As a physics student with a deep prepararion in particle physics, I was really curious to see how renormalization would play out in a condensed matter scenario, as in QFT this "coarse graining" procedure is really pushed under the rug and messy paperwork involving reabsorbing infinities into physical constants is commonly used instead. I love the idea of studying fundamental physics (or at least the closest thing we have to it), but the astonishing variety of phenomena that arise from emergent physics and the beautiful maths behind them has been capturing my attention recently. Amazing video!
Great video! When looking into QFT, I had heard of "renormalizaiton" and the "renormalization group" countless times, but I could never find a quick introduction that explained what it meant for beginners. Those vector fields towards the end that show fixed points are an amazing visualization that really helped things click.
As someone who hasn’t understood RG flow conceptually after attempting many times over 2 years, I really want to thank you for this awesome video!! Will definitely revisit calculations with this in mind :)
Glad to hear it was helpful! I had a similar experience of only half understanding it after seeing it a few times in different places, and I made this shortly after it finally clicked after taking a course on it. I think the trouble is partially that it is fit into physics curricula in less than optimal places, but that is a topic I could write an essay on... and will probably blog about eventually. :)
I hadn't heard of this topic before, but it's really interesting! Especially the part about phase flows as you zoom out - that's a really nice schematic way of showing how you'd need fewer parameters to describe the state at larger scales.
This is a great video, but I do agree with QuasarEE. As somebody who attempted to self teach statistical field thoery via working through Kardars Stat Physics of Particles & Fields MIT OCW videos & textbooks, I can personally attest to just how confusing this subject is for those outside of the field (and even largely within.) I think it merits a slightly longer video. I'm going to re-watch this a 2nd or 3rd time and see what specific advice I can offer.
Amazing video! It was a long time ago when I had that realization moment last time. Most of the SoME videos I watched were about just interesting little questions, but with this one I feel like it actually increased my understanding of the world a little. I love it, please make more.
I always wondered what was meant by "the numbers go to infinity, which physics says is impossible" always being thrown around in documentaries and explanations of quantum physics and renormalization. This explains the process quite nicely as a sort of projection operation.
It's more that reality says infinity is impossible, so if your equations give the answer of infinity then your equations are missing something. This avoids wondering whether "physics" means the equations (which are always a simplification) or reality (which is too complicated to model perfectly). For example, what's the density at the center of a black hole? The correct answer is "nope", meaning the equations give infinity so they are missing something; in this case the quantum nature of space-time at the smallest scale. More familiarly, what happens when an infinite force meets an object of infinite mass? Nope. What would you see if you flew _at_ the speed of light rather than close to it? Nope. And so on.
This is an OUTSTANDING video. Very nicely done - I've never seen renormalization presented in a way that really made the key ideas clear. Thanks for your effort.
As someone who doesn't study physics and was only interested in this topic to better understand a sci-fi concept, I have to say that this is an incredibly good and easy to follow explanation. Thanks for the video!
Unexpecetedly lesser views than what the content quality deserves. Kudos though , keep coming up with these simplistic videos explaining the confusing and lesser understood concepts of physics.
Great presentation. This idea is very powerful and kind of needs a lot of detailed examples for it to really stick. That said, this video is great at presenting the relevant basic intuition, quite a lot Bette than many books and lectures I’ve come across. Well done!
I have been reading about this topic in many QFT books the last weaks, comparing it to other fields ofcourse makes it much clearer, perfect, thank you. Pls make more videos.
Beautiful and insightful video. Thank you so much. Please make more videos like this if you can. I am sure that anyone physically minded will enjoy them very much.
Wow, what a hard topic to tackle. This was a really interesting video, and I had the same questions about phase transitions when I took chemistry. I think the video would have been a little easier to follow if you interweaved the graphics animations with the math for intuition. Really interesting topic though. I want to come back and watch it a few more times to really understand the renormalization technique, because that renormalization group flow diagram was so neat.
Thanks for the feedback! Are there any spots in particular where graphics needed math or where the math needed graphics? I am planning on making a written version of this with more details and recommended reading that I hope will function as an easier to use reference, so any suggestions are actively useful.
