Particle Physics 5: Basic Introduction to Gauge Theory, Symmetry & Higgs

hello today we're continuing in our series on particle physics looking amongst other things at gauge Theory spontaneous symmetry breaking and the Higgs mechanism but first a quick review we've already learned that there are four fundamental forces the strong nuclear force the electromagnetic force the weak nuclear force and the force of gravity and we've learned that three of these can be incorporated into a model on particle physics at the moment we cannot get gravity into that model and in that respect it's not complete but let's look at those three forces we'll start with the electromagnetic force because in some ways that simplest what the electromagnetic force does is it essentially is the force that operates between two charged particles so if for example we take two electrons which are light light charges and therefore they will repel because like charges repel it means that if you bring two electrons together they will push one another apart but the question is since they don't actually have to be touching how does this electron know that this electron is here in order to push it away and what we've discovered is that the reason that the force exists is because of virtual photons which are called gauge bosons or if you like exchange particles which are virtual because they do not exist forever they come into being and then they go out of being but they travel between these two charges and they communicate the force so the force communicator or the exchange particle or the gauge boson whatever you want to call it in this case is a virtual photon photons are of course massless and that whole principle is called quantum electrodynamics and you'll recall that that was represented in mathematical form by the unitary matrix and one-dimensional you won then we looked at the weak nuclear force now this is a force which amongst other things is responsible for changing the flavor of quarks so for example you can take a Down quark and convert it into an up quark ups and downs are what are called flavors by the emission of a w- boson so in this case it's the w- which is the exchange particle or the gauge boson that is equivalent to the virtual photon in the case of the electromagnetic force but the w- doesn't last very long before it decays into an electron and an anti-electron neutrino the w- is 80 times heavier than the neutron from which it was formed this typically you don't have individual quarks this will typically be a neutron which consists of three quarks so that will be an up-down down neutron because a neutron has two downs and one up and then two of the particles two of the quarks don't change they stay as they are but one of the down quarks changes into an up quark so now you have up down up and that of course is a proton and so what you've got is a neutron converting to a proton by virtue of the fact that one of the quarks in the neutron specifically the down quark converts into an up quark by the emission of the W - but as I was saying the W - is 80 times heavier than the neutron from which it comes Neutron is approximately 1 GeV a W - is approximately 80 GeV so the question is how can something that weighs 1 GeV as it were produce a particle that is 80 times more massive and the answer is that we had to resort to that other version of Heisenberg's uncertainty principle which says that Delta e del T must be less than H far that is to say that the amount of energy that essentially you borrow from the vacuum multiplied by the amount of time you borrow it for must be less than Planck's constant which is a very small number so this is saying that you can borrow energy from the vacuum provided a you pay it back and be you don't keep it for very long and the more energy you borrow the less time you can borrow it for so we're borrowing a lot of energy from the vacuum here 80 GeV so that has to be paid back very quickly in fact in ten to the minus twenty five seconds so the W minus doesn't last for more than ten to the minus twenty five seconds before it decays into these long term particles in ten to the minus twenty five seconds a W miners will barely be able to cross a part of a proton that's as far as it will get before it decays and that's why the neat weak nuclear force is a very short range force because the W - which is the exchange boson only lasts for ten to the minus twenty five seconds and can't get very far in that time this whole process is called quantum flavor dynamics qfd and in mathematical terms is represented by the special unitary matrix su-22 dimensional because you're changing from downs to ups or as we shall see in a moment you can change from ups to downs let's just look at this process of the down changing to the up via the emission of a w- particle in a little bit more detail we could represent that as saying that you start with a down which stays down and then you have an up ante up creation out of nothing so out of the vacuum you get a particle antiparticle creation and what that appears to look like is that the down particle has changed into an up particle via the emission of a Down ante up and that down ante up of course is essentially the w- boson free neutrons that is neutrons which are not part of a nucleus will convert to protons about every 15 to 20 minutes so if you have a free Neutron it is not a stable particle it would it will convert and become a proton protons we think are stable or if they are not they have got half-lives of very much greater than the entire age of the universe but neutrons unless they are in the nucleus