I just love love how you motivate every definitions. My biggest gripe with Physics courses is that often they, for example, just define isospin, define the up and down quarks with their value of isospin in a vacuum and then are like "look, this just happens to explain how hadrons works" and you‘re just left feeling like the definitions are completely arbitrary, why things couldn’t be defined another way and how anyone could have figure this out. The fact you did this entire explanation without once pronouncing the word "quark" is amazing.
Cool video! What can you recommend to read on such a 'bottom-up' construction of quark theory out of observations of hadron properties? I have physics background, but always found discussions in textbooks a bit unsatisfactory as most of them just say 'hey lets look at this SU(3) and classify it' right from the first pages.
Thanks for the great explanation! However, even though isospin (and for that matter: Eightfold Way) discussions seem "easy" on the surface (just like QM coupling of angula momenta), I always get somewhat lost in the details. So I have a couple of questions, which I grouped into two blocks, the first of which is more technical while the second is more philosophical. 1) Which quark combinations are allowed and what are the correct prefactors in superpositions? (First, this is not about color charge; I already watched the next video of the series on QCD and understand, that hadrons should be SU(3)-color singlet states, which can be formed from three quarks (baryons) or a quark-antiquark pair (mesons), while for example ud is not allowed. Also, regarding the prefactors, I do understand Clebsch-Gordon coefficients; it's also not about that.) In my understanding, spin and isospin are completely independent. For mesons, (total) spin and isospin each can take values 0 and 1, and for baryons, (total) spin and isospin each can take values 1/2 and 3/2 (if we restrict to up- and down-quarks only). For both mesons and baryons, this gives 4 possibilities. However, on your overview at 3:50, there is no meson isospin 0 singlet with spin 0, and no baryon isospin 1/2 doublet with spin 3/2 and isospin 3/2 quadruplet with spin 1/2. I.e. there is no spin 0 version of the omega0, spin 3/2 version of the nucleon, and spin 1/2 version of the Delta. Regarding the correct prefactors in superposition states: When I looked up the neutral pion pi0, I noticed it is mathematically represented as 1/sqrt(2) (u ubar - d dbar), which corresponds to an I=0, I_3=0 state. However, your video would suggest it should be represented as 1/sqrt(2) (u ubar + d dbar), being an I=1, I_3=0 state. I guess this is why at 12:40 you only wrote "linear combinations of u ubar and d dbar" without an explicit expression. When I tried to find out, what particle actually corresponds to 1/sqrt(2) (u ubar + d dbar), I found that there is not such a particle, but that additionally the strange quark contributes to the eta mesons like 1/sqrt(3) (u ubar + d dbar + s sbar). Shouldn't 1/sqrt(2) (u ubar + d dbar) be totally an allowed particle, and why is that not the correct form of the pi0? Is there then also a particle 1/sqrt(4) (u ubar + d dbar + s sbar + c cbar), and why is isospin at all helpful anymore if 1/sqrt(2) (u ubar + d dbar) does not exist in nature, but adding in s sbar does? In general, I understand that the SU(2)-isospin symmetry is not exact, as the up- and down-quark masses are different, and that mixing of states due to the weak interaction is a thing, see for example the Wikipedia article on the eta mesons. So maybe all those questions are clarified by just using the proper standard model. I also tried to understand how the full state of for example a spin up or spin down proton look like, as writing down only superpositions of 3-quark-states uud, udu, duu neglects the spin information. Basically I tried to combine the isospin doublet superposition and spin doublet superposition. I couldn't really do it myself, but I found the expression for the spin up proton on Wikipedia in the proton article, section "Quarks and the mass of the proton". I would be interested to understand how you get the 4 spin 3/2 states of the delta0, for example. 2) How are different isospin states different particles? Historically, isospin was only introduced to group particles, but isospin is not an actual physical quantity of a particle, like its charge, mass or spin. It's basically a different name for its up- and down-quark content. So why do states like 1/sqrt(2) (u ubar - d dbar) and 1/sqrt(2) (u ubar + d dbar) describe different hadrons, assuming they are also coupled such that their spin is the same? After all, they have the same quark content, measured with the same probabilities, and have otherwise the same charge and spin. So their mass (or total energy) must be different, but in contrast to spin, where anti-alligment can be energetically preferred, how is that the case with isospin, if it's just a different word for quark content? Finally, this is the end of my questions. I would love a follow-up discussion on strangeness and the Eightfold Way, which you talk about at 1:40. Unless I'm mistaken, I think that video is not out yet on your channel. I'm sorry my questions are so long. I think they are generally interesting, but maybe a RUclips section is not the right place to discuss that much detail. But it is kind of hard to find someone qualified to answer something this detailed, and your explanations are always so helpful.