I will add something from me. Good topic, visualisations a little to fast ( will be better to let visualisation follow your words, sometimes you can add shortened definitions like for words like "concetration" . It will help to catch the idea faster for people who don't know much about it. Put micro closer to you. Even if you have good articulation and the correct pace of speech, you sound too soft and indistinct.
I had to watch the video 2 times... but it was worth it! It's very difficult to the balance the length and complexity for such a hard topic. I personally liked it. Thanks.
Just beautiful! My only feedback is that the Renormalization group is actually a Renormalization semi-group as it doesn't always have unique inverses (as the number of parameters reduce at lower energy scales).
Thank you so much for this intuitive overview! I am really looking forward to your detailed explanation. It would be great to see how the math plays out in an example in a more slower way and also how to get the renormalization flows. I can see already how this has far-reaching applications beyond physics as well (I'd love to see this eventually applied in economics, but unfortunately they're all sub-par in math...)
This is fantastic! I've been meaning to learn about renormalisation for years, but never got around to it. This is a wonderful overview. One thing that I feel you might have missed (or maybe not, I'm not sure) is the link to universality classes. Is it the case that something about the fixed points of the renormalisation flow (maybe their value in some suitable coordinate system, or maybe their topology, or something else) determines the universality class of the system? In any case, wonderful video! 👏
This idea also explains the coexistence of both liquid and gas phases for a range of temperatures, as you are moving near the "divergent line" that separates the renormalization flow towards liquid or gas
Wow great video! This is a very meta subject analyzing what dynamical systems arise from trying to recursively approximate larger scale behavior. Small remark; I think you could’ve spent a bit more time on explaining the coarse graining concept, especially around 4:23
Nice job, it's a great overview of fluids mechs and this tool. Fully linear algebra friendly and computer programming intuitive by linear transformationss🤗🤓🌶️🌶️
This is an actual masterpiece. I learned all this during my statistical physics class in my bachelor, but I just realized that I never understood it before today. Thank you for creating this brilliant piece of work. Can I ask you what you're working on/researching?
How would you recommend someone to learn this topic with basic math background (cal, DE, Linear) and basic physics courses (mech, E&M, waves, QM)? Is there any book that you recommend?
Amazing video, sir! Is there any chance to see next part with more practical examples of renormalization? I am especially interested in application of this technique to gases and fluids.
Very nice video, though it leaves me with a question: You say that going from small to coarse scale is an averaging process. However, in your renormalization calculation I see nothing that resembles averaging. The only assumption you make on your delta_m term is that it is a small perturbation. But how do I link it to averaging out what happens at coarse scale? This is where the method does not sound very rigorous. Could you please comment a bit on that? Thank you so much, it is a great video!
Thanks for the feedback! First, I should say that the description I give is definitely not rigorous and deliberately glosses over many subtleties for the sake of clarity. When actually doing these calculations, the steps are much more exact and mathematically rigorous, but it becomes much harder to keep track of the big picture. I plan to do a more detailed job in the written version of this presentation, and I will try to recommend some good textbooks etc on the topics. The "averaging" happens when we evaluate the sum over delta m. We are taking all values of m that go to m bar (equivalent to fixing m bar and taking all values of delta m), and saying the probability of m bar is the sum of the probabilities of all those ms. Since we also are dividing out by a normalization factor (which I dropped to make things more legible), this sum is an average.
@@brokensymmetries6641 Thank you for your reply. When I say rigorous, I do not mean "mathematically rigorous", I mean coherent, in the sense that if you introduce the concept of averaging, then in the rest of the video it should be clear where that averaging comes to play. My first impression is that the idea of averaging disappeared in your calculations. I will watch the video again to make sure I did not miss important parts.
Dude, I feel the same. I love science, I love learning about all of these concepts...but this math makes me feel like one of the apes in the opening of "2001: A Space Odyssey"...just grunting and trying to comprehend how tools work. And I have an IQ in the 98th, or 99th percentile, based on several IQ tests I have been professionally administered between age 11 and age 49 (I am 51 now) and I understand a lot of difficult concepts...but I can't even *comprehend* how someone could even begin to understand this math. It's all random symbols, and I don't even see how you can use these to get an answer in like, numbers.
