The Biggest Ideas in the Universe | Q&A 12 - Scale

hello everyone welcome to the biggest ideas in the universe I'm your host Sean Carroll today we're doing the Q&A video for idea number 12 which was scale where we talked about the size of things I'd hoped to get a lot farther because the size of things is a big topic ironically enough but the questions they were actually very good so I'm not gonna try to extend what I did in the video I'm just gonna go through the questions some of them were things that I should have thought of to answer others were once I wanted to get to but didn't quite have time so the first one is what I definitely should have thought of to answer it's a classic question we talked a lot in the last video about the Compton wavelength of a particle and the question is simply what is the difference between the Compton wavelength and the Deroy wavelength which we talked about earlier so the debroglie wavelength came about early in the days actually it might have been around the same time when the Compton wavelength or the diploid wavelength came about but both of them were before quantum mechanics had been completely formulated in its final form so a bunch of concepts come in and only later on do we figure out what they're good for so the diploid wavelength lambda lambda D boy there you go the equation for it is just H I'm going to put Planck's constant in here over the momentum of the particle or in the nonrelativistic reading what we don't need to worry about special relativity etc it's H over the mass times the velocity and the point of this was roughly speaking debris was saying it wasn't the wavelength that was important what matter was he was saying it matter has wave-like properties this was the first explicit statement of that idea remember you had the Bohr atom where you had quantized energy levels and the orbits of electrons around nuclei but the idea that the reason why the orbits were quantized this is because the electrons are fundamentally wave-like had not yet appeared and here is de boy saying exactly that and this is the wavelength corresponding to a particle with a certain momentum okay compare that to the wavelength of a photon before we get to the Compton wavelength this is what came out of plunks original idea in 1905 he said that we all know that photons have wavelengths we know they work sorry we know there were photons back in the year 1900 we knew there was light we knew that light had a wavelength and what plunk did was to say that the light is coming or at least is emitted in these quanta of energy than it was Einstein who said that the reason why light was emitted in quanta of energy is because light is in some sense quanta of energy what we would say now is that light is the vibrations in the quantum electromagnetic field and when you observe it when you measure it when it interacts with something in D coheres you measure it in discrete chunks of energy and so what plunk would have said anyway wrapping all that up into a formula for the wavelength versus the momentum plunk would have said that it's just H divided by P I don't know why I'm thinking so hard about this it's exactly the same formula as the deployed wavelength is it this is the point let's call this the plunk no I can't cause the pause a flame can I that's something else let's call the photon Lambda gamma okay gamma being the photon lambda being the wavelength this was how debris got his formula we had known from plunk that an individual particle could be associated with a certain amount of energy and momentum an individual particle of light which we now call the photon and this was the relationship between the wavelength of the classical electromagnetic wave and a little individual particle that has an energy and a momentum okay finally you can compare that to the Compton wavelength which we introduced in the scale video lambda Compton and this is H over m the mass of the particle okay so we can see something from these equations just from the mathematical form of them a relationship between these different notions of the idea of a wavelength the photon wavelength is the wavelength of a particle with zero mass a photon moving at the speed of light we express it in terms of the momentum the way that Planck would have written it was H over e the energy but the energy is equal to momentum for a particle moving at the speed of light okay so when de rooy wanted to invent a formula for the wavelength of a matter particle he just you is the same formula that palanca given for the photon but he used the momentum okay and then we see from comparing the debris wank way to the Compton wavelength that the de Blois wavelength is just the Compton wavelength divided by the velocity and even though I'm putting in Planck's constant here I'm still setting C equals one the speed of light equals one so this is always greater than the Compton wavelength okay the Devoy wavelength is always greater than the Compton wavelength fine but what are they like what do they physically mean okay well I think of the secret here is I've never quite seen this written down or expressed in this way so maybe some experts on the history of quantum mechanics will correct me but in my mind the point of the Compton wavelength is not the wavelength it's not a wavelength of anything in some sense the Compton wavelength is a scale it's a distance it's the distance at which given quantum mechanics and relativity it's the smallest scale at which you can sensibly talk about a single particle at a time it's sort of the intrinsic size of the particle although there's a footnote there we'll get to later lambdas see the Compton wavelength is the smallest scale for a particle and it's not necessarily the scale which quantum mechanics kicks in it's the scale at which quantum mechanics cannot help but kick in that's the