Symmetry and Quantum Electrodynamics (The Standard Model Part 1)
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- čas přidán 6. 03. 2021
- The Standard Model of Particle Physics is an absolutely incredible theory and a triumph of modern physics capable of explaining almost all of the physical phenomena we observe in nature. However, to understand it, we need to dive into some deep ideas including symmetry and how these relate to conserved quantities in physics. Here, we begin our journey of the standard model by introducing these ideas an showing how they can be used to arrive at one of the most successful theories in history: quantum electrodynamics.
Thanks for the Standard Model Lagrangian series!
Best video on QED. Symmetry foundation made the difference. Thanks
What makes the Standarn Model such an accurate depiction of physics... is that is is built from experiment. Experiments yield conserved quantities, which are inserted into the standard model as mathematical symmetries.
What makes the standard model somewhat incoherent and non-unified is the exact same. Thus we desire a theoretical model of symmetries that yields the conserved quantities in experiment.
Wow, this was a great introduction! I'm currently taking a QFT course and this video helped me to grasp the bigger picture
This is well done because although it was a simplification, it remained a fully correct description.
Really amazing series, thanks a lot
Great work!
Thanks for this nice video and your amazing channel 😊😊😊😊😊😊😊😊😊😊
i dont know why i didnt know your canal before
This is amazing stuff!!!
Brilliant!!
Amazing video
Wow! Big thanks
You read my mind I wanted to learn abt this n only saw grand unified celery
Im gonna make a prediction :
2 years from now this channel will get 500k+ subs
ur wrong mate
sadly not even close
Wowww thank uu
wow awesome
The Video is so nice that i would like to use it as a source for my Bachelor-thesis. Which sources (Books) have you used for the video.
3:11 I'm pretty sure Noether's theorem only applies to global (spacetime and internal) symmetries, but not local ones.
A question: why would one want to gauge a symmetry? (if we didn't already know that the photon exists and is a U(1)-connection and is coupled to the electron via a given lagrangian term, why would we find it natural that our Lagrangian should be invariant under the local symmetries?)
@rv706 Sure it is natural to consider such a symmetry! First and foremost, it is a very simple way of including such a local symmetry into a theory, so why not investigate it, especially because the result is interesting physics? The study of how symmetries (whether they are physical or not) impact physics is incredibly common due to the fact that these can reveal fundamental aspects of QFT that are easier to extract due to the additional symmetry. For example, supersymmetry and conformal symmetry are not physical symmetries (that we know of), but there are huge communities of physicists that study theories featuring such symmetries because they can give more insight into QFT as a whole. Another important example of this is large-N gauge theories which again, are not physical but give insight into physical theories such as QCD and electroweak theory.
If we want to talk about actual physics, the whole U(1) connection, etc. is fairly irrelevant for the original motivation of including such a symmetry in a physical QFT. Really, the motivation came from originally quantizing the free, non-interacting electromagnetic field (one of the simplest Lorentz-invariant field theories that one can write down and one that we know is physical). In classical electromagnetism, the electromagnetic 4-potential features a symmetry under shifts of 4-gradients of some scalar field, known as a gauge symmetry. After quantizing the free theory, this symmetry is shared by the quantum theory. We also know that in classical electromagnetism, the electromagnetic potential couples to a conserved current in a way which is also invariant under this same transformation, so one would also like an interacting quantum theory of electromagnetism to also share this feature. It turns out that the free Dirac theory has a global U(1) flavor symmetry which leads by Noether's theorem to a conserved 4-current. So, it is very natural to consider a theory where the quantized EM field couples to this conserved current in the same way as it does in the classical theory. However, it turns out that including such a coupling breaks the gauge symmetry. One can save the gauge symmetry by upgrading the global U(1) symmetry to a local one (really, you also keep the global symmetry) and the whole theory is invariant under the combined transformation of the Dirac fields and the quantized EM field.
Great summery indeed
What about scale transformations (which could also be interpreted as shape transformations)?
For instance pressure is a special kind of transformation or what do you call it? I am not that good in math. But it does come about when you want to calculate entropy.