First and foremost, I would like to preface this by saying that these are fantastic questions. Unfortunately, the answers are not super straightforward, and perhaps not as satisfying one might like. I will also like to say that your first question in particular has a lot to do with non-perturbative QCD, which I have limited experience working with (especially outside of chiral perturbation theory), so take my answer with a bit of a grain of salt. I'll go ahead and try to answer in order. 1.) First of all, I want to say that it is hilarious that you called me out on not providing the explicit expression for these states, because I intentionally didn't write this down to avoid this exact question due to its complexity lol. For the mesons, the answer approximately all comes down to symmetry. If we pretend for the moment that only the up and down quarks exist, and on top of that, if we pretend that they are massless (a lot of pretending, but bear with me), then there is an exact SU(2) flavor symmetry of QCD. (Really, it is an SU(2)_LxSU(2)_R symmetry corresponding to the left- and right-handed components of the quark fields which is spontaneously broken down to a SU(2)_V symmetry which only corresponds to one linear combination of these left and right fields. This is actually extremely important when discussing the hadron mass hierarchy, but I won't worry too much about it here.) Now, once the quarks confine in low-energy QCD, we still can't forget about this SU(2) flavor symmetry, and so we have to choose our hadrons so that they are not only color singlets, but also so that they form representations under this SU(2) symmetry, from which we can actually build the theory. The way to do this is to combine the fundamental pieces (the quarks) using the Clebsch-Gordan coefficients, just like we do for finding similar SU(2) representations when combining spins. So, this (halfway) explains how we get the coefficients for the linear combinations (note: you end up with some weird minus signs because of the fact that the anti-quarks transform in the "opposite" representation of the quarks). So then, the question is why we don't have a pseudoscalar meson which is an isospin singlet? This is when things get fairly tricky because there are really two factors to this. The first is that the SU(2) is actually not the full symmetry. If we include the strange quark, this whole thing gets upgraded to an SU(3) flavor symmetry instead. So basically, we need to make sure that we form SU(3) representations, not SU(2) (the eightfold way is just a way of categorizing these representations based on combinations of the fundamental representation, and is basically just an upgraded version of combining spins). In some cases, the SU(2) representations are also SU(3) representations (hence, why we have the pions and rhos), but not always. When working this out, one finds that combining a fundamental quark and anti-fundamental anti-quark state gives an octet of states (this contains the three pions, four kaons (plus, minus, neutral, and anti-neutral), and eta8 mesons), and a singlet state (the eta1 meson). So really, there is just no "pure" representation of SU(3) which corresponds to 1/sqrt(2)*(u ubar + d dbar). So why is "pure" in quotation marks? Well, we can, of course, form linear combinations of the SU(3) representations to build such a state, so why don't we? For this, we need to recognize that this SU(3) symmetry *is not an exact symmetry*, just as you said. It is explicitly broken by electroweak interactions as well as the non-zero quark masses. The pseudoscalar mesons essentially correspond to the "ground state" mesons, which are the least affected by these symmetry-breaking effects. Therefore, we expect that their structure is mostly going to be the pure representations we would see if the quarks were massless and there was no electroweak interaction. In fact, the eta and eta' are really both admixtures of eta8 and eta1, it just turns out that eta is close to eta8 and eta' is close to eta1, so you typically see them used interchangeably. (Also, as an interesting tidbit, the SU(3) singlet state basically corresponds to a phase, and such a phase shift is a classical symmetry of QCD, but is explicitly broken by quantum effects, a phenomenon known as an anomaly. This is actually why the eta' has such a larger mass than the other pseudoscalar mesons.) However, when we look at the vector mesons, these are much more impacted by symmetry-breaking effects, most notably, the masses of the quarks. So, not only do these vector mesons have much larger masses