The Biggest Ideas in the Universe | 11. Renormalization
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- Опубліковано 1 чер 2020
- The Biggest Ideas in the Universe is a series of videos where I talk informally about some of the fundamental concepts that help us understand our natural world. Exceedingly casual, not overly polished, and meant for absolutely everybody.
This is Idea #11, "Renormalization." When you include particles in Feynman diagrams of all possible energies, you often run into infinite results, which are clearly wrong. The modern approach to this problem is to work with "Effective Field Theories," in which we admit that we only understand physics up to some cutoff energy scale. While enormously successful, this EFT paradigm also runs into issues with the Higgs mass and the cosmological constant.
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Hundreds of thousands of people learning about renormalization in QFT. Astonishing! There is hope for mankind.
With all of the ugliness going on in the world right now, these videos remind me of how incredible humanity can be at our best. Thank you very much Prof Carroll.
What ugliness you are thinking about ? (Just want to know)
@@srghma everything was about covid 3 years ago
I am a theoretical physicist, working in the field of quantum gravitation, and I can say that this is the most straightforward explanation of the concept of renormalization compared to a lot of actual physicist books. You got yourself a new subscriber, Sean!
Does a black hole center have lower energy density, than a crust? In holography they renormalize the fields on the boundary towards lower energies. Going from the shell towards the center we encounter lower energies, no?
This is the best explanation i have ever seen on why infinities occur, why they aren't real, and how we correct for them without skewing results. Keep the great vids coming!
Poor Sean, wanted to keep the episodes short, but they are just getting longer and longer. :) I'm not complaining tho.
Curiously, the opposite of his hair! :3
As a person who studies Philosophy, and likes Science (especially Physics) I'm super happy to see a serious Scientist that takes Philosophy seriously and gives it the proper respect it deserves!
Love your work! Keep it up!
3:30 Sean Carroll is the Bob Ross of painting lush quantum fields with little trees with branches coming out.
Everytime a probability wave collapses, it's a happy accident
CoinStudio Crosstec I love that!
We need Sean Ross Happy Fields memes and Tshirts... NOW!
Denis Goddard Ha! Yes!
Haha exactly!🤣
This series is precious
Yep. Him and the Brian Greene ones are so good. The format is awesome and in particular the Q&A stuff.
I have an exam tomorrow, but who cares? Sean Carroll posted a new awesome video! :-)
I am really enjoying how deep we are going here, keep doing Dr.Sean!
Very cool comment
That’s what she said
Definitely the best public explanation of renornalization that I have ever seen. AND he even justified it by citing the fact that when we renormalize we implicitly accept that we are just writing an EFFECTIVE field theory that approximates some deeper theory that describes interactions at energies above the cutoff (e.g. maybe String Theory, but probably not)
Beautiful!!
I am not sure your interpretation is correct though. In renormalizable theories (not EFTs), the renormalization scale is arbitrary and there is no need for new physics at some scale, unlike EFTs. In EFTs, you can still renormalize your theory order by order choosing your renormalization scale arbitrarily (hence the RG group flow just like renormalizable theories) but there is a cut-off. These are two different things. Renormalization itself does not necessitate any kind of physics beyond a renormalizable theory (e.g. QCD).
@@quantumgravity7704 The modern (majority) opinion in the field is that QFT is a framework for writing effective field theories. Given the symmetries (and broken symmetries) that we observe at the energy scales probed, no matter the form of the "True" theory that applies at higher energies (Strings, Loops, etc), the world will "effectively" appear to be composed of quantum fields.
Renormalization has become my favorite topic in this series of lectures, and Ken Wilson is a hero. I'm so glad that he figured out how to get rid of all those "infinities." There is a point when concepts exceed available experiments, and it becomes a necessity to have a precise language to communicate coherently. Thanks
Like a lot of big discoveries, Ken Wilson wrapped up the ideas of his predecessors like Gel-mann.