in which case for various reasons they are held in stability if they are just free they will change the protons by this process and the fact that it takes 15 to 20 minutes to do so shows how weak the force is it shows why this if this w- were massless like the photon if it were massless like the photon this process would happen almost spontaneously and neutrons would just akane to protons instantly but because it's a weak force and it's a weak force because you've got to borrow the energy from the vacuum to create the w- it takes time for neutrons to decay now I mention that it's also possible what protons to decay into neutrons and the way that works is that you've got one of the quarks in the proton which is the an up quark changing into a down quark by virtue of the emission of now a w+ and that will quickly decay into a positron which of course we'll find in the electron and annihilate and an electric sorry and an electron neutrino not an anti-electron neutrino now because the antiparticle is the positron and of course there are two other quarks which do not change so there'll be an up-and-down up and down and so one of the Clarkes the up quark that's this one here changes into a down quark and say you've got an up-down up which is a proton changing into an up-down down which is a neutron by virtue of the w+ now i said to you that protons do not generally decay into neutrons so why is that and the answer is that in this case the neutron can decay into the proton because the neutron has a marginally greater mass than the proton so since e equals mc-squared some of that mass can be converted into energy so the neutron can decay into a slightly smaller mass proton and the energy that's left it doesn't of course create the w- because there's not enough that comes from the vacuum and has to be paid back by this formula but the excess mass of neutron over proton is what can create the electron and the anti neutrino but when we come to this process ordinarily this can't occur because the proton has a less mass than the neutron so you can't create a long-term particle when you've got less mass because there's no spare energy to create these additional particles here so this arrangement can only occur in circumstances where you've got a huge amount of energy already available to you for example in the Sun and that's exactly what happens in the Sun the honey the Sun is just a huge ball of hydrogen the electrons have been stripped off the hydrogen because it's so much energy there so the hydrogen is ionized and hydrogen without his electron is just a proton so essentially the Sun is just a massive ball of protons and what is happening is that the some energy is available to enable protons to convert to neutrons and then you can take two protons and two neutrons and bring them together and form what is essentially an alpha particle the nucleus of helium and ultimately that's all the sun is doing and it takes 10 billion years for the Sun to do that it's been going for five billion it's still what five billion to go and the reason that it takes ten billion years is because the W plus particle is so massive at 80 GeV and that's and because it's so massive it has to borrow energy from the vacuum in order to create the W Plus which lasts for about 10 to the minus 15 seconds before it decays if the W plus were massless like the photon this pota process would happen almost instantaneously the Sun would burn out in about a few beat a few million years if that and so there would never be any prospect of life forming because there just wouldn't be long enough for it to do so so it's actually the reason we are alive is because the W Plus has 80 GeV of mass that makes this process weak in other words it rarely happens so proton protons do not spontaneously decay into neutrons even in the Sun it takes a while think about it there are protons in the Sun that have been there for five billion years and they still haven't converted into neutrons and there are some that won't even for another five billion years so it's the weak nuclear force the SU 2 that causes the Sun to shine finally let's look at the strong nuclear force in the case of the strong nuclear force this is where the colors of the quark remember that they aren't colored at all this is just a way of labeling them but where for example a red quark this is a red quark meets up with the position where you get a blue anti blue creation of nothing this is just matter antimatter creation from nothing and so what appears to happen is that a red quark converts into a blue quark via the emission of a red anti blue particle and that particle is cool a gluon and that is called quantum chromodynamics and because there are three colors of quarks red green and blue you need a three by three matrix and that's the special unitary matrix three and that's what's happening in the middle of the nucleus that's what holds the protons and neutrons together it's also what holds the quarks together within the proton and the neutron and look you can see the way that works you could draw a Fineman diagram whereby you have a red anti red combination here's a red ante read the to come together and annihilate here and you can have a blue take that blue through the red there you can have a blue anti blue creation and so what this looks like is that a red quark has converted to a blue quark and the red bar quark has changed to a blue bar quark via the exchange of a red anti blue glue on and it's that combination of gluon exchange that goes on in the Sun which is essentially the exchange particle the gluon is the exchange particle that