PLEASE go learn how to normalize audio levels properly. This video’s audio is WAY too low volume. The quiet audio makes it harder to hear, but also risks damaging ears because of the sudden volume increase that can come from the *next* video with normal audio levels suddenly blasting afterward.
When the wise point at the moon, the fool only see the finger pointing at the moon. You’re the fool here in case you are too dim to understand the analogy.
Useless comment in the thread. When the wise point at the moon, the fool only see the finger pointing at the moon. You’re the fool here in case you are too dim to understand the analogy.
COARSE graining, not COURSE graining at 1:50 :D
Indeed. Woops.
Thanks for pointing it out!
@@brokensymmetries6641 Ein typisch deutscher Fehler xD
course grinding
@@brokensymmetries6641 COuld you share the code that allowed you to make this?
The best intuitive no-bs explanaion of renormalization group I have seen on youtube.
By some miracle of your genius I actually understood this. You sir actually made me smarter. This deserves millions of views.
As a physics student with a deep prepararion in particle physics, I was really curious to see how renormalization would play out in a condensed matter scenario, as in QFT this "coarse graining" procedure is really pushed under the rug and messy paperwork involving reabsorbing infinities into physical constants is commonly used instead. I love the idea of studying fundamental physics (or at least the closest thing we have to it), but the astonishing variety of phenomena that arise from emergent physics and the beautiful maths behind them has been capturing my attention recently. Amazing video!
Great video! When looking into QFT, I had heard of "renormalizaiton" and the "renormalization group" countless times, but I could never find a quick introduction that explained what it meant for beginners. Those vector fields towards the end that show fixed points are an amazing visualization that really helped things click.
hey big fan of your work, I am trying to do QFT too
As someone who hasn’t understood RG flow conceptually after attempting many times over 2 years, I really want to thank you for this awesome video!! Will definitely revisit calculations with this in mind :)
Glad to hear it was helpful! I had a similar experience of only half understanding it after seeing it a few times in different places, and I made this shortly after it finally clicked after taking a course on it. I think the trouble is partially that it is fit into physics curricula in less than optimal places, but that is a topic I could write an essay on... and will probably blog about eventually. :)
@@brokensymmetries6641 indeed, tedious calculations often overshadow the concept
Same dude😂
@@brokensymmetries6641 do you have a patreon?
I hadn't heard of this topic before, but it's really interesting! Especially the part about phase flows as you zoom out - that's a really nice schematic way of showing how you'd need fewer parameters to describe the state at larger scales.
This is a great video, but I do agree with QuasarEE. As somebody who attempted to self teach statistical field thoery via working through Kardars Stat Physics of Particles & Fields MIT OCW videos & textbooks, I can personally attest to just how confusing this subject is for those outside of the field (and even largely within.) I think it merits a slightly longer video. I'm going to re-watch this a 2nd or 3rd time and see what specific advice I can offer.
Looking forward to it!
Amazing video! It was a long time ago when I had that realization moment last time.
Most of the SoME videos I watched were about just interesting little questions, but with this one I feel like it actually increased my understanding of the world a little.
I love it, please make more.
I always wondered what was meant by "the numbers go to infinity, which physics says is impossible" always being thrown around in documentaries and explanations of quantum physics and renormalization. This explains the process quite nicely as a sort of projection operation.
It's more that reality says infinity is impossible, so if your equations give the answer of infinity then your equations are missing something. This avoids wondering whether "physics" means the equations (which are always a simplification) or reality (which is too complicated to model perfectly). For example, what's the density at the center of a black hole? The correct answer is "nope", meaning the equations give infinity so they are missing something; in this case the quantum nature of space-time at the smallest scale. More familiarly, what happens when an infinite force meets an object of infinite mass? Nope. What would you see if you flew _at_ the speed of light rather than close to it? Nope. And so on.
This is an OUTSTANDING video. Very nicely done - I've never seen renormalization presented in a way that really made the key ideas clear. Thanks for your effort.