This has very quickly become my favourite series on youtube, thank you for the in-depth explanations Sean.
I felt that this video was where the prep work started to crystallize. Sean is a star - love the style. Cannot help smiling when Sean pauses to clarify x, y and z and draws a little axis ……….. then rolls on to Fourier transforms, Hamiltonian, Lagrangian, Hilbert space and solving the Schroedinger equation in about 10 secs without skipping a beat. Definitely looking forward to the rest of the videos (not lectures)!
A welcome break from everything going on right now. Thank you!!
I am not a physicist but have a genuine interest in it. So glad Dr. Carroll explains it so beautifully and includes math to explain concepts that are understandable for a non-mathematician like myself. Can’t wait for more like these on other topics from Dr. Carroll. Thanks again 😊
Absolutely fascinating and enlightening. This is the first time I’ve heard the problematical infinities explained. Thank you!!
This soothes my soul, thx. I don’t mean all that crap mixing pseudo spirituality with physics, just staying on the logical and technical ground of it it’s so rewarding
Sean Carroll and Brian greene sir my role model sean sir lot's of love from india
As a (semi-retired) Canadian professor of psychology, apart from my own field of social psychology, one of my passions is physics. During this pandemic lock down I am thrilled to be able to watch UA-cam videos from some of my favourite physicists including Sean Carroll, Brian Greene, and Lawrence Krauss. What a shame it will be when these videos come to an end. The promotion of the physical, biological, and social sciences in society is a must when certain populations, especially in the United States, appear to be turning away from science and filling their knowledge void with religion and superstition. Humanity needs a greater knowledge and understanding of science, not superstitious nonsense.
Totally agree and very elequently expressed.
There is no question that the basic claims of religion are false. One has to wonder though why this meme managed to survive for so long. Is it the ferocity in fight it gives its bearers? Do groups need a strong common "banner" to tell friends from foes? Or is it the fact that a false positive in the wild is just safer than a false negative?
@@zwz.zdenek when you get right down to it, I have found, by asking many people, it is the fear of absolute death. It's one of the greatest challenges of being sentient, and, born in a time when death is an absolute certainty. Put it this way, imagine a time in the future where you could chose, to either age naturally, and die, or age naturally, and transfer your body to a younger one, or not age at all, or transfer to some synthetic body, I wonder how many would allow themselves to end, given that life in the future could be a total transformation from the crappy way we live today, chasing wealth accumulation just to live out our last days in some level of partial comfort, if life in the future, due to technology, was a utopian paradise, the need for a god, or religion, becomes less necessary to believe in, to be indoctrinated in. I don't think that religions are needed to teach people to be decent to each other, given a paradise, there's no need. If we can reach a state where technology can really save us, god , the notion of it, becomes meaningless.And it is my hope, that one day, gods and religions are just an ancient illogical curiosity, some are already.
Religion and science are able to exist together. If someone makes an excuse by claiming religion they are simply not smart enough to work out the science. Doesn’t make their religion wrong.
@@zwz.zdenek interesting to know how you now this. Prove it.
Hi Sean, this is the first one I've caught so far, will definitely go back and watch the others. You've pitched this at the absolute perfect level for someone like me, who kind of gets what your talking about but doesn't have the maths to back it up! Thanks very much for all you do in promoting physics!
Stopping everything and starting to watch, as usual! Thanks Sean!
Prof. Carroll, my gratitude field is in the Ultraviolet 🎇 Thank you for taking the time to share this knowledge
Best Physics Series on youtube. Keep them coming Dr. Carroll!
I do not have the education to understand this. I'm just a guy with a bit of math (nothing above diff eq) and almost no physics outside the occasional Wikipedia binge and memories of a basic physics class fifteen years ago.
While I certainly couldn't follow much of this subject matter, I do feel like I got something out of this, even if it's only a small intuition of how physics theories work.
The fact that I got anything at all out of the video is a testament to your presentation skills. Excellent video!