creates the force the strong nuclear force that holds both the nucleus and indeed the nucleons together now I just want to think about gauge theory or sometimes gauge symmetry and this is very simplistic basically you could think of gauge as meaning the same as co-ordinate and in order for gauge theory to work you need what's called gauge invariance or in my terms you could call it coordinate invariance imagine that this is the surface of the earth and that there is a region above the surface of the earth let's say the first 30 meters also where the gravitational acceleration can be regarded as pretty much constant if I were to say to you what is the potential at that point what is the gravitational potential at that point you couldn't actually tell me because you don't know where my coordinate system is you might think that I mean what is the potential with respect to the surface of the earth and if that is true you could tell me but I might mean what is the potential with respect to the top of the table in which case it would be different what I have done is to change my co ordinate frame from one where the frame of reference has zero at the surface of the earth to one where the coordinate frame has zero at the surface of the table and so the change of coordinate frame or if you like the change of gauge changes what you would say that that potential was but if I ask you what was the potential difference between two points the gravitational potential difference between two points now you can tell me and that potential difference is entirely independent of where I set the coordinates frames it doesn't matter you could do the same sort of thing with a wire and I could say to you here is a wire what is the electric potential at the end of that wire you would know unless I gave you two wires and asked you to measure the potential difference between the two and then it wouldn't frankly matter if one wire was at nine volts and the other was at North ult's or one was at 109 volts and the other was at a hundred volts either way you're still going to measure a potential difference of nine volts so although it's a good deal more complicated than this when we talk about gauge invariance what we're actually talking about is a system whereby what you're measuring is independent of the frame that your frame of reference that you're using to measure it so since the mathematics of the week and the and the strong forces the su 2 and su 3 rubric involve transformations in the case of su 2 it's a flavor transformation from up to down or down to up in the case of su3 it's a color transformation right to green to blue those transformations must be independent of the frame of reference that you're using to measure them what about spontaneous symmetry breaking well again a very simple example is to consider water imagine that you are a molecule of water in a bowl of water and you look all around you and what do you see symmetry everywhere you look there are water molecules h2o they are all lined up in some orderly form in every direction you have got complete symmetry now let us call that water to naught degrees centigrade and below depending on the circumstances pertaining at the time as I call that water I might get ice I might get snow I might get frost and I might get REME which is a kind of verb fog frost or frozen Frost you could say that what you've got here is spontaneous symmetry breaking something which was the same has now changed into something which is completely different and if you look at things like for example a snow crystal which I cannot draw very well but it has that kind of hexagonal shape to it and that in a sense is symmetric but only if you rotate it every 60 degrees if you rotate that shape by 30 degrees it wouldn't be symmetric anymore certainly not symmetric with the original form it wouldn't be gauge invariant in that sense but but in a sense what we're saying is that you start with something that is exactly the same and you end up with things that are or appear to be completely different and that in essence is the argument about how the forces were formed the argument goes like this at the time of the Big Bang which was about 13.7 billion years ago there was a single force there was energy but in a sense it's rather like the water everything is the same there is energy there is as it were one force but at the time of the Big Bang huge energy energy equals temperature so massive temperature and then things begin to cool and when you get to some ridiculously small time which is ten from sorry ten to the minus forty six of a second different books will give you slightly different times but the idea is that one of the forces separates out that's the force of gravity that's the one that we do not yet include in the particle physics theory of all the forces and then after ten to the minus thirty six seconds so still ridiculously small the gravity is there but now another force falls out and that's the strong nuclear force and then between 10 to the minus 36 seconds and 10 to the minus 32 seconds you get what's called a period of massive inflation no one's quite sure why or indeed even if it happened but generally that's the thinking that the universe suddenly expanded dramatically now remember this is only 10 to the minus 32 of a second after the Big Bang so what we're really talking about is a universe expanding from the size of a proton to the size of an orange you know we're not talking massive at this stage but but nonetheless that expansion in that amount of time is is huge and then the pattern goes on that at 10 to the minus 12 