Hmm I'm not sure exactly what you are referring to with pressure/entropy, but scale transformations are actually quite interesting! Having a scale-invariant quantum theory is actually quite tricky because quantum mechanics ties together energy scales and length scales. So if you want a scale-invariant theory, you also need a theory which doesn't change when you change the energy scale, which turns out to be pretty difficult to do! This actually falls under an extension of Lorentz transformations, known as conformal symmetry and a lot of very interesting, very important results have come from conformal field theories!
Great video! Well needed break from hours of mathematic mayhem being thrown at me on wikipedia pages. Maybe at some point, if you havent all ready, you could cover hilbert space or the higgs field (which is asymmetric from what I've read). Thanks!
Symmetry is dual to conservation -- the duality of Noether's theorem.
Global is dual to local.
Generalization (waves) is dual to localization (particles).
Internal is dual to external or inclusion is dual to exclusion.
Positive is dual to negative -- electric charge or numbers.
Null vectors (photons, Bosons) are dual to null spinors (matter, Fermions).
Sine is dual to cosine or dual sine -- the word co means mutual and implies duality.
Duality is a symmetry and it is being conserved according to Noether's theorem.
Space is dual to time -- Einstein.
A pattern is emerging here!
"Always two there are" -- Yoda.
Pronunciation tip: look up the IPA on Wikipedia (for people like Noether) or use translate.google.com set to the appropriate language and hear what it sounds like. Again, for people like Noether - not “Nether”!
So what is the difference between positive and negative charges? I know they attract and stuff, but what are they in terms of the phase and its symmetry? Why do fields have an intrinsic charge and what determines it?
@David Hand This is a fantastic question. The charge of a particle actually determines how much and in which direction this phase rotation actually acts on the field. So, if I make a gauge transformation (a phase rotation by some amount, theta) on an electron (charge -1) and an up quark (charge +2/3), the electron will rotate clockwise by theta whereas the up quark will be rotated by 2/3*theta counterclockwise (note again that all these rotations are happening in this internal space: these aren't actual physical rotations). In a sense, you can think of the charge as telling you how "strongly" the transformation acts on the field which directly determines how "strongly" the field couples to the gauge field. The reason why the fields have an intrinsic charge is simply because they do couple to the gauge field in the first place, so they must be affected by these transformations somehow.
As for what determines this charge: this is a more complicated question. If we were to look at QED on its own, the answer is nothing. The charges can be completely arbitrary and everything is completely consistent. However, when we start putting together the standard model, we end up finding that at some point, QED was unified with the weak interaction (into an "electroweak" interaction), forming a set of different gauge symmetries with a whole slew of weird interaction rules. Many of the charges under these new gauge symmetries are determined by making sure that these interactions respect the gauge symmetry. However, this doesn't actually completely fix everything, but all this has done is make sure that the symmetry is respected classically. When we look at quantum corrections, we find that these can break the gauge symmetry, even if it is a true symmetry classically (this is known as an "anomaly"). Ensuring that the anomaly cancels and we maintain our symmetry does fix all of the electroweak charges up to an overall normalization. Once the eletroweak symmetry is spontaneously broken by the Higgs mechanism, combinations of these electroweak charges end up becoming standard electric charges.
It's all a bit confusing, but the short answer is that the charges are determined by the fact that *all* of the gauge symmetries of the standard model are good symmetries, not just QED.
@@zapphysics can you name some books on QED and Standard Model? Beside Feynman's "Strange Theory of Light" that you've already recommended :)
Suggest me an awesome book for this
I can't wait for this
great video just what I needed!
why the global transformation is no good though? (I understand that because its particle like its can be local but why is has to be local?)
@yuval bechar Glad you enjoyed the video! And this is a good question. Here is another way to think about it: we know from classical charge/current conservation that, in a given region of space, the change in the amount of charge in that region is equal to the amount of charge that has left or entered that region (this seems trivial, but it's saying that charge can't just disappear or appear, which is exactly what we expect from conservation). The key is that different points in spacetime can be conserving charge in different ways (in your house, you might be pumping electrons in, but in mine, I am pumping protons in), and the two don't depend on each other. The region of spacetime we choose can be arbitrarily small. This is the definition of a local quantity: something that depends only on what is happening immediately around it.
@@zapphysics got it thank you so much!