These are such amazing lectures. Especially these last two-three QFT lectures are so useful, gaining so much knowledge and finally understanding terms I heard about a lot but were a mystery to me, like the meaning of UV-cut off for instance. You're awesome Sean! Thank you!
Ooh here comes the big stuff
Thank you Sean for this amazing series. Wish i was younger and smarter to really grasp all these fantastic ideas but what i can grasp is so unbelievably satisfying. i can tell you truly love teaching physics and it shows.
This is a pretty deep dive into physics right here I've learned a lot already. I'm kind of sick and tired of all the beginning level programs and videos that assume that you can't follow the math so they don't have any equations or anything and although I'm not a mathematicia and I can't really follow the math John Carroll does a good job of explaining what the numbers mean as he's writing them and I don't have to know how to do any of these equations myself just by listening to him I understand what they mean and that is the main point for me cuz I've always been mystified by how they convert things of the real world into the different number value so they do their equations and he does a good job of explaining that
Interactions was a doozy, Normalization was no less! ty Sean for getting us through :)
Very very very beautiful lecture, I really appreciated it.
Thanks professor Carroll and please don't stop making video-lectures like this one.
Some of the nuts /bolts/secondary concepts/mechanisms of physics are just a inspiring as more main stream bells & whistles!
Really Fascinating lecture!
Sean Carroll is a legend! I love him.
Awesome explanation!!! Fantastic Sean!!
This is a brilliant series, the best I have seen. Thank you for attempting to educate us.
Thank you Sean Carroll, this was a great lecture, one of the few lectures I watched at normal speed :D
thanks for this, it's a good complement to the more technical and localized introductions to this topic.
Thanks for these excellent videos! I especially appreciate how you point out the parts that still need work. Some physicists talk as if all is known, my guess is it will never be. We just add piece by piece as we learn more. The progress and the relentless effort are still amazing even if, as always, a new more comprehensive theory will likely arise in the future that will recast some of these things in different concepts that have more predictive power.
Just. Wow. You made my Spring.
Wonderful presentation! Thank you. I really look forward to your UA-cam videos.
Thank you. Well done, great format, enormously appreciated.
This is great stuff. You make it seem so simple.
I hope there are some young Einsteins watching and learning from these and what Brian Greene is doing !
Present 🙋
I’m here too! However, I would rather pass all of this off to my 6 year old daughter!! So she can conquer space and I can have a mars hotel 🏨
It’s a golden age of self-learning
What is Brian Greene doing that I am missing out on?
And Sabine Hossenfelder
This is so neatly presented, thanks for making it public.
Amazingly clear and insightful, as always. Thanks a lot and I hope you will write a textbook on these thorny topics one day.
This was definitely one of the better lectures of this serie!
I really enjoy the (relative) simple but still encapsulating math in order to show the important insights.
Outstanding teacher, thank you
thank you for that great introductory video!
Brilliant series.Thank you.
Really appreciate these videos. Makes you wonder if we will ever wake up one day with no more mysteries to solve, and how depressing that day might be. But for now the rabbit hole is still deep!
Great video, thanks Sean.
Dr. Sean Carroll, in the Q&A would you spend some time on the “quantum foam” of the vacuum? I understand that Feynman virtual particles are placeholders for the complicated back-reactions of the fundamental fields. But what about these foamy short-lived particles at the ground state? Thank you.
I feel like I am getting a free education on my favorite side hustle. This is really awesome and noble of you Sean!
Side note, seems computer programmers really like physics. Several I work with are studying the subject. I wonder why that is. Maybe the simulation is reality after all:)
The series is great! Alway look forward to every video...
Great Explanation 😍😍😍😍😍😍😍
I love how down to earth this guy is!!!!! Great stuff. [GxQ=Universe]
joyfully informal!!
I finally get why astrophysics is important. We simply cannot creat tests here on earth to test tgese ideas. We have to look in nature fro answers.
best explanation ever
Awesome! Thank you :D
Masterpiece.