seconds gravity is still there the strong nuclear force of course is still there but now the other two forces separate out to become the weak nuclear force and the electromagnetic force and so from a single force the argument is that within ten to the minus twelve of a second 1 million millionth of a second all the four separate forces have four and out and are quite different if we just complete the picture by ten to the minus six seconds which is one millionth of a second you get what's called quark confinement which I'll come on to in a moment which basically means quarks can never live by themselves again they always bundle together in twos or threes within three to twenty minutes you have the basis of nuclei in other words protons and neutrons are coming together really only to form things like the hydrogen nuclei the deuterium nuclei and the helium nuclei that's basically all you get but it would take another 380,000 years before you got atoms and the reason for that is of course that atoms have to get electrons to orbit the nuclei and you can take electrons out of atoms you can essentially ionize the atoms if you give them enough energy and the problem is there's too much energy going around for the electrons to be captured by nuclei they can easily be ionized so all the electrons are free until 380,000 years after the Big Bang at which point the temperature is called sufficiently that the nuclei can start getting the electrons bound to them and forming atoms of hydrogen and helium so the argument goes that from a single force four separate forces have fallen out let's look at those forces and just compare them first of all we'll take the strong nuclear force which will give a relative strength of one just so we can compare all the others that operates of course only within the nucleus so 10 to the minus 15 meters and the force carrier or the gauge boson is the glue on the electromagnetic force is the next strongest but by comparison with the strong nuclear force it's about only 1% of its strength specifically one over 137 137 is the fine-structure constant the range of that force is infinite because it's a 1 over R squared force as the distance increases the strength of the force decreases but it never reaches zero and the gauge boson or the exchange particle for the electromagnetic force is the photon next we have the weak nuclear force weak nuclear force and the relative strength compared to the strong nuclear force is about 10 to the minus 6 as we said before this has a range which barely gets it across a proton let alone the nucleus 10 to the minus 18 meters because the W boson lasts for only 10 to the minus 25 seconds so it's range is very very short and the bosons are the W minus the W plus and a boson we haven't come across yet the Z the W minus is the gauge boson that carries away a negative charge the W plus is the gauge boson that carries away a positive charge the Zed is neutral so you have a Zed gauge boson wherever you have neutral particles interacting and that would for example be the neutral neutrinos and then finally we have gravity which whose strength is about 10 to the minus thirty eight that of the strong nuclear force is pathetic by comparison but like the electromagnetic force it has an infinite range because it's a 1 over R squared and nobody knows whether or if it has an exchange particle but if it has then that particle would be called the graviton but I put in brackets because a we don't know whether it exists and if even if it does exist we've never found it so if you look at this you'll find that there are hugely different strengths of these forces and hugely different ranges for these forces well in fact there's two that had an infinite range and two that have ranges within the size of a nucleus and yet we are asserting that all of them fall out of a single force so how can that be hold that thought and we'll come back to that a little later but first I just want to bring to your attention an experimental fact when we are talking about quantum flavor dynamics that is where quarks change their flavor so I'm going to redraw the diagram where the down quark changes to an up quark typically of course this is where a neutron changes to a proton so you would have an up down and up down and those two quarks the up and down don't change but the third down quark changes to an up quark so this is a neutron which changes to a proton and it does it by the emission of the W minus gauge boson which of course lasts from mere 10 to the minus 25 seconds before it decays into an electron and an anti-electron neutrino we drew that diagram earlier in this presentation but here is the important point and before I tell you it let me just explain what I mean if you remember art quantum mechanics concepts we consider the thing called electron spin let's suppose the electron is traveling in this direction shown by the arrow I can measure the spin of the electron in any axis or any direction I like I choose to measure it along the direction of travel of the electron and we know that when you measure the spin of an electron you can only get one of two answers you will either get up or down with respect to the coordinates you choose to measure along so in this case up will be in the direction of travel and down will be contrary to the direction of travel what we mean by up or down is essentially the direction of the axis and consequently the spin is around that axis so if we are measuring an up spin that means that the if we're viewing from here that means that the electron will be appearing to spin clockwise or we could call that