeah nuclear processes sorry nuclear Decay sometimes you we used the planks con uh plank time and plank distance and things like that well we're not doing that plank time and plank distance correspond to setting G equal to one okay yeah so we're not doing that now the one of the reasons that we might might not want to do that is once you set three of these equal to one let's say then you have a natural unit of length a natural unit of time and a natural unit of mass the natural unit of length when you said G equal to 1 and all of them equal to one is called the plunk length and it's very very much smaller than anything that comes up in normal particle physics so you would not want to measure particle sizes particle radi and so forth in units of the plunk M plunk length it's just too small it's much smaller than anything that occurs in so that's the reason for not doing it you you would use it like in black holes or cosmology yeah and anything that really involves gravity and quantum mechanics together and relativity it makes sense to put all three of them to one uh but if only two of them are important you may only want to set two of the constants equal to one okay um let's see I want to go a little bit F further yeah let's go a little bit further with the basic Concepts that we'll draw on over and over I mean today I'm just listing basically the preliminary Concepts practically establishing uh language energy Mass particles waves Fields let's talk talk about another concept that comes up over and over in particle physics in fact it comes up over and over in almost all physics momentum momentum if you take an object and it's at rest it has no momentum at all it may have energy it has eal mc^ squ energy but it has no momentum an object at rest if it's moving it typically has momentum momentum is concerned D just like energy when two objects hit each other the net amount of momentum doesn't change right so momentum is a conserved quantity and because it's a conserved quantity it has an importance uh anything that's conserved is important momentum is a combination of the mass of an object or better yet its rest its energy its energy and its direction of motion its mass its velocity and its direction of motion it's a vector quantity it's a vector quantity and as a rule it's proportional or it's as a vector quantity it points along the direction of motion of an object points along its velocity for a non-relativistic object an object moving with much slower than the speed of light the momentum of course is equal to the mass times the velocity the arrow on top means that it's a vector quantity it has a direction okay so mass time velocity is momentum in non-relativistic physics but it's not quite the right expression for in relativistic physics and in particular it's not quite the right thing for things moving with the speed of light so let's talk about light does light have first of all does light have energy yes a beam of light shining on something Heats it does light have momentum now ordinary light if it hits you in the chest or something doesn't give you much of a push why it's because the the light so dilute and it just doesn't have much of a kick okay but if you got hit by this laser beam that they make in uh where is it in across the bay on the other side with what's that place um Livermore yeah they got this great big laser and Laser shines its light and when it hits a piece of material it just implodes it what is it that's imploding it it's the momentum of the light just pure sheer momentum and it can be huge so yes light has momentum and a pulse of light moving along let's imagine a pulse of light moving along the x-axis every pulse of light moving along a given Direction now of course real light might have some dispersion it might uh some of it might go out some parts of the light wave may go one way some parts me go the other way but if the light is very columnated so it's moving along a particular axis then the right formula now I'm not going to prove this I'm not going to prove it I'm just going to tell you the right formula for a light beam is that it is the energy of the light beam divided by the speed of light let me just compare it with this or another way to write it is the energy is C * P but let's leave it in this form here now let me just compare these two things momentum is mass times velocity momentum is energy divided by velocity just a simple question are they dimensionally the same are they dimensionally the same so to inquire whether they're dimensionally the same all you have to remember is that the dimensions of energy are mass times the speed of light squar so just in terms of units energy is like mc^ squ divided by C just tells you that the momentum of a beam of light is it's mass times its velocity not really it's Mass it's Mass the rest the mass of a light beam is really zero it has no Mass rest Mass but in terms of units it's equal to an energy * c^ 2 sorry a mass time c^2 divided by C you get the point it's just a question of units this doesn't look like this in terms of units one has a velocity upstairs one has a velocity downstairs but it is the same in units when you remember that E equals mc^2 okay so this is the formula for the momentum or the Rel relationship between the momentum and the energy of a light beam and it points in the direction along the state along the motion that's right that's right uh how to write this let's just say the magnitude of the it points along the direction of the light beam but the magnitude of the momentum is equal to the energy divided by C the magnitude of the momentum the direction