The need for renormalization essentially points to the fact that we don’t as yet have a handle on the ultimate underlying theory.
Hey Sean, thanks for these videos! One question that I still struggle with (and see contradictory answers) is whether Virtual Particles have any physical significance or if they are just mathematical "tricks" for doing calculations of complex field interactions. If they were the latter, there would be situations (like a free particle in a non-interacting field) where they should not matter. However, in this video, you indicated that they still cause vacuum polarization. Besides, as I understand it, Virtual Particles are directly responsible for static field forces (i.e. when a static electromagnetic field pushes/pulls on an electron). Is there a reason why they cannot be accepted as existing in reality, i.e. as another type of particle that cannot be directly observed and violates some principles, but is otherwise perfectly "real"?
Enlightning.
Though it, the explanation, seems to be very lucid and simple, but really it is not. A teacher knows the handwork behind it. It is your skill Sean. Great, fantastic ! Keep it up ! Thanks!....
Thank you
You do exactly in handwriting what I do ever since I could write... my hand is slower than my thinking, so I skip letters, start writing what I am thinking of next.
Hi the video is so good .. Can you maybe do more videos about renormalization group equation and fixed points ?
I'm interested in fixed points of renormalization group equation of high partial waves of two nucleon-scattering it will be very helpful
Pushing the effective field theory to high E's and then concluding you need new physics (i.e. postulating more particles or forces to be added to the zoo) because the results contradict experimentation implies that the theory is already presumed to be perfect but just needs some adjustments from new experimental information.
Science becomes fine-tuning without new paradigms, something that would eventually collapse in absurdities.
I feel like there's an echo in my house because every time I make a comment asking a question about something I Observer think about as he speaks the very next thing he speaks of there's something I just made a comment about. Maybe that means he's doing his job and explaining things properly maybe that means he's a good teacher.
I found the dark energy pressure estimate under an Emergent gravity model. It would be interesting to compare with an order of magnitude to the cosmological constant at quantum scales.
A couple of questions. 1. Can you think of the original UV catastrophe or the Plank theory of Black body radiation in terms of EFT? 2. A little more prosaic, what hardware & software are you using to produce your videos?
This is an absolutely outstanding lecture -- thank you soooo much !!!
PS: Could you address the "cosmological constant" in more detail. Including your comment at the very end of this lecture.... about only two items that ...
Many thanks in advance...
PS: I keep re-watching episodes to better understand -- for example --- for decades I couldn't figure out just why (and how) eV unit is being created/used....
PS2: "..electron is, as we know, NOT a fundamental particle -- it is just an excitation in electric field " .... breaks my electronics engineer's heart ... ;-))
For many purposes the electron can be considered a particle.Many great physicists considered them as particles. Sean is in the other camp .
Question about the loop-feynman diagram? What about using a harmonic oscillator on the loop? Could this solve the infinity of this loop ,an oscillator has an infinity momentum?
(1) It would be great to know where Lorentz invariance comes in. I remember reading that the Feynmann diagram approach maintains this invariance for each term. (2) Does a conformal field theory lack a cut-off? (3) It would help to know how the mass of the Higgs is measured. It is obtained as a peak in some curve. What does that curve mean?
at 11:34 i just now see, that the problem is that from E1 to E3 you have E_bar adding one way round the loop and minus E_bar going round the other way
I thought I had read that the LHC search for the Higgs boson "expected" a mass in the 120 Gev range. How does this jibe with your discussion of the hierarchy problem?
Is the numerical discrepancy in Higgs mass and the cosmological consented related to the relative difference of electrical and gradation always forces?
Love keeping the hair growing...
Deep down SC is as pure as PAM Dirac it is pragmatic to do it. We are waiting for the reality to show itself someday.
This lecture is awesome, except for one thing: The plot of the fine structure constant vs. energy should show that it’s asymptotically the true value. Unfortunately it appears as if the electric charge measured increases without bound.