point the debris wavelength is the actual quantum scale quantum wavelength of the particle it really is a wavelength so there was an experiment done by Davisson and Germer in around 1920 that I write down no I didn't in the 1920s they did an experiment where they actually showed a thing in 1927 where they actually did the interference experiment you know we talked about the double slit experiment the double slit experiment is usually given as a way of thinking about measurement and what it means an interference of what it means but it was Davisson and Germer who actually showed that if you have an electron or a set of electrons they will interfere with each other just like waves do and that interference pattern you can figure out what the wavelength is and it's the debroglie wavelength it's the actual wavelength of the wave function oscillating up and down for that particle so of course it makes sense the Debye wavelength must be larger than the comp and wavelength because the Compton wavelength is just the size smaller than which quantumness takes over in fact you can't even say it's just a single particle anymore if you squeeze down the uncertainty in the position of the wave in the quantum fields - less than the Compton wavelength you're not even talking about a single particle anymore whereas when you're larger than the Compton wavelength when your wave has a wavelength larger than that then number one you can talk about a single particle and number two you can do the experiment to have them interfere and that's an actual honest-to-goodness wavelength you're talking about there so they mean different things the Compton wavelength is really you know it's it's kind of a more fundamental thing as you can see the Compton wavelength just depends on the mass of the particle since we're setting h equal to 1 you could equally well write this as 1 over m depending on where you want to put the two PI's the smaller the massed larger the Compton wavelength larger the mass the smaller the Compton wavelength this is where you cannot help but pay attention to quantum mechanics but the point being even for a very very massive particle where the Compton wavelength is very small and therefore you can imagine a state in which the wavelength was confined to that region you can also imagine states in which the particles all spread out and that would be when the diploid wavelength is very large so I hope that helps a little bit here's a related question our particles are elementary particles if you like really point like hmm this is a tough question actually so sometimes you hear people talk about you know the proton which is made of quarks and gluons is not a point-like particle right because it's made of other things rattling around in there whereas the electron is a point-like particle that is what you will hear but we just talked about all these different wavelengths that it has you know that there's a Compton wavelength below which it's intrinsically quantum is there any sense at all in which a particle is point-like at all I think you know that the short answer is no my favorite short answer is no because the world's not made of particles the world's made of quantum fields as far as we know and those quantum fields are vibrating nothing point-like about them they have an extent and even if they were particles even if the quantum theory of the world was obtained by starting with particles and quantizing them it would still be a quantum theory would still be a wavefunction okay there's nothing point-like about it when people say that the electron seems to be point like what they mean is as far as we can tell there's no sub structure to the electron the electron is not made of other things of course it could be we don't think it is honestly most of us don't but it could be made of other things but there's no evidence that it is so point like is just a shorthand for saying not made of smaller things it does not mean you can actually shrink the wave function of the electron down to a point you can't really sensibly shrink it down swallow in the common wavelength I mean you could but then it wouldn't be electronic okay next question this is and this is sort of I'm cheating by allowing a question that was more appropriate for a previous video but that's okay it relates to these questions if you say that the energy of photon is H Planck's constant times the frequency okay which we do we just did where where is the amplitude in that formula why doesn't the amplitude of the wave matter why is it just the frequency that matters okay and this is of course a very important question I could have talked about it earlier but I mean maybe I did allude to it but this is where quantum mechanics comes in so the status of the question the context of the question is we're saying that there are waves we're saying that you know photons are coming from waves in the electromagnetic field but they have certain particle-like properties and this equation here the answer to this question is this equation is for one photon a single photon corresponding to a wavelength of light or frequency of light given by F has an energy given by this formula that's what this formula means the point is if you change the amplitude what that changes is the number of photons the amplitude of the wave and this is very roughly speaking because again we're really dealing with quantum mechanical wave functions not classical waves but roughly speaking the amplitude corresponds to the number of photons and we can even think since we've already done our quantum field theory introduction we understand that a little more sophisticated level the electromagnetic wave bouncing up and down is kind of like a simple harmonic oscillator okay so it will always be bouncing up and down a little bit there's always some tail the wave function of the wave