a right-handed spin on the other hand if we're viewing from here an electron whose spin is down then that will appear to be anti clockwise or counterclockwise and we could call that left-handed so in a sense all you're doing is calling right-handed or left-handed whether or not the spin is measured as up in the direction of travel or down in the direction of travel what we find experimentally so this is an experimental fact when the down quark changes to an up quark by the emission of a w- boson which then decays into an electron and an anti-electron neutrino the electron is always a left-handed electron you never get a right-handed electron what is actually happening in terms of charge in this diagram is that the w- is carrying away a negative charge from what was a neutral particle the neutron and if it carries away a negative charge then for charge conservation it must leave a positive charge which is why the proton has a positive charge similarly when the w- decays for charge conservation purposes it must be so it's charged onto one of these particles of course it it bestows its charge onto the electron but what you could consider this is a way of looking at it is that for the purposes of the weak nuclear force not for the purposes of just general electromagnetism of course because right-handed left-handed electrons are of course both charged there are electrons are charged particles you can't get away from that but for the purposes of the weak nuclear force which is what we're talking about here you could argue that the w- can only bestow its negative charge on the left-handed electron because for the purposes of the weak nuclear force only a left-hand electron has a charge a right-hand electron does not now I repeat of course electrons whichever way you measure them for the purposes of the electromagnetic force have charges but what you could consider the way you can think about this is that the w- bestows its charge on the left-handed electron because for the purposes of this particular weak nuclear force the right-handed electron cannot accommodate a negative charge that's the sort of way to think about it but we know that right-handed electrons can change into left-handed electrons and vice-versa we know that for at least two reasons the first one is this diagram I've just drawn you here and let me just redraw it let's say this is the direction of travel and let's say that I am viewing the electron from here and let's say that I do indeed measure a left-hand electron which means that the spin is counterclockwise as viewed from here now electrons do not travel at the speed of light so it's theoretically possible that I could run along and get in front of the electron and then view it from here the electron hasn't changed it's still spinning in exactly the way it was before but from my new perspective I will see that an electron that was spinning counterclockwise I'll say that again was spinning counterclockwise when viewed from here will now appear to be spinning clockwise when viewed from here try it yourself you simply turn something in a direction that's anti-clockwise when you're behind it so this is anti-clockwise if you now look in front of it you will see that that actually appears to be clockwise so in other words the left hand spin electron viewed from here has become a right hand spin electron when viewed from here it hasn't changed at all it's just the gauge if you like or the way I've looked at it has changed so I can I can actually see your right hand electron simply by overtaking it and looking at it the other way but we also know that you can get electrons that change from left to right from the Dirac equations which we derived in an earlier video in this series and let me just remind you what they were we said that I decide right by DT is equal to minus I alpha where alpha you may remember was a matrix decide right by the X plus M side left and the reason it was I left is that there was another matrix here which was beta and what beta did was to act on essentially a combination of sy right and sy left to give you sy left I refer you to the way we derived it earlier so I don't have to redo it there was another equivalent equation which said that ID sign left by DT is equal to minus I alpha D sy left by the X plus m where m is the mass term sy right so essentially what you've got since I could actually if you like I could take these terms over on the other side of the equation so I cross out the equals and make those pasterns and then I put the equal sign here so what I've done is to move these terms on the other side of the equation I've now got a sidelight term plus a sy right term equals a sign left term and the sy left turn times thus I left so I plus as I left term is a sine right term and so this is a left to a right this is a sorry that's a right converting to a left this is a left converting to a right so now we've got the Dirac equations showing us that you can change from left to right but I have just asserted and in a fairly hand-waving way but somehow when you've got the weak nuclear interaction the w- can only bestow its charge on a left-handed electron which means that for the weak nuclear force purposes there is actually a difference so when you've got a right-handed electron changing into a left-handed electron by virtue of these equations here somehow you must have some other field which I will call Phi which is as it were in this case bestowing the charge on the left-hand electron because we're saying that for the weak nuclear force the right-hand electron doesn't carry charge but the left hand does