is along the direction of axis of Light Beam along the state of along the direction of motion of the light beam but the magnitude of the momentum the size of it is equal to the energy of the light beam divided by the speed of light C okay you can see now momentum is energy divided by C that's why that's why the momentum is so small you can detect the energy of a light beam sure you can it heats up uh it heats up a little bit of water it heats up it evaporates water and so forth it's not hard to detect the energy but it's quite hard to detect the momentum of the light beam and that's because there's this C in the denominator here momentum of a light beam is very small typically of course if you as I said if you pump up the light beam enough it can give quite a kick all right so that oh oh let's uh let's do one little exercise all right let's just um yeah the momentum of a light beam is its energy divided by the speed of light now we had a formula do you remember the formula for the energy of a photon let's take one Photon now one photon is an example of a light beam let's figure out what the momentum of a photon is so it is equal to its energy divided by the speed of light but what's the energy of a photon H bar Omega so the momentum in magnitude is equal to H Omega divided by the speed of light now do you remember the relationship between frequency wavelength and the speed of light we had that before that yeah what was it the fre frequency time wavelength is equal to C right frequency wavelength and now if I if I put Omega here uh Omega * Lambda is what 2 pi * C or 2 Pi / c 2 pi * C right 2 pi * C No 2 pi C over 2 pi C over 2 pi good C over 2 pi is that right wait Omega is bigger than F Omega is bigger than F right all right yeah right so wait a minute I I don't believe you I don't believe you I got to do it myself I got we have frequency C * Lambda equal C right so therefore yeah so now wait Omega is equal to 2 pi * frequency right so frequency is Omega over 2 pi so this is Omega over 2 pi and I say that Omega * Lambda is 2 pi * C I was right right Omega * Lambda is 2 pi C so let's get rid of the Omega here and write Omega is equal to 2 pi C over Lambda I've just divided by Lambda let's just see what we get we get momentum of a photon is H ided by C and now times Omega and Omega is 2 pi over Lambda times C the C's cancel out that's good because I know the C's should cancel out and what do we find we find the momentum of a photon is 2 pi H bar that's a number divided by the wavelength what H what's that yeah yeah yeah 2 pi H bar equals H right right we could that's right right so right so so p is also equal to just oldfashioned H ided by Lambda there's an example where we was POS possibly not so smart to use H bar right okay look the two pies are going to get you one way or another someplace they're going to get you the pies always come up somewhere you can't get rid of them okay um what does this say this says the shorter the wavelength the larger the momentum of a photon a a single Photon of a radio wave has a very very small momentum a single Photon of a gamma ray a gamma ray is a very very short wavelength Photon has a good kick to it one Photon it won't hit it's still a pretty small kick but what this is telling you is that the momentum is related to the wavelength the shorter the wavelength the bigger the momentum that is an extremely important lesson that the shorter the wavelength the bigger the momentum and also of course the bigger the energy the energy and the momentum are related or proportional to each other so if you try to make very short wavelength photons the result will be that you have to spend a lot of energy to make them now it becomes clear why physicists have to build bigger and bigger machines to see smaller and smaller things the reason is if you want to see a small thing you have to use short wavelengths if you try to take a picture of me with radio waves I would look like a blur if you wanted to see any sort of distinctness to my features you would have to use wavelengths which are shorter than the size of my head if you wanted to see uh um a little hair on my head you would have to use wavelengths which are as small as the thickness of the hair on my head the smaller the object that you want to see in a microscope the shorter the wavelength of light that you have to use okay if you want to see an atom literally see what's going on in an atom you have to illuminate it with radiation whose wavelength is as short as the size of the atom but that means the shorter the wavelength the smaller the object you want to see the larger the momentum of the photons that you would have to use to see it so if you want to see really small things you have to use very make very high energy particles very high energy photons or very high energy particles of different types uh how do you make high energy particles you accelerate them in bigger and bigger accelerators you have to pump more and more energy into them to make very high energy particles so this equation and its near relative what is its near relative E equals H bar Omega these two equations are sort of the central theme of particle physics that particle physics progresses by making higher and higher energy particles because the higher and higher energy particles have shorter and shorter wavelength and allow you to see smaller and smaller structures that's the pattern that has held sway over basically A Century of particle physics or almost a century of particle physics uh they're striving for smaller and smaller distances that's obviously what you want to do you want to see