than their pseudoscalar counterparts, but since the strange quark has such a large mass compared to the other two light quarks, a sizeable mixing between the neutral vector mesons is generated. This mixing is such that the physical vector states are essentially mostly 1/sqrt(2)(u ubar + d dbar) (the omega meson) and the mostly s sbar (phi) states. Again, we shouldn't be too shocked about this splitting because the SU(3) symmetry sees ~25% symmetry breaking effects from the strange quark mass, but only ~1% or less from the up and down masses, so the vector states which are much more influenced by these effects see much larger splittings. This is outlined pretty succinctly here: physics.stackexchange.com/questions/376805/how-are-the-physical-isospin-zero-states-determined As for the inclusion of c cbar states, the problem here is that the charm mass is so large that we can't even approximately write down an SU(4) flavor symmetry of QCD. Another way to think about it is that the symmetry breaking is so severe that even the ground-state pseudoscalar mesons experience huge splittings, which basically force all charm effects to decouple from the light-quark physics. I'm honestly not very familiar with the baryons, but I would imagine that the story is somewhat similar. Basically, it comes down to finding eigenstates of the Hamiltonian, which is in general non-trivial due to the strong dynamics. Finding the exact representations of the particles can be a bit tricky, but you can use the fact that isospin and spin commute, so you can treat them entirely separately. So, you can form a spin-3/2 state and an isospin-3/2 state separately and basically just multiply them together. I don't think that the result will be pretty, but it should work. 2.) Isospin is definitely a tad bit nebulous, mainly because it is hard to get a good, intuitive picture of the strong interaction. Basically, you can think of a particle's isospin as its charge under this interaction. It doesn't work exactly the same way, because it isn't a gauged interaction (there is no analog to the photon/gluon), but according to the strong interaction, it is a conserved quantity, exactly the same way that electric charge and angular momentum are conserved. Of course, this conservation is broken due to electroweak interactions, but it still gives a way to keep track of what interactions are actually possible (really, on what timescales one would expect to see certain interactions happen since strong interactions and electroweak interactions occur on vastly different timescales). I know that might not be the most satisfactory answer, but this is essentially what isospin does for us. 3.) Yes, the last video in my standard model series will be about the additional fermion flavors (it is still in progress, since it can be a pretty tricky topic to talk about). I won't go too in-depth about the eightfold way in that video, since I'm really only going to be talking about the discoveries of the quarks, but I'm not opposed to making a separate video about this since it seems like there is quite some interest (you are not the first person to tell me they would want to see this). I hope I addressed your questions. If not, please feel free to ask some more!
@Higgsino physics I think there is even another one where maybe Dirac(?) said roughly "the Nobel Prize should go to the person who *doesn't* discover a particle this year!" I couldn't find any records of this one, though, so I went with the Lamb quote, which I also find quite funny.
Thank you. But at 12:50 why so coy about the linear combination? You were quite explicit when talking about (1/√2)(|↑↓⟩ + |↓↑⟩) and (1/√2)(|↑↓⟩ - |↓↑⟩) earlier, which was very helpful since they behave so differently. So it seems weird not to be explicit about the linear combination now.
Question: why do electrons have unit charge, even though they are not composite, while protons (or i guess antiprotons) have the same unit charge, yet are composed of fractional charged fundamental particles? Seems like the strong force conspires to bring together building blocks in a way to work together with another building block which though doesn't see the strong force at all...
Had to watch this one twice to follow, but that may be me being tired. Have you talked about what parity is as a property of particles before? I know you talked about it in the CPT video, but that was as a general symmetry. Do we know at that point in the story why all these observed particles have integer electric charge, even though the isospin combinations would allow other values?