Does string theory give same predictions as these effective field theories do? I mean if we can't detect the effects of the string theory framework, can we just replace the current one with it to see if it gives the same predictions? Or is each of these frameworks bound to their specific energy region?
16:24 - Groovy! ^.^
Hahah “it works very effectively - as it were”
Hi, you said that the effective charge is dependent on the cutoff scale but I thought this was only true for bare charge ( couplings) and that renormalized charge (couplings) are dependent on energy at which one probes it but is independent of the cutoff
Would fields be mere fictitious instruments to avoid the idea of unmediated action from a distance?
the effective field theory looks similar to the method of truncating an asymptotic (divergent) series that comes from a singular perturbation system. Truncate the series and take the limit of the epsilon to zero to get the leading order solution... Are the two related?
I've noticed that the values for all these units depend on time or space as a multiplier or some kind of factor in the equation. What what is the value for time in space?
Could you explain at 38:00 what the time derivatie of the Field is? As far as I understand it, it is not moving like a particle.
Sean, would the use of thermodynamic variable like pressure, volume, and temperature be considered a kind of renormalization? Admittedly, thermodynamics isn't a field theory, but it does seem to be an "effective" theory for describing physical systems that uses a cutoff distance instead of a cutoff energy. Or is this thermodynamic thinking not a faithful analogy? It seems to me that this kind of "effectiveness" is reminiscent of your discussion of appropriate levels of description in The Big Picture. Is Wilson's renormalization group an extension of this approach to encapsulating detailed mechanisms where our knowledge is limited or does it represent something entirely new and different. Thanks for these great videos! - Marc
no those variables are in a diferent category
How does the vacuum energy calculated by this method compare with the vacuum energy during the inflationary period? Could the vacuum energy be responsible for the rapid inflation? Perhaps a working theory of quantum gravity would tell us that gravity almost cancels the vacuum energy somehow.
Is the hierarchy problem actually a physical problem? It could be simply a "coincidence" that the Higgs Mass is not at the order of the Planck scale.
It seems to me that units can be replaced with terms like cardinalities. Also the different algebraic terms that stand for different numbers but have to be the same for you to do mathematical operations with a very similar in my way of thinking. So how do you assign values to cardinalities or units and make them a hierarchy? I think imaginary numbers is the solution or something very similar
Can someone provide the link to Dr. Carroll's lecture notes?
Dr. Caroll , can we say that the cutoff Energy , E* can be view as the Energy that defines our reality , because of the emergence phenomena ? I mean , if we define our reality as emergent , then the E* should be the Energy that its first ''born'' into our reality , because everything greater that E* dont matter for us ? Like the fact that Newtons equations are good enough for our day to day life , but at relativistic speeds you find it has limits .
The difference its that , we will never get more that E* ....because..well ....reality breaks down ( like a black hole for example ) .
By the way , what its the E* max ? I understand that you can have many cutoff E*, but just one should be the E* that Im talking?
I think its the E* max , where a black hole should form . Thank you !
Is it one of the options for the universe to have some maximum energy density? It would make the field equations non linear at higher energies, but what if linearity is an approximation?
There should be a msximum energy density within the universe because at some point the energy density would be sufficiently high to form a black hole, which would then promptly evaporate by emitting a load of particles and spreading the energy around.
So if I understood correctly: quantum gravity is not renormalizable essentially because it couples to too many other fields?
Seems to me that the ebar going down in the Ibarra coming up with cancel each other out as you already said the same way that these counter operations are expressions or whatever you called them do. Kind of like how a negative integer and a positive integer of the same value would make 0
What analysis of QFT!
At 10:00, you say that energy (E bar) can be any number from minus infinity to plus infinity and you add them up and what you get is an infinitely big contribution.
Can that statement be clarified further because my intuition tells me that adding everything from -∞ to +∞ is zero.
how do measure/observe the vacuum energy?