always has some support at very very large amplitudes but for one particle States for the minimum excitation of that simple harmonic oscillator the typical oscillation the typical amplitude is not very large as you excite the field more and more as you introduce more and more particles the typical amplitude of oscillation goes up that's where the amplitude comes in and this is you know historically this is a crucially important insight there's something called the photoelectric effect and this is actually the explanation for which this is what Einstein wrote about in 1905 where he essentially introduced the idea of the photon even though he didn't call it that yet and this is the paper that he won the Nobel Prize for despite also completing special relativity in 1905 so the point was this you can there's a certain kind of metal that you can shine light on and occasionally the metal will kick off an electron an electron will leave the metal because you're shining light on it you're just shaking loose an electron not surprising the question is when does the electron when do the electrons get shaken free so you might think that what matters is the intensity of the light right the brightness of the light the more light you're shining on it the more electrons get shaken free but that is not what is observed if you do a very very faint amount of light you might be able to shake an electron free what matters is not the intensity but the color of the light the frequency of the wave right the wavelength if you go to blue or violet or ultraviolet those have the ability to shake loose Tron's and that's true even when it's very faint as well as when it's very very bright whereas very red light or infrared light will not shake loose electrons no matter how bright it is okay and so this was the idea in fact before quantum mechanics came along people had exactly this idea the more bright a beam of light is the more energy it has the easier it should have the ability to shake electrons free but when you think of that light instead of as waves as individual particles hitting the the metal being observed by the metal if you like then this formula kicks in so a bright beam of red light is a huge number of photons but that are very very individually very very low energy none of those photons has enough energy to break loose an electron whereas a beam of blue light I don't actually know what the actual colors or wavelengths are but a higher shorter wavelength of beam of light let's put it that way it can be very faint but those photons individually pack a lot of energy so it just being very faint just means there aren't a lot of photons so you won't shock lose a lot of electrons but even a very faint beam of blue light can break loose a couple of electrons that's the difference the wavelength tells you the energy of the individual photons the amplitude tells you how many photons there are so they both go into telling you how energetic that beam of light really is okay here's a related question on our little plot okay you know we had the plot of energies and we went from 10 to the minus 3 or 10 minus 6 electron volts up to the Planck scale 10 to 27 electron volts okay so one question was where are photons on that well there's a good reason why photons were not there because we were actually not plotting the energy of particles we were plotting the mass of particles we were using the fact that mass and energy are the same same units when you set C equal to 1 so a photon which is low-frequency long wavelength can have an arbitrarily small amount of energy per photon a photon with a very short wavelength of very high frequency will have an arbitrarily large amount of energy per photon so on this plot am I doing this correctly yes look at that on this scale photons are everywhere depending on the energy of the photon nevertheless it might be interesting to plot some representative interesting photon energies that you might know about so let's go to you know one electron volt ten hundred thousand ten thousand hundred thousand remember the mass of the electron is about five hundred thousand electron volts okay so a little bit here so maybe here's the mass of the electron and what you could do is look up the electromagnetic spectrum that goes from you know radio waves infrared visible light ultraviolet x-rays gamma rays and you could plot it you could just convert from whatever they give you the units in you know the wavelength of the light in angstroms or whatever two electron volts that's something you can do at home so I'm not going to do the whole thing but here's sort of some typical numbers you know where we are visible light is roughly here okay between one and ten electron volts visible light literally what is visible to our eyeballs whereas x-rays are maybe between one and a hundred thousand electron volts so in between there's ultraviolet over here there's infrared etc okay so different photons have different amounts of energy but what you see is all of these photons that you're used to have energies that are lower than the energy in a single electron right so an electron and a positron come together to annihilate in two photons they will be typically giving off that doesn't say me that says mass of the electron they will be tipping typically giving off a gamma rays gamma rays are the next highest in energy after that and these words you know infrared visible UV x-ray gamma ray these are not physics words I mean they may be used by physicists but there's no physical distinction between these photons other than their energies other than their wavelengths okay they're just photons of different energies so that's where photons fit on the plot and of course you can you could imagine having Planck energy photons maybe you could have higher than Plake energy photons who knows we don't know the laws