@Narf Whals yes, this whole discussion of isospin can be quite tricky (I still get tripped up on it as well!). You make a good point about parity, I don't think I have talked about what exactly the parity of a particle means. Luckily, it is pretty simple: it is just what happens to the state of a single-particle system when we act with a parity transformation. So if it has parity +1, the state stays the same and if it has parity -1, it picks up a minus sign. Either way, I really just wanted to include it in this video to emphasize the similarities of the particles in the same isospin multiplets. At this point in the story, no we don't really know why we don't see hadrons with fractional charge. For example, just because the omega meson can't be a ud state due to its electric charge, why do we not see an isospin zero hadron with Q = 1/3 which IS made up of ud? To give a hint to future videos, as is often the case when there is something whose existence seems like it should be possible, but we don't observe it, there is probably some underlying symmetry we aren't taking into account which forbids that state. Spoiler alert: in this case, it is the "color" symmetry which gives rise to quantum chromodynamics. These bound states should be color-symmetric (at least, so we think, this hasn't been formally proven as far as I'm aware) and a quark-quark bound state will always carry color charge, whereas a bound state of a quark-antiquark as well as three quarks can be color singlets. Hence, why we only see mesons made up of quark-antiquark pairs and baryons made up of three quarks (really, one should be a bit more careful and call these the "valence quarks" of the mesons and baryons since QCD is a whole non-perturbative mess at hadronic scales, so talking about individual quarks doesn't make a whole lot of sense).
Wonderful series! Thank you 😊 I was recently goofing with quark models as I'm an educator and noticed a geometry which evolves if we treat quark chaste as axes of charge rather than points. This was just...hmmm...3 dimensions... ruclips.net/video/y7isYNCK5bo/видео.html
I just love love how you motivate every definitions. My biggest gripe with Physics courses is that often they, for example, just define isospin, define the up and down quarks with their value of isospin in a vacuum and then are like "look, this just happens to explain how hadrons works" and you‘re just left feeling like the definitions are completely arbitrary, why things couldn’t be defined another way and how anyone could have figure this out. The fact you did this entire explanation without once pronouncing the word "quark" is amazing.
Yeah i prefer it when graduate physics is explained from first principles or at least as an unraveling mystery
Cant wait to watch this new crispy fresh vid
Another great explanation!
great video as usual! keep them coming!
Cool video! What can you recommend to read on such a 'bottom-up' construction of quark theory out of observations of hadron properties? I have physics background, but always found discussions in textbooks a bit unsatisfactory as most of them just say 'hey lets look at this SU(3) and classify it' right from the first pages.
Thanks for the great explanation! However, even though isospin (and for that matter: Eightfold Way) discussions seem "easy" on the surface (just like QM coupling of angula momenta), I always get somewhat lost in the details. So I have a couple of questions, which I grouped into two blocks, the first of which is more technical while the second is more philosophical.
1) Which quark combinations are allowed and what are the correct prefactors in superpositions?
(First, this is not about color charge; I already watched the next video of the series on QCD and understand, that hadrons should be SU(3)-color singlet states, which can be formed from three quarks (baryons) or a quark-antiquark pair (mesons), while for example ud is not allowed. Also, regarding the prefactors, I do understand Clebsch-Gordon coefficients; it's also not about that.)
In my understanding, spin and isospin are completely independent. For mesons, (total) spin and isospin each can take values 0 and 1, and for baryons, (total) spin and isospin each can take values 1/2 and 3/2 (if we restrict to up- and down-quarks only). For both mesons and baryons, this gives 4 possibilities. However, on your overview at 3:50, there is no meson isospin 0 singlet with spin 0, and no baryon isospin 1/2 doublet with spin 3/2 and isospin 3/2 quadruplet with spin 1/2. I.e. there is no spin 0 version of the omega0, spin 3/2 version of the nucleon, and spin 1/2 version of the Delta.