or similarly if you want to draw the other diagram when the left hand changes into a right hand there is a kind of a opposite version of the field which I described as Phi bar which interacts in order to as it will absorb the left-handed charge and produce a charge less right-hand electron I say it again this is for weak nuclear force purposes only not in terms of electromagnetic so we also said in particle physics that this is all really about quantum field theory these particles are not really particles at all they are excitations of fields so actually these are fields which are interacting the right-hand field interacts with another field which I have called Phi to produce the left-hand field and vice-versa what is this thing called Phi well of course it's going to turn out to be the Higgs so let's just draw the this thing called Phi let's draw Phi and we'll consider you know all fields have energy and let's consider the potential energy stored up in this field called Phi and let's suppose that it has a pattern that looks like this which is something you might think to be the case when the field has a value of zero the energy has a value of zero but as the field increases so the energy increases now that you might think is a perfectly reasonable pattern if there were such a field then of course the lowest energy state where would you sit in order to minimize your energy the answer would be at a point at which the field Phi had a value of zero and if the field Phi has a value of zero it isn't going to do much good when you interact it with left and right-handed electrons because it's not going to have any value because its value is zero to have any effect but suppose that the diagram instead this is still potential energy against that should be fine or Q against that the field suppose it looks something like this which is going to be in three dimensions so this is a you can consider this as some people do as a Mexican hat or in some cases a wine bottle the bottom bottom of a wine bottle where the the bottom is indented like this in order the sediment can accrue in the ditch as it were or the trough that is a three dimensional trough and around the base of the wine bottle you could consider of course if you took let's say this is a wine bottle I could think about balancing a marble on the top of the inverted part of the bottom of the bottle and if I was very very careful I could just about get an equilibrium and that would be perfectly symmetric but it would be inherently unstable because I've only just got to knock that bottle a little and the marble will roll down into one of the troughs now which way will it roll down we have no idea it will roll down into a trough somewhere around this base and then it will be stable once it's rolled down let's say to here it's stable it is at its lowest potential energy but the field now has a value instead of being zero the field has a value and therefore can interact with the fields of these other particles now let's take this marble analogy a little bit further we can't go too far with this because it doesn't quite work but for introductory purposes I think this is okay this marble can do two things in terms of movement firstly it can just roll around the trough at the bottom of the bottle and when it rolls around the trough it is staying at potential energy equals zero so no energy is required to roll around the bottom and that was called the Goldstone boson it's a massless particle because it has no it it requires no energy the other thing the marble can do is to oscillate up and down these walls so it can kind of you know oscillate and around not around the trough but as it will up and down the sides that of course does take energy and tap in fact it takes quite a lot of energy because these are very steep sides and when it oscillates that is called the Higgs boson and it's the Higgs boson that is effectively the exchange particle that gives certain of the fundamental particles their mass and I've done a separate video on the which you'll find in the playlist on particle physics and you may want to stop and look at that now so now let's get back to that question what makes the four forces significantly different when we are asserting that they all came from the same basic force at the time of the Big Bang well let's consider first of all gravity and electromagnetic forces those are the two that are infinite in range and we could contain as it were do you have an analogy of a light beam a light beams intensity falls off as one over R squared in other words the further you go away the intensity falls off one over R squared in exactly the same way that the gravitational force and the electromagnetic force fall off on the one over R squared term they are infinite because no matter how far you go away no matter how large R is one over R squared never gets to zero so using this analogy what could we do to create a situation where that light beam had a very very small range well the answer is we could confine it we could put it in a box and if we put it in a box now the light has a very narrow range the range of the box you can't get out as long as the box is not transparent but if it's a cardboard box you can't see the light anymore that's called confinement and that in essence is what happens for the strong nuclear force the force is confined within the nucleus the other thing you could do with this light in order to stop it from having an infinite range is to surround it by a bit of fall now here you'll have to work with me on the analogy because fog doesn't quite work like this fog tends to reflect