of physics up there the Planck scale so we're not sure but the point is the mass of even an electron which is sort of the smallest particle that makes up you is still pretty massive compared to the photons that you're looking at it would take a lot of photons to make up one electron then there's a related question here's another fun one that I could have mentioned once again what about the quarks where are they because we mentioned the electron 500,000 electron volts in energy in mass we mentioned the proton of the neutron so let me write that down mass of the electron is around 5 times 10 to the 5 electron volts mass of the proton which is about the same of the mass of the neutron that's about 10 to the 9 electron volts 1 GeV so that's why you get GV this is very very common units in particle physics so what about the quarks you might think it would be perfectly natural to think that given that there are 3 quarks in a proton or neutron that the mass of a typical quark is about 1/3 of the mass of the proton or the neutron we're not going to explain why just yet we'll get there pretty soon actually but in fact quarks are much lighter than protons and neutrons atleast some quarks are the quarks that are inside the protons and neutrons are much lighter than that so here are the answers there's six quarks up quarks have masses of about two times 10 to the sixth electron volts whereas down quarks have masses of around 5 times 10 to the sixth electron volts I'll tell you others are in a second but let me just pause to notice here the up quark and the down quark are only a little bit heavier than the electron right an up quark is about four times the mass of the electron whereas the down quark is about 10 times the mass of the electron compared to protons and neutrons which are about 2,000 times the mass of the electron so up and down quarks not that heavy the mass of the proton and the mass of the neutron which is where most of your mass because you're made of atoms and atoms are made of electrons protons and neutrons and protons and neutrons have most of the mass in them most of the mass in you does not come from those quarks where it comes from is the interaction energy of the gluons that are holding the quarks together in a complicated way we have to try to explain that a little bit but it's not the masses of the up and down quarks themselves in fact these numbers that I'm giving you here are a little problematic because when you talk about the mass of something you want to isolate it from everything else and put it on a scale or you know push it and use F equals MA or something like that but as we'll talk about for quarks you cannot isolate them from everything else quarks are confined you can have enough quark inside a proton or neutron but you can't have one all by itself outside so in a very real sense the very notion of the mass of an up quark or a down quark isn't even really well-defined as these complications that made me hesitant to even mention this in the first place but that's okay we'll just put it there there's also the strange quark that's the next heaviest it's about 10 to the 8th electron volts there's the charm quark which is about 10 to the 9 the bottom which is about 4 times 10 to the 9 electron volts and of course the top quark is a big leap upward it's about 10 to the 11 electron volts so the charm quark the fourth heaviest quark is about the mass of a proton right it's about 1 GeV and the bottom and top quarks are much heavier than that as we said as I said in the previous video when you have these heavier particles they tend to decay away it is a process of entropy increasing because when a heavy particle decays into lighter ones there are more lighter particles than there were heavy ones and therefore there's more stuff going on and therefore the entropy is higher someone asked in the question you know why do we have heavy particles we don't have every particle there's no top quarks lying around there's no Higgs boson lying around particles decay until they reach decay products that are stable the electron the proton and the photon and the tree nose those are stable particles they have nowhere to go of course the proton is still pretty heavy but it carries what what is called baryon number it's a conserved quantity Berrien number is not created or destroyed in any experiment we've ever seen and therefore the proton is nowhere to go it can't decay into anything lighter because it is the lightest particle carrying baryon number likewise electrons and positrons are the lightest particles carrying electric charge so they can't decay either neutrinos are the lightest particles carrying Fermi on number the total number of fermions etc so basically that's the story in particle physics things decay until they're in the lightest possible state that has some conserved quantity that you can't get rid of so it makes you staple then you're stuck there now there's a little footnote there because of course we have things like the helium nucleus or the iron nucleus or the carbon nucleus which are stable mixtures of neutrons and protons and neutron all by itself out there in the wild can decay neutron will decay into a proton and electron and antineutrino but because of the dynamics of the strong interactions in the quarks certain combinations of neutrons and protons become stable even though individual and do Tron's by themselves or not thank goodness because that's the origin of the periodic table the elements which is kind of a big deal okay all this is just to say the quarks have a wide range of masses and their masses are not sort of easily interpretable in any way because the quarks are stuck inside protons and neutrons and other strongly interacting particles okay here's another good question this is a fun question actually can you what about if you had hydrogen's