As someone who doesn't study physics and was only interested in this topic to better understand a sci-fi concept, I have to say that this is an incredibly good and easy to follow explanation. Thanks for the video!
Unexpecetedly lesser views than what the content quality deserves. Kudos though , keep coming up with these simplistic videos explaining the confusing and lesser understood concepts of physics.
Absolutely beautiful! This video clarified ideas I have been struggling with for years. I'll look forward to your upcoming work :)
Best video I’ve seen on the topic by far.
Wow, this was a great introduction! :) Hope to see more of you soon
Great presentation. This idea is very powerful and kind of needs a lot of detailed examples for it to really stick. That said, this video is great at presenting the relevant basic intuition, quite a lot Bette than many books and lectures I’ve come across. Well done!
Excellent video, looking forward to what else you make
This is the best summary of renormalization flow I have encountered so far.
This is one of the best!
Absolutely amazing video! Subscribed.
I have been reading about this topic in many QFT books the last weaks, comparing it to other fields ofcourse makes it much clearer, perfect, thank you. Pls make more videos.
Beautiful and insightful video. Thank you so much. Please make more videos like this if you can. I am sure that anyone physically minded will enjoy them very much.
Wow, what a hard topic to tackle. This was a really interesting video, and I had the same questions about phase transitions when I took chemistry.
I think the video would have been a little easier to follow if you interweaved the graphics animations with the math for intuition.
Really interesting topic though. I want to come back and watch it a few more times to really understand the renormalization technique, because that renormalization group flow diagram was so neat.
Thanks for the feedback! Are there any spots in particular where graphics needed math or where the math needed graphics? I am planning on making a written version of this with more details and recommended reading that I hope will function as an easier to use reference, so any suggestions are actively useful.
I will add something from me. Good topic, visualisations a little to fast ( will be better to let visualisation follow your words, sometimes you can add shortened definitions like for words like "concetration" . It will help to catch the idea faster for people who don't know much about it. Put micro closer to you. Even if you have good articulation and the correct pace of speech, you sound too soft and indistinct.
I already had a little knowledge of this, so I might be biased, but I found this really helped to clarify some ideas as to what's going on!
I had to watch the video 2 times... but it was worth it!
It's very difficult to the balance the length and complexity for such a hard topic. I personally liked it.
Thanks.
Just beautiful!
My only feedback is that the Renormalization group is actually a Renormalization semi-group as it doesn't always have unique inverses (as the number of parameters reduce at lower energy scales).
Thank you so much for this intuitive overview! I am really looking forward to your detailed explanation. It would be great to see how the math plays out in an example in a more slower way and also how to get the renormalization flows. I can see already how this has far-reaching applications beyond physics as well (I'd love to see this eventually applied in economics, but unfortunately they're all sub-par in math...)
Nice, this gave me a high level conceptual understanding of renormalization. Would need to go through the calculations myself to get all the details.
This is fantastic! I've been meaning to learn about renormalisation for years, but never got around to it. This is a wonderful overview. One thing that I feel you might have missed (or maybe not, I'm not sure) is the link to universality classes. Is it the case that something about the fixed points of the renormalisation flow (maybe their value in some suitable coordinate system, or maybe their topology, or something else) determines the universality class of the system? In any case, wonderful video! 👏
We need more CMT on TH-cam!
Great video btw :)
Awesome video. Thank you for making it.
astonishing video, gave me some really interesting new insights to things I've worked for some time!
This is an awesome explanation Ben!! Hope to see more from you soon.
This idea also explains the coexistence of both liquid and gas phases for a range of temperatures, as you are moving near the "divergent line" that separates the renormalization flow towards liquid or gas
Thank you very much for the great video!
Wow great video! This is a very meta subject analyzing what dynamical systems arise from trying to recursively approximate larger scale behavior.
Small remark; I think you could’ve spent a bit more time on explaining the coarse graining concept, especially around 4:23
Amazing video!!
This is very good! Thanks! Looking forward to more videos!