Regarding the correct prefactors in superposition states: When I looked up the neutral pion pi0, I noticed it is mathematically represented as 1/sqrt(2) (u ubar - d dbar), which corresponds to an I=0, I_3=0 state. However, your video would suggest it should be represented as 1/sqrt(2) (u ubar + d dbar), being an I=1, I_3=0 state. I guess this is why at 12:40 you only wrote "linear combinations of u ubar and d dbar" without an explicit expression. When I tried to find out, what particle actually corresponds to
1/sqrt(2) (u ubar + d dbar), I found that there is not such a particle, but that additionally the strange quark contributes to the eta mesons like
1/sqrt(3) (u ubar + d dbar + s sbar). Shouldn't 1/sqrt(2) (u ubar + d dbar) be totally an allowed particle, and why is that not the correct form of the pi0? Is there then also a particle
1/sqrt(4) (u ubar + d dbar + s sbar + c cbar), and why is isospin at all helpful anymore if 1/sqrt(2) (u ubar + d dbar) does not exist in nature, but adding in s sbar does?
In general, I understand that the SU(2)-isospin symmetry is not exact, as the up- and down-quark masses are different, and that mixing of states due to the weak interaction is a thing, see for example the Wikipedia article on the eta mesons. So maybe all those questions are clarified by just using the proper standard model.
I also tried to understand how the full state of for example a spin up or spin down proton look like, as writing down only superpositions of 3-quark-states uud, udu, duu neglects the spin information. Basically I tried to combine the isospin doublet superposition and spin doublet superposition. I couldn't really do it myself, but I found the expression for the spin up proton on Wikipedia in the proton article, section "Quarks and the mass of the proton". I would be interested to understand how you get the 4 spin 3/2 states of the delta0, for example.
2) How are different isospin states different particles?
Historically, isospin was only introduced to group particles, but isospin is not an actual physical quantity of a particle, like its charge, mass or spin. It's basically a different name for its up- and down-quark content. So why do states like 1/sqrt(2) (u ubar - d dbar) and 1/sqrt(2) (u ubar + d dbar) describe different hadrons, assuming they are also coupled such that their spin is the same? After all, they have the same quark content, measured with the same probabilities, and have otherwise the same charge and spin. So their mass (or total energy) must be different, but in contrast to spin, where anti-alligment can be energetically preferred, how is that the case with isospin, if it's just a different word for quark content?
Finally, this is the end of my questions. I would love a follow-up discussion on strangeness and the Eightfold Way, which you talk about at 1:40. Unless I'm mistaken, I think that video is not out yet on your channel.
I'm sorry my questions are so long. I think they are generally interesting, but maybe a RUclips section is not the right place to discuss that much detail. But it is kind of hard to find someone qualified to answer something this detailed, and your explanations are always so helpful.
First and foremost, I would like to preface this by saying that these are fantastic questions. Unfortunately, the answers are not super straightforward, and perhaps not as satisfying one might like. I will also like to say that your first question in particular has a lot to do with non-perturbative QCD, which I have limited experience working with (especially outside of chiral perturbation theory), so take my answer with a bit of a grain of salt. I'll go ahead and try to answer in order.
1.) First of all, I want to say that it is hilarious that you called me out on not providing the explicit expression for these states, because I intentionally didn't write this down to avoid this exact question due to its complexity lol. For the mesons, the answer approximately all comes down to symmetry. If we pretend for the moment that only the up and down quarks exist, and on top of that, if we pretend that they are massless (a lot of pretending, but bear with me), then there is an exact SU(2) flavor symmetry of QCD. (Really, it is an SU(2)_LxSU(2)_R symmetry corresponding to the left- and right-handed components of the quark fields which is spontaneously broken down to a SU(2)_V symmetry which only corresponds to one linear combination of these left and right fields. This is actually extremely important when discussing the hadron mass hierarchy, but I won't worry too much about it here.)
Now, once the quarks confine in low-energy QCD, we still can't forget about this SU(2) flavor symmetry, and so we have to choose our hadrons so that they are not only color singlets, but also so that they form representations under this SU(2) symmetry, from which we can actually build the theory. The way to do this is to combine the fundamental pieces (the quarks) using the Clebsch-Gordan coefficients, just like we do for finding similar SU(2) representations when combining spins. So, this (halfway) explains how we get the coefficients for the linear combinations (note: you end up with some weird minus signs because of the fact that the anti-quarks transform in the "opposite" representation of the quarks).