you have proton and electron but you tried to replace the electron with a muon instead the muon is just a heavier particle heavier cousin of the electron could you make muonic hydrogen it's a clever question yes you can you can you can try to make it I'm pretty sure it's been made they've done all sorts of crazy things this is a fun thing for physicists to try to do the important thing that I wouldn't mentioned is that the mass of the muon again the properties of the muon are exactly this as the properties of the electron except for its mass so it has charge minus one just like the electron does it has spin 1/2 there's an anti particle called the anti muon etc in fact there was a point of time when the only known elementary particles were the electron the proton and the neutron okay these are the first three that we found and then it was like literally a few meters away from my office at Caltech where Carl Anderson by building a big cloud chamber and looking at cosmic rays coming from the sky he discovered the positron the anti electron and then he discovered the muon and he discovered the anti muon so the positron shook people up because anti particles were not yet accepted they've been predicted by Dirac but people didn't know whether to take that prediction seriously the muon was a complete surprise no one knew that this is that's the origin of the famous comment biii Rabi who said who ordered that when the muon was discovered but the point of the anecdote is there was a little moment of time when Carl Anderson had discovered the positron the muon and the anti muon and the only other known particles were the electron the proton the neutron so he discovered half of elementary particles that were known at the time which is pretty good he deserved and he got the Nobel Prize ask yourselves why he discovered the positron muon and the anti muon before the antiproton in the antineutron I won't tell you but you can figure it out give him things we've already said anyway the mass of the muon is about 200 times the mass of the electron so the point is you can make an atom so you have here's a proton P and then orbiting around it we'll do our little trick where we do oops that's not right we'll do our little trick where we color in to give the impression of a wavefunction okay there you go this is the wavefunction of the muon now mu - but the point is the size of the muon academ the equivalent of the Bohr radius remember the for radius gives you the size that the hydrogen atom the ordinary hydrogen so this is only gonna be one two hundredth of the Bohr radius it's gonna be a much more compact atom because the muon is heavier so when I said you know ant-man is impossible the point of that was you can't squeeze things down to really tiny distances of course the one way you can is by making them heavier right you can't keep the mass of the electron what it is and squeeze it down below its Compton wavelength but the muon is heavier so it is smaller so you can make smaller things out of muons and people have the problem is the mu1 also has a lifetime it is not a stable particle because it can decay into electrons in fact the muon can decay into an electron plus two neutrinos a neutrino and antineutrino and the lifetime of the muon is about 10 to minus 6 seconds one millisecond so that's not good you're not going to get a lot of stable structures that you are gonna make out of muons and other things nevertheless you know physicists are ambitious sometimes you might know that we have a Large Hadron Collider in Geneva before that we have the Tevatron at Fermilab and we're still thinking about what the next big Collider will be so here's an idea yeah so sorry let me let me back that up there's roughly speaking to different kinds of particle colliders that people like to build hadron colliders and lepton colliders so hadrons are the protons and neutrons nuclei that you can make out of them leptons or electrons basically electrons and positrons etc hadrons also include anti protons so Fermi laughs I've had the Tevatron where they were colliding protons and antiprotons the SSC sorry the LHC large hadron collider is just protons and protons they could do anti protons but it's hard to make them so you're gonna get more collisions if you just make protons hit protons so that's that's why they did that but there's also and the reason why you want to do these hadron colliders these proton antiproton colliders is because they're heavier than electrons you can get up to very high energies so if you're trying to make the Higgs boson or some other new particles or whatever you want to get as much energy into a tiniest face as possible heavy particles are good for that because they have a smaller company wavelength right but once you've discovered them you might want to do very delicate measurements you might want to figure out exactly what the mass of the Higgs boson is and exactly all of its decay products and things like that that's harder to do at a Hadron Collider it's not impossible we've done it to some precision but you can do it more precisely by colliding electrons or electrons and positrons together because they're exactly because they're smaller and they are as far as we know fundamental particles I said they're smaller they're not smaller because there are fundamental particles because they're not made up of other things you know two protons hitting each other you don't know exactly where the energy is if it's in this quark or that quark or a gluon or whatever whereas in an electron you know exactly where the energy is an electron and positron for example so there's a good reason to still build electron or lepton colliders even though you can get more energy out of a Hadron Collider so check it out you could build a muon Collider and this is a very active idea people are thinking about this