light or cause it to scatter I want you to imagine that there's a fog around this light which absorbs the energy and thus prevents it from traveling very far so that is any sense what is happening with the weak nuklear force that the whole energy is just absorbed before you can get very far so here are ways in which analogies in which you can imagine you've got the same force for two of them you've got an infinite range for the other two there are mechanisms which happened when the spontaneous symmetry breaking took place which effectively reduced as it happens extremely reduced the range of those forces by virtue of confinement or absorption how does quite quark confinement actually work well let's take um a particle it could be a neutron it could be a proton it consists of three quarks and the reason I'm drawing it like this is we can have some kind of experiment which is going to attempt to separate out one of the quarks so we've got to essentially find some experimental mechanism of pulling one quark away from the other two in the hope that we can then break the bond and we are then going to have what we want which is an isolated quark now it turns out that what happens is as you try to do this as you pull this quark further away from these two the energy between the two parts increases and it just keeps on increasing the further you pull these quarks apart so if you have for example a proton which of course is two ups and down what you would find is that you get this kind of tube of energy as you try and pull one quark out until there is so much energy that in fact what you get is particle creation and of course you always get matter and antimatter created whenever you have this particle creation from a high energy so we've got a huge amount of energy so much so that there's enough energy for particle creation and you get an up ante up quark pair formed and then what happens is this up particle goes here and the up bar or the Antioch particle goes here and so all that happens is you get an up up down which is the proton you essentially started with but over here instead of getting a single quark you now get a meson which is an up ante up that of course is just an ordinary PI on so you never get a quark on its own because before you can get to a quark on its own there will be so much energy that there will be pair production and the pair production will just leave you with the proton you started with plus a meson that's called quark confinement you can never ever get one quark separate from all the others okay then so now I want to look at the question of how it is that these four forces have such significantly different strengths from the strong nuclear force which we weighted as one to gravity which was ten to the minus thirty eight the size of the strong nuclear force so let's just think about what those forces actually are for the electromagnetic force that we know is Coulomb's law which is just Q 1 Q 2 that is the charge on two particles multiplied together divided by 4 PI epsilon naught R squared where R is the difference between them sort of the distance between them and I can rewrite that if I like as k q-1 q-2 over R squared where K is just 1 over 4 PI epsilon naught Y is the gravitational force this is of course in Newtonian this will simply be G the gravitational constant times the first mass times the second mass divided by R squared where R is the distance between them so now let's think of two electrons of course the electrons will have a charge of V electronic on the electron and they will have the mass of an electron so now I can write that the electromagnetic force of two electrons will be equal to K and Q 2 Q 1 and Q 2 are both e the charge on the electron so that's ke squared divided by R squared so that's the electro magnetic force between two electrons what is the gravitational force between two electrons well that will equal G and now M 1 and M 2 are both the mass of the electron which we'll call em so there's M Squared over R squared at this point I just need to remind you of some of hein Stein's formula we know that the momentum is equal to H over lambda that is to say the momentum of a particle whether it's a photon or as Louis de Broglie pointed out an electron the momentum is Planck's constant divided by the wavelength of the wave associated with that particle and we can kind of think of that as H over R in other words if the distance between the two particles is of the order of its wavelength so they are very close together then we're going to say that the mentum is H over R we're also going to recall that e equals PC which is equal to since P is H over r HC over r then einstein's famous formula e equals MC squared which means that m is equal to e over c squared and since E is HC over R that is HC over R C squared because HC over R is e and then you go to C squared here and that is equal to H over RC so what we're saying is that the mass of let's say the electron is equal to e over C squared which is H over RC because we got that from here so what I'm now going to do is to take this M term the mass of the electron which I'm now asserting is H over RC and I'm going to stick that into this equation here so now FG which the force the gravitational force between the two electrons which remember we said was GM squared over R squared that's just to remind you here now I'm going to say that M is H over RC so that is going to be G over R squared G over R squared times M Squared which is just going to be H squared over R squared C squared and that's G H squared divided by R to 1/4 C squared so now I've got a force