So then, the question is why we don't have a pseudoscalar meson which is an isospin singlet? This is when things get fairly tricky because there are really two factors to this. The first is that the SU(2) is actually not the full symmetry. If we include the strange quark, this whole thing gets upgraded to an SU(3) flavor symmetry instead. So basically, we need to make sure that we form SU(3) representations, not SU(2) (the eightfold way is just a way of categorizing these representations based on combinations of the fundamental representation, and is basically just an upgraded version of combining spins). In some cases, the SU(2) representations are also SU(3) representations (hence, why we have the pions and rhos), but not always. When working this out, one finds that combining a fundamental quark and anti-fundamental anti-quark state gives an octet of states (this contains the three pions, four kaons (plus, minus, neutral, and anti-neutral), and eta8 mesons), and a singlet state (the eta1 meson). So really, there is just no "pure" representation of SU(3) which corresponds to 1/sqrt(2)*(u ubar + d dbar).
So why is "pure" in quotation marks? Well, we can, of course, form linear combinations of the SU(3) representations to build such a state, so why don't we? For this, we need to recognize that this SU(3) symmetry *is not an exact symmetry*, just as you said. It is explicitly broken by electroweak interactions as well as the non-zero quark masses. The pseudoscalar mesons essentially correspond to the "ground state" mesons, which are the least affected by these symmetry-breaking effects. Therefore, we expect that their structure is mostly going to be the pure representations we would see if the quarks were massless and there was no electroweak interaction. In fact, the eta and eta' are really both admixtures of eta8 and eta1, it just turns out that eta is close to eta8 and eta' is close to eta1, so you typically see them used interchangeably. (Also, as an interesting tidbit, the SU(3) singlet state basically corresponds to a phase, and such a phase shift is a classical symmetry of QCD, but is explicitly broken by quantum effects, a phenomenon known as an anomaly. This is actually why the eta' has such a larger mass than the other pseudoscalar mesons.) However, when we look at the vector mesons, these are much more impacted by symmetry-breaking effects, most notably, the masses of the quarks. So, not only do these vector mesons have much larger masses than their pseudoscalar counterparts, but since the strange quark has such a large mass compared to the other two light quarks, a sizeable mixing between the neutral vector mesons is generated. This mixing is such that the physical vector states are essentially mostly 1/sqrt(2)(u ubar + d dbar) (the omega meson) and the mostly s sbar (phi) states. Again, we shouldn't be too shocked about this splitting because the SU(3) symmetry sees ~25% symmetry breaking effects from the strange quark mass, but only ~1% or less from the up and down masses, so the vector states which are much more influenced by these effects see much larger splittings. This is outlined pretty succinctly here: physics.stackexchange.com/questions/376805/how-are-the-physical-isospin-zero-states-determined
As for the inclusion of c cbar states, the problem here is that the charm mass is so large that we can't even approximately write down an SU(4) flavor symmetry of QCD. Another way to think about it is that the symmetry breaking is so severe that even the ground-state pseudoscalar mesons experience huge splittings, which basically force all charm effects to decouple from the light-quark physics.
I'm honestly not very familiar with the baryons, but I would imagine that the story is somewhat similar. Basically, it comes down to finding eigenstates of the Hamiltonian, which is in general non-trivial due to the strong dynamics.
Finding the exact representations of the particles can be a bit tricky, but you can use the fact that isospin and spin commute, so you can treat them entirely separately. So, you can form a spin-3/2 state and an isospin-3/2 state separately and basically just multiply them together. I don't think that the result will be pretty, but it should work.