because muons have 200 times the mass therefore 200 times the energy of an electron and so you could get some of the benefit of smashing protons together and we get heavy particles and a lot of energy but also some of the benefit of Smashing electrons together that there are fundamental particles you know what all the energy is doing this is the problem this is why it's it is so far proven impractical to do this because the individual muons decay in a millionth of a second now you can to a large extent combat that by just having the muons move very fast you can use relativity right if the muons are moving in 99.999% the speed of light then it seems to us that they live a lot longer than a millionth of a second and that's the trick that's how you can try to get a muon Collider but even at that look at a particle accelerator you're not just keeping two muons or one yuan and one han time you want and colliding them together you're generally getting millions or billions or trillions or much more than colliding them together in bunches and hoping to get some good interesting collisions out of them so when you get that many muons together some of them are going to decay even if they're all moving very close to the speed of light and when they decay they give off these very high-energy electrons but also neutrinos that can pass right through matter usually but then they also hit you so this there was this idea that a muon Collider with a lot of muons with you know 10 to the 20 muons in it would be constantly radiating super high-energy particles and give rise to what we called the ring of death everyone near the collider would be killed by this high-energy radiation so that was an engineering problem that also people not yet overcome as far as I know I mean maybe they've overcome it they certainly haven't build a muon Collider yet okay that was you know that was a digression but it's a fun by Gresham um what next just two more questions I wanted to get to one question is can there be unknown yet as yet undiscovered low energy particles low mass particles the idea of this question which is a perfectly good question is look it's hard to make the Higgs boson hard to make the top quark hard to make particles even heavier than that because equals mc-squared you need energy in a tiny region to make these new particles but in accion these hypothetical particles that I mentioned might have masses of like 10 to the minus 4 electron volts incredibly incredibly tiny right that can't be that hard to make them well so I'm not going to talk too much about what accion's are neutrinos by the way also M nu might have energies around 10 to minus 3 or 10 demised to electron volts so and neutrinos have the benefit of actually existing but the point is we discovered neutrinos why haven't we discovered accion's if they're so light and easy to make we might not have discovered them so they don't exist we're not sure yet but you don't need just to be able to make them you'd be able to need to be able to make enough of them to notice so the acción in particular is a neutral particle it has zero electric charge that's what makes it a good candidate to be the ARC matter dark matter is dark dark means you don't interact with photons okay if you have a charged dark matter particle you know look people clever and the try those things but the simplest thing in the world the most obvious guess is the dark matter is electrically neutral and the accion's don't feel the weak nuclear force or the strong nuclear force they feel electromagnetism in a weird off-kilter indirect way so it is possible to try to detect them but those interactions are very very very weak so typically accion's are one of these things much like neutrinos where accion's could be in the room all around you right now going through your body and you would never know so the reason why there could be low mass particles we haven't yet detected is our ability to create them depends on their mass but our ability to know we've created them to detect them and to see them taking away energy and momentum depends on their coupling depends on the strength of their interaction and so if someone says they have a new candidate for dark matter or whatever just some particle they made up which has a mass less than the mass of the proton or less than the mass of the electron for that matter you can immediately assume that those particles are very very weakly interacting they're just hard to know that they're there the neutrino very famously was suggested by Wolfgang Pauli because of I think was beta decay it was certainly energy conservation issues beta decay is neutron we already discussed this neutron goes into proton plus no distrait plus electron plus as we now know a electron antineutrino so if momentum is conserved the neutron has a momentum the proton has momentum the electron has momentum and those proton and neutron momentum you can add them up and you can ask is the momentum of the outgoing proton electron equal to the momentum of the neutron and the answer was no so obviously there's another particle taking away some of the energy some of the momentum but back in the day like these days you know the standards are a lot looser now than they used to be everyone would just say sure there's a new particle they'll be instantly what people said back in the 1930s before much or reluctant to just predict new particles that had never been observed so Wolfgang Pauli was the one who said you know maybe we should take this energy thing seriously hello people were saying things like maybe energy is not conserved right that was on the table as a possible prediction but instead Polly said maybe there's a new particle but he's very embarrassed about it he said like you know you know don't don't be mad at me which is which was ironic cuz everyone knew that polly was the