Excellent
Wow this was super amazing introduction to the topic. Well done and keep up.
so helpful
GREAT video! Please make more lvideos like this
Thank you so so much for this absolutely brilliant video !!!
I would love to see the blog version of this video with some additional details
Nice job, it's a great overview of fluids mechs and this tool.
Fully linear algebra friendly and computer programming intuitive by linear transformationss🤗🤓🌶️🌶️
Wow Thanks!
This is an actual masterpiece. I learned all this during my statistical physics class in my bachelor, but I just realized that I never understood it before today. Thank you for creating this brilliant piece of work. Can I ask you what you're working on/researching?
You enlightened me. Thank you very much!
The best explanation I have ever encountered on the RG... can't wait the next video. Keep up the wonderful work!
How would you recommend someone to learn this topic with basic math background (cal, DE, Linear) and basic physics courses (mech, E&M, waves, QM)? Is there any book that you recommend?
Great video. If you can get the volume a bit higher it would be easier to hear on more devices. Thanks!
אחלה סירטון
GREAT !!!!!!!!!!
Thank you!
Amazing video, sir! Is there any chance to see next part with more practical examples of renormalization? I am especially interested in application of this technique to gases and fluids.
Thanks, this is a fantastic video! I was wondering what a good textbook is to study this stuff in the context of materials!
wonderful video!
Is it safe to assume the temperature parameter in the example is interpreted the same way at all scales?
Very nice video, though it leaves me with a question: You say that going from small to coarse scale is an averaging process. However, in your renormalization calculation I see nothing that resembles averaging. The only assumption you make on your delta_m term is that it is a small perturbation. But how do I link it to averaging out what happens at coarse scale? This is where the method does not sound very rigorous. Could you please comment a bit on that? Thank you so much, it is a great video!
Thanks for the feedback!
First, I should say that the description I give is definitely not rigorous and deliberately glosses over many subtleties for the sake of clarity. When actually doing these calculations, the steps are much more exact and mathematically rigorous, but it becomes much harder to keep track of the big picture. I plan to do a more detailed job in the written version of this presentation, and I will try to recommend some good textbooks etc on the topics.
The "averaging" happens when we evaluate the sum over delta m. We are taking all values of m that go to m bar (equivalent to fixing m bar and taking all values of delta m), and saying the probability of m bar is the sum of the probabilities of all those ms. Since we also are dividing out by a normalization factor (which I dropped to make things more legible), this sum is an average.
@@brokensymmetries6641 Thank you for your reply.
When I say rigorous, I do not mean "mathematically rigorous", I mean coherent, in the sense that if you introduce the concept of averaging, then in the rest of the video it should be clear where that averaging comes to play. My first impression is that the idea of averaging disappeared in your calculations.
I will watch the video again to make sure I did not miss important parts.
Good video.
I'm a commercial student who loves science,and somehow I am here XD Nd all I can do is wonder how y'all are this smart,I understood nothing
Dude, I feel the same. I love science, I love learning about all of these concepts...but this math makes me feel like one of the apes in the opening of "2001: A Space Odyssey"...just grunting and trying to comprehend how tools work.
And I have an IQ in the 98th, or 99th percentile, based on several IQ tests I have been professionally administered between age 11 and age 49 (I am 51 now) and I understand a lot of difficult concepts...but I can't even *comprehend* how someone could even begin to understand this math. It's all random symbols, and I don't even see how you can use these to get an answer in like, numbers.
Super
PLS MAKE MORE VIDS :O
Physicists are magicians
Thêm intro di cô
thumbnail go dark when scroll
PLEASE go learn how to normalize audio levels properly. This video’s audio is WAY too low volume. The quiet audio makes it harder to hear, but also risks damaging ears because of the sudden volume increase that can come from the *next* video with normal audio levels suddenly blasting afterward.
When the wise point at the moon, the fool only see the finger pointing at the moon. You’re the fool here in case you are too dim to understand the analogy.
you sound tired... put some more juice into your voice
Useless comment in the thread. When the wise point at the moon, the fool only see the finger pointing at the moon. You’re the fool here in case you are too dim to understand the analogy.
Amazing video!!