2.) Isospin is definitely a tad bit nebulous, mainly because it is hard to get a good, intuitive picture of the strong interaction. Basically, you can think of a particle's isospin as its charge under this interaction. It doesn't work exactly the same way, because it isn't a gauged interaction (there is no analog to the photon/gluon), but according to the strong interaction, it is a conserved quantity, exactly the same way that electric charge and angular momentum are conserved. Of course, this conservation is broken due to electroweak interactions, but it still gives a way to keep track of what interactions are actually possible (really, on what timescales one would expect to see certain interactions happen since strong interactions and electroweak interactions occur on vastly different timescales). I know that might not be the most satisfactory answer, but this is essentially what isospin does for us.
3.) Yes, the last video in my standard model series will be about the additional fermion flavors (it is still in progress, since it can be a pretty tricky topic to talk about). I won't go too in-depth about the eightfold way in that video, since I'm really only going to be talking about the discoveries of the quarks, but I'm not opposed to making a separate video about this since it seems like there is quite some interest (you are not the first person to tell me they would want to see this).
I hope I addressed your questions. If not, please feel free to ask some more!
lool loved that story about the fine :D
@Higgsino physics I think there is even another one where maybe Dirac(?) said roughly "the Nobel Prize should go to the person who *doesn't* discover a particle this year!" I couldn't find any records of this one, though, so I went with the Lamb quote, which I also find quite funny.
Please keep uploading, I also love your videos
Thank you. But at 12:50 why so coy about the linear combination? You were quite explicit when talking about (1/√2)(|↑↓⟩ + |↓↑⟩) and (1/√2)(|↑↓⟩ - |↓↑⟩) earlier, which was very helpful since they behave so differently. So it seems weird not to be explicit about the linear combination now.
This video opened my mind. You are awesome
Not it didn't wtf
Question: why do electrons have unit charge, even though they are not composite, while protons (or i guess antiprotons) have the same unit charge, yet are composed of fractional charged fundamental particles? Seems like the strong force conspires to bring together building blocks in a way to work together with another building block which though doesn't see the strong force at all...
nice. what a cliffhanger cant wait to find out about the strong force and also how did they figure out 3 different color charges exist
Had to watch this one twice to follow, but that may be me being tired.
Have you talked about what parity is as a property of particles before? I know you talked about it in the CPT video, but that was as a general symmetry.
Do we know at that point in the story why all these observed particles have integer electric charge, even though the isospin combinations would allow other values?
@Narf Whals yes, this whole discussion of isospin can be quite tricky (I still get tripped up on it as well!). You make a good point about parity, I don't think I have talked about what exactly the parity of a particle means. Luckily, it is pretty simple: it is just what happens to the state of a single-particle system when we act with a parity transformation. So if it has parity +1, the state stays the same and if it has parity -1, it picks up a minus sign. Either way, I really just wanted to include it in this video to emphasize the similarities of the particles in the same isospin multiplets.
At this point in the story, no we don't really know why we don't see hadrons with fractional charge. For example, just because the omega meson can't be a ud state due to its electric charge, why do we not see an isospin zero hadron with Q = 1/3 which IS made up of ud? To give a hint to future videos, as is often the case when there is something whose existence seems like it should be possible, but we don't observe it, there is probably some underlying symmetry we aren't taking into account which forbids that state. Spoiler alert: in this case, it is the "color" symmetry which gives rise to quantum chromodynamics. These bound states should be color-symmetric (at least, so we think, this hasn't been formally proven as far as I'm aware) and a quark-quark bound state will always carry color charge, whereas a bound state of a quark-antiquark as well as three quarks can be color singlets. Hence, why we only see mesons made up of quark-antiquark pairs and baryons made up of three quarks (really, one should be a bit more careful and call these the "valence quarks" of the mesons and baryons since QCD is a whole non-perturbative mess at hadronic scales, so talking about individual quarks doesn't make a whole lot of sense).
If omega-zero is a linear combination of u and anti-up, wherein is the numerical coefficients (=1) recorded?
Wonderful series! Thank you 😊
I was recently goofing with quark models as I'm an educator and noticed a geometry which evolves if we treat quark chaste as axes of charge rather than points. This was just...hmmm...3 dimensions...
ruclips.net/video/y7isYNCK5bo/видео.html