harshest person on everyone else whenever they made new predictions for things but he turned out to be right one of many things that Pelle he was right about so there can be low mass particles as long as they interact weakly the neutron neutrino rather does interact very weakly literally through the weak interactions it took us a while to detect it directly okay the final set of questions was what I don't know if it's a set of questions or not but it had to do with grand unified theories so I mentioned grand unified theories because they might be right you know grand unified theories we have this situation right now where electromagnetism definitely exists figured out classically by Maxwell in the 19th century quantum mechanically by I think was direct who first started down the road but people like climbing sugar tomonaga showed it how to make it a consistent quantum theory then there's the weak interactions Fermi Enrico Fermi was the first person to come up with a sensible theory of the weak interactions and then it was unified by Weinberg Salaam and Glasgow into the electroweak theory there's a complicated story of why three people get credit for it they never wrote a paper together but um so you can I do this what am I doing here yet but I think Weinberg sort of got it right let's say that and this is very successful we'll talk a little bit about what's going on there but then you also have the strong interactions so once this works once this trick works of unifying the electromagnetic and weak interactions into electroweak it is natural to say let's unify strong and electroweak into grand unified theories ok so the question I'm not even sure that's had the question was that sorry if it people who are asking this question but it brings up two issues that were talked about one issue is that grand unified theories predict proton decay so I think what it was was I mentioned proton decay and people said why would the proton ever decay I just mentioned a few minutes ago there's this quantity called baryon number which is conserved so protons can't decay so if protons can decay then that means a barrier number is not exactly conserved and this is a feature that was figured out in the 1970s when Glashow and howard George I first suggested grand unification their unifying weak interactions with the strong interactions but they don't just unify the forces they unified them matter as well they unify the electrons and the neutrinos which we now call leptons with the quarks okay so in that basically there are new forces of nature that are very very weak because the bosons carrying them are very very heavy that can turn an electron or rather a quark into an electron or vice-versa that can somehow couple the baryon number carrying things namely the quarks to things without baryon number namely electrons and neutrinos and then you can go through this is one of the you know fun interesting anecdotes in the history of science you could go through in the 1970s and you could say knowing what we know about grand unification it needs to have an energy scale something like 10 to the 16 GeV okay 10 to the 25 electron volts just a little bit below the Planck scale so number one that's interesting it's interesting that it's within spitting distance of the Planck scale because gravity is where the Planck scale comes from and gravity it didn't get mentioned here okay so this was a and this is a big deal this was one of the reasons why people took grand unification so seriously the data you have in the 1970s is all from experiments done at some numbers of GeV right you know the mass of the proton or ten or a hundred times the mass of the proton but you can use that data and this theoretical idea to extrapolate to a new energy scale we're grand unification should happen and the answer is it happens very close to the Planck scale a factor of 100 is nothing in this game right so that was that it just seems like an accident there seems like a coincidence and maybe it is because maybe granny fication isn't right but at the time that was taken as very suggestive and exactly because that energy scale is so large the bosons carrying this new force would be very very heavy hard to make and therefore the interactions they mediate are very rare and therefore protons will decay very very rarely so in another coincidence they could figure out how long it would take proton to decay in their theory they made a prediction and beautifully the prediction was I forget exactly the number but the lifetime for a proton in gran unification might be something like 10 to the 35 years compared to the lifetime of the universe right now is around 10 to the 10 years so you might think well that's hopeless you're never gonna see a decay you have to wait around 25 10 to the 25 times the sorry yeah you have to write around 10 to 25 times the age of the universe in order for this to happen but of course the answer is you don't wait proton by proton you don't take one proton and wait for it decay you take a large number of protons you take 10 to the 30th or 10 to the 35 or 10 to the 40 protons right and well 10 to the 40 is a lot but you take a lot of protons and wait for some of them to decay and it turned out in the 1970s that this just about seemed doable with the technology that they had at the time and so they built proton decay detectors and they haven't found it that's the short answer it's been decades now that that's been going on and they've not seen the proton decay so the simplest versions of grand unification have been ruled out they're just not right but of course physicists are very clever they have assigned their ingenuity to this problem they've come up with other versions of grand unification where the life time is a little bit longer and therefore you can avoid the current experiments so then it becomes a question