Could someone explain in easy words, so global tranformation are external transformations and local transformation are internal transformation ?
No. Global transformations are the same everywhere. The external transformation is done externally. Like rotating the system. But if your system is a ball, another external transformation could be to squeeze it into an ellipse. This transformation has affected the ball in a different way at different points. Thus it is not global. A global transformation also needn't be external, imagine giving your field a global phase shift, try multiplying each field with exp(ig\phi). This will be a global transformation if g and phi is independent of spacetime x.
This is not external (it would be internal), because you couldn't simply implement this shift 'in real life'. If you let this shift be dependent on x as well, this transformation would also be a local one.
Atleast that's how I understand it.
@@willys6403 i did not understand last part what do you mean by phase shift, what is that i do not get it. I am not a physiscist
@@elizabethreyna8354 A phase shift means to multiply your field with a complex number with modulus one. The reason why we want this symmetry, is because quantum mechanically, we cannot measure different phases.
An analogy to this is the following: if your field is an ocean, then you can imagine a phase shift as moving each wave in the ocean by some amount. Say you let each wave move a meter in its direction. The ocean will look (more or less) the same. Since we moved each wave in the ocean (a wave "phase shift") by the same amount, this transformation was global :)
@@willys6403 still confusing what a ohase means 😢😢😢😢. You say like an ocean but i cannot grasp the analogy. All information i look for says the same like your refering to multiply that by a modulus but what means that.
I can't keep up with this... and am trying desperately to cope with the effusive response of other commenters
Spectacular video!
Spinors are most naturally represented by complex numbers, but we don't have to, do we? We can use a sin and cos and a bunch of cumbersome algebra. Does that mean we can take apart the symmetry into two parts and get two conserved quantities? (electric and magnetic?) Or are they so fundamentally connected that only the combined object is symmetric and corresponds to electric charge and no magnetic monopoles?
@Narf Whals We certainly don't have to express spinors as complex objects! A real spinor is known as a Majorana spinor. Due to the fact that they are real, it turns out that we actually can't couple them to gauge fields in a way that preserves all of the spacetime symmetries of the theory. In other words, if we have a Majorana fermion, it has to be charge-less. This is why neutrinos could possibly be Majorana fermions (they aren't charged under either QED or QCD) whereas charged leptons and quarks can't be.
@@zapphysics Symmetry is dual to conservation -- the duality of Noether's theorem.
Global is dual to local.
Generalization (waves) is dual to localization (particles).
Internal is dual to external or inclusion is dual to exclusion.
Positive is dual to negative -- electric charge or numbers.
Null vectors (photons, Bosons) are dual to null spinors (matter, Fermions).
Sine is dual to cosine or dual sine -- the word co means mutual and implies duality.
Duality is a symmetry and it is being conserved according to Noether's theorem.
Space is dual to time -- Einstein.
A pattern is emerging here!
"Always two there are" -- Yoda.
It seems so obviois. Do permutations of symmetrical systems, and if theyre not syymetrical, as in providing a result that is not consistence with our observed reality, find a field, or force that does.
czcams.com/video/J3xLuZNKhlY/video.html in this video at 1:05 there's an simulation it is called as energy density of gluon field fluctuation ,now i wanted to know is this simulation an image of one of 17 quantum fields(i.e gluon-field)?
Heh, 'Emmy Nether'. German: Nurt-her
Wow, great introduction to why symmetries are so important in modern physics! :D I can't quite believe how you managed to put this AND a smooth intro to gauge theories into a 10 min video 🤯
You guys are pioneers thats how it be dog.
@@umwhoalol 😊
@Pretty Much Physics @umwhoalol You are too kind! I really appreciate your support!
Wooo, looking forward to this series!!
Absolutely loved the video. Please continue!!
What if symmetry under rotations leads to conservation of angular energy? That is what is conserved in reality.
Local symmetry doesn't correspond to any conservation !
We need a slightly deeper video about QED. Never mind going over to the other Standard Model theories before giving a better understanding of it. Giving clearer definitions of things. Not the 20 hour university course but maybe the 1 hours beauty only if that is doable. I wonder.
A man once said that about quicksand. Be careful what you ask for :)