which is now expressed in these terms this is a C a speed of light so now I'm ready to say what happens is there is there a possibility that those two forces the electromagnetic force ke squared over R squared could be equal to the gravitational force well let's set them equal the electromagnetic force is ke squared over R squared and that I'm going to say is going to be equal to the gravitational force which is G H squared over R to the fourth C squared and if you work that out what you should find is that the art of the fourth cancels the R squared to give you an R squared term here and that is G H squared over K e squared C squared in other words when R has when R squared has this value which you'll notice is all constants all of these terms are constant when R squared has this value the gravitational force between the electrons is equal to the electromagnetic between the electrons so let's just get an idea of the order of magnitude we don't want to do this too precisely because it doesn't quite work like this but it'll just give you a flavor forget the numbers associated with it G is 10 to the minus 11 it's actually 6 times 10 to the minus 11 but looks forget about that h squared will H is 6 times 10 to the minus 34 10 to the minus 34 squared is 10 to the minus 68 K I can tell you is actually 10 to the 10 that is 1 over 4 PI epsilon naught e squared will that's the charge on the electron squared that's 1 point 6 times 10 to the minus 19 we'll call that 10 to the minus 30 8 C squared is of course the speed of light squared well that's 3 times 10 to the 8th we'll call that 10 to the 16 you can do this more precisely if you want so on the top we've got 10 to the minus 79 and on the bottom we've got 10 to the minus 12 and if you and that of course is going to become 10 to the minus 67 and that of course is R squared which means that R is to all intents and purposes 10 to the minus 33 meters so when two electrons are 10 to the minus 33 meters which is of course amazingly absurd small distance when they are that separated the gravitational force and the electromagnetic force are the same and of course when you talk about the Big Bang you're talking about something that grew from it essentially what we call a singularity so actually everything would be at that distance at a minut time after the Big Bang and all the forces could therefore be the same if you if you use the same kind of analogy we've got the gravitational and the electromagnetic force being the same and if they are this distance apart well remembering that R is 10 to the is 33 meters let's consider what the energy would have to be in order for that to be the case so just to remind that e equals PC which equals HC over R because we said that P is H over lambda but when lambda and is of the order of R we can call this H over R and what is that going to be in numbers well again we're just doing a hand waving an exercise H is 10 to the minus 34 C is 3 times 10 to the 8th so we call that 10 to the 8th and R we said was came to the minus 33 and that comes to 10 to the 7 that's energy and energy is measured in joules to convert joules to electron volts you essentially have to multiply by or sorry yeah multiply by 10 to the not 10 to the 19 so 10 to the 7 times 10 to the 19 is now in electron volts so that essentially tend to be 26 evie and that is the equivalent of 10 to the 17 GeV so when the energy was 10 to the 17 GeV the electrons would have been 10 to the minus 33 meters apart and the strength of the forces would be the same now if I tell you that the Large Hadron Collider when it's working at its peak will have something of the order of 10 to the 4 GeV you can see that it's a long way short of the 10 to the 17 GeV that I have calculated which would be the conditions fractionally after the Big Bang in fact if you do the calculations you often find that the energy is calculated at more like 10 to the 15 Givi but look you know what's a couple of orders of magnitude between friends so the argument is that if you stretch back over time this is time this is strength of forces at the moment you've got the strong nuclear force the electromagnetic force I'm not drawing this to scale the weak nuclear force and the gravitational force which are all entirely different strengths in fact gravity is ten to the minus thirty eight the size of the strong nuclear force but the argument is that if you pop those back to the time of the Big Bang what you find is that at that point they all had the same strength but the energy at that time was about 10 to the 15 GeV I calculated it stented 17 but hey never mind so that's the thinking that they all had the same strength when they were at incredibly high energy where the particles were incredibly close together but that spontaneous symmetry breaking has led to a situation where it looks as though we've got four completely different types of forces but in fact the assertion is that they all stem from the same

Channel: DrPhysicsA

Views: 160,685

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Keywords: Physics, Particle physics, quantum mechanics, quantum field theory, wave particle duality, De Broglie, Einstein, quantised angular momentum, energy, hamiltonian, Schrodinger Equation, Higgs, spin, creation operator, annihilation operator, fermions, bosons, SU3, SU2, U1, SU3xSU2xU1, gauge theory, gauge invariance, spontaneous symmetry breaking, QED, QCD, Standard Model, Feynman diagrams, Supersymmetry, SUSY, Strong Nuclear Force, Weak Nuclear Force, Electromagnetic Force, QFD

Id: v6bgABUyT3c

Length: 59min 5sec (3545 seconds)

Published: Tue Nov 05 2013