of how much is it worth it to you to improve the experiments you can do the experiment better but cost money and you know in the 1970s or 80s it was like yeah this is probably there let's do it and now it's like maybe it's there we don't know so it's harder to justify spending that money so we're not sure yet that's the sad story the other part of the grand invocation story is mana poles so we know that electricity I don't get too much into this call it's a electric charge okay electric charge comes in plus or minus so you have a proton positively charged you have an electron negatively charged magnets on the other hand they have north and south poles but a magnet always has one of each as a North Pole and a South Pole and if you were to cut the magnet in half then this would become a South Pole and that would become a North Pole okay you cannot separate a magnet into one pole at a time so a magnetic monopole when we say mono poles we usually but not always mean magnetic monopoles would be a particle which was just a North or just a South magnetic charge all by itself no evidence of these existing in nature there's a joke because there's been a couple of experimental claims that people have found magnetic monopoles most people think of those claims were just false and the joke is no one has ever claimed to find two magnetic monopoles people have claimed if I'm one probably this haven't found them yet and guess what grand unified theories predict that magnetic monopoles should exist for topological reasons we're not gonna get into that right now but they also predict they should have this huge energy this huge mass so they're impossible to make in particle accelerators right now this is way these energies are way way higher than anything we can make in a particle accelerator however the universe is the poor man's particle accelerator as David Tran like to say if you didn't do anything weird if you just had ordinary Big Bang cosmology at very very early times the universe was SuperDuper hot and dense and you could make magnetic monopoles and they would try to annihilate away but they were not very successful so what you could do calculate if grand unified theories were correct should you have leftover remnant magnetic monopoles and the answer is yes in fact the total energy the total mass in magnetic monopoles today should be something like 10 to the 10 times the actual amount of energy in the universe the universe should be all magnetic monopoles if this theory were correct this is what is called the monopole problem of grand unified theories and the monopole problem was what actually inspired Alan Guth to invent oops wonderful problem to invent the inflationary universe scenario inflation is this idea in cosmology that there was a period in the very very early universe with a kind of temporary dark energy dark energies the stuff that exists everywhere in space and is pushing the universe apart and making it accelerate but imagine that there was dark energy up with the grand unification scales not at the wimpy little scale that it's at today today the energy scale characteristic of dark energy e lambda lambda is the cosmological constant the vacuum is something like 10 to the minus 3 electron volts and what that means is this 10 electron volts to the fourth power is the energy density of empty space today so during inflation what you want is the energy scale of inflation is near the gut scale or near the grand unified scales that's 10 to the what do we call it had a 25 electron volts way higher so the point is if there's a temporary period of dark energy that makes the universe accelerate and it will dilute away all the magnetic monopoles so you have a huge overabundance of magnetic monopoles an inflation can get rid of them and then inflation turns all this dark energy back into ordinary matter and radiation but at a lower temperature the temperature low enough that it won't make any magnetic monopoles so we can dilute away all the mono poles now today we still believe in inflation many of us think that is a very promising idea to discuss what happened in the early universe we don't know we don't know if we're absolutely sure I would put it it you know more than 50% chance but not a lot more if I were forced to bet but the motivation has changed complete so Guth's original motivation was this magnetic monopole problem but in the back of his head he knew there were these other problems in cosmology what we call the horizon and flatness problems and he showed that inflation also was a solution to those problems and we can debate whether or not those problems are interesting but the point is they're still there whereas the monopole problem depends on you really wanting grand unification to be correct if granny fication isn't there then there's no monopole problem there's no mechanism for making magnetic monopoles so mono poles are an interesting theoretical idea they cause good things and also bad things they could be problematic if you don't have inflation but they could be wonderful if you were able to detect them right you win the Nobel Prize for doing that so you know we've we've been introduced here in this little Q&A to a bunch of particles that we don't know whether they exist or not the acción is one magnetic monopole czar or another that's the fun part about particle physics you know we haven't discovered a new surprising particle one that hadn't been already predicted since 1970s but maybe it'll happen soon we don't know that's what physics is all about you gotta wait got to do your experiments gotta let nature tell you what's going on

Channel: Sean Carroll

Views: 28,397

Rating: 4.9242902 out of 5

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Id: OGgQ4-Ak9ew

Length: 47min 42sec (2862 seconds)

Published: Sun Jun 14 2020

Reddit Comments

[u/nicernicer]

nice