smaller and smaller things and at the same time the striving for shorter and shorter wavelengths which means either higher and higher momentum or higher and higher energy particles theoretical limit is there a limit to shorter and shorter yeah we think there is well yes and no yes in some sense yes we think when you get down to the plunk length something new begins to happen and we can talk about that at some point in these lectures where it may bottom out but we're very far from the place where it bottoms out if it bottoms out it probably bottoms out at the plunk length which is you know 17 orders of magnitude smaller scale than uh what we're trying to see at the LHC so we got a long ways to go a very long ways to go even if it does bottom out all right those are the basic facts that I wanted to uh to get out in front of you they sort of determine largely how particle physics has progressed and as I said it has progressed by going at every stage to shorter and shorter wavelengths larger and larger momentum and energy and smaller and smaller objects question um would there be any urtic saying that the wavelength or the size of the particle you want to look at is inversely related to the size of the cyclop draon You're Building you realize it's a ridiculous ratio but is is that sort of you need one roughly speaking roughly speaking yes that's correct roughly speaking that's right um if you have a given capacity to accelerate now what determines the capacity to accelerate the size of the electric and the magnetic fields that you can create so let's suppose you take the largest fields that you can create in a magnet made of steel is big and that determines uh that determines your ability to acceler accelerate ability to accelerate means the energy that you can pump into something per meter given a meter of accelerator how much energy can you pump in all right so to double the amount of energy that slack produces it would have to be twice as long or round or round but uh that that's right but round gives you another problem the problem that round gives you is that when particles move in circular orbits they radiate and when they radiate lose energy so let's take the case of a linear accelerator the longer the linear accelerator is the higher the energy that you can pump the particles to and pretty much linearly linearly proportional to the size of the accelerator and it's going to get half the double the resolution Yeah so basically resolution times size is the constant order yeah yeah so if you wanted to get to this plunk length how big an accelerator would you have to have well as I said 17 orders of magnitude longer than the CERN accelerator no Universe no I think it's more like the Galaxy the ring Engineers yeah I call it the gatron right right yeah higher I mean the highest cosmic ray energy are 10 21 electron volts or something like that uh which is 21 - 9 is what quick 21 - 9 12 10^ the 12 gev whereas the accelerator in uh well no it it actually doesn't work the highest energy cosmic rays are 10^ the 12 gev um but but the problem is you see the problem is cosmic rays they may have this huge energy but they hit stationary targets whereas in the accelerated CERN they're going to be colliding targets and so you get more bang for your buck from the colliding particles but still still cosmic rays have much more energy than U effective energy than the accelerators the problem with them is in order to really do good experiments you have to have a few a huge flux of particles you can't do an experiment with one high energy particle it will probably miss your target or it probably won't be a good dead on head-on collision you don't learn anything from that you learn very little from that so what you want is enough flux of particles so that uh so that you have a good chance of having a significant number of head-on collisions that takes a lot of particles when the targets are small so I told you how big an accelerator you would have have to make now I would tell you how many particles have to collide in order to see something interesting and I once worked out how much energy it would take to fuel this accelerator in order that you could do experiments in a reasonable amount of time and I think I got something like 100 trillion barrels of oil a second so uh you need the accelerator as big as the Galaxy being fueled by something um I think it was 100 trillion barrels of oil a second and uh it's going to be a while till we do experiments like that yeah yeah right but these are but these are real distance scales I mean they really do come into physics and um the puzzle and the question is how to probe them how to get at them without being able to spend 100 billion barrels of oil and build a Galactic size accelerator so what's the G energy level hopeful from from the LHC is it hopeful in what sense in what sense would you ask is it hopeful compared to this 10 12 G you get from you need it's not comparable to the 10 the 12 uh GV from uh no uh when you have a particle hitting a stationary Target take that 10 12 and take its square root it's 10 the 6th it's like having 10 the 6th gev in colliding particles each one colliding so if you have two particles colliding each one with 10 to the 6th gev it's like having one particle with 10 to the 12th hitting a stationary particle now 10 the 6 that's a million gev that's a th000 teev so we're still very low compared to what uh to what cosmic rays can do but if you have a handful of cosmic rays coming in the chances are that it's going to do an interesting Collision un negligible for more please visit us at stanford.edu