The Biggest Ideas in the Universe | 11. Renormalization
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- เผยแพร่เมื่อ 1 มิ.ย. 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?
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
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!
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!🤣
I am really enjoying how deep we are going here, keep doing Dr.Sean!
Very cool comment
That’s what she said
I have an exam tomorrow, but who cares? Sean Carroll posted a new awesome video! :-)
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.
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!
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.
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.
A welcome break from everything going on right now. Thank you!!
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!
Best Physics Series on youtube. Keep them coming Dr. Carroll!
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!
Absolutely fascinating and enlightening. This is the first time I’ve heard the problematical infinities explained. Thank you!!
Wonderful presentation! Thank you. I really look forward to your TH-cam videos.
Prof. Carroll, my gratitude field is in the Ultraviolet 🎇 Thank you for taking the time to share this knowledge
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.
Thank you. Well done, great format, enormously appreciated.
Awesome explanation!!! Fantastic Sean!!
Very very very beautiful lecture, I really appreciated it.
Thanks professor Carroll and please don't stop making video-lectures like this one.
This is great stuff. You make it seem so simple.
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)!
thanks for this, it's a good complement to the more technical and localized introductions to this topic.
Some of the nuts /bolts/secondary concepts/mechanisms of physics are just a inspiring as more main stream bells & whistles!
Really Fascinating lecture!
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 😊
This is a brilliant series, the best I have seen. Thank you for attempting to educate us.
This is so neatly presented, thanks for making it public.
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.
Amazingly clear and insightful, as always. Thanks a lot and I hope you will write a textbook on these thorny topics one day.
Thank you Sean Carroll, this was a great lecture, one of the few lectures I watched at normal speed :D
thank you for that great introductory video!
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.
Sean Carroll is a legend! I love him.
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 TH-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.
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.
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!
Brilliant series.Thank you.
Great video, thanks Sean.
Outstanding teacher, thank you
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!
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:)
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
Stopping everything and starting to watch, as usual! Thanks Sean!
Sean Carroll and Brian greene sir my role model sean sir lot's of love from india
Interactions was a doozy, Normalization was no less! ty Sean for getting us through :)
I love how down to earth this guy is!!!!! Great stuff. [GxQ=Universe]
joyfully informal!!
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
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
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"?
Ooh here comes the big stuff
The series is great! Alway look forward to every video...
Great Explanation 😍😍😍😍😍😍😍
best explanation ever
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
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?
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?
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.
(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?
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.
Awesome! Thank you :D
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?
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?
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
Is the numerical discrepancy in Higgs mass and the cosmological consented related to the relative difference of electrical and gradation always forces?
Masterpiece.
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 .
Would fields be mere fictitious instruments to avoid the idea of unmediated action from a distance?
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!....
hey, are these in a podcast format somewhere? i would love to listen to them while driving but its hard with youtube.
How possibly can you listen only and understand?
Enlightning.
Can someone provide the link to Dr. Carroll's lecture notes?
Thank you
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
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.
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.
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 !
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
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?
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.
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
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.
how do measure/observe the vacuum energy?
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?
What analysis of QFT!
So if I understood correctly: quantum gravity is not renormalizable essentially because it couples to too many other fields?
Sean Carroll please answer my one question even if it's not from the topics. I'm indeed very needy for the answer.
Do we observe dark matter in voids?
I can't find a source of observations.
If it only does near matter particles, it really can be the dark gravity indeed. Or a fake gravity from a fake velocity due to closeness of matter. Which is indeed big in numbers.
Can we observe dark matter around small localities than a galaxy?
I just need a yes or no for both the questions.
entropy is the inability of the electrical field to maintain bonding when interacting with the weak(muonic) and strong(tauonic) fields, an interaction that exceeds these electrical bonds part of my idea for the Yang-Mills existence and mass gap for the Millennium Prize, would you like to have a share in the 1mill US??
How do you calculate Phi without getting infinities? Is there a cutoff?
Where would someone bring their information on these.
Question: what if we did the double slit experiment, recorded on a harddrive which slit the electron went through. Then we deleted the harddrive directly or after 5 minutes. Then we can rule out or confirm if the experiment is dependent on a (subjective) observer. Owing to if there is a interfenerce pattern or not. But I assume this already is done. The result would be that there is no interference pattern, I belive, but then we can rule out that the wave collpase when we are looking at it.
They often make a popular phrase that the mind is what makes an observer. It doesn't work like that. For a particle to remain ambiguous, there needs to be very little energy exchange between it and the environment. Once there is such exchange, it already counts as an observer and the result is ruined. A computer recording the information is a much bigger "leak" than needed.
On top of that, the retention of superposition is bounded by time. So even if your computer was processing very low energy, you would have to delete the information in femtoseconds, or the decision would have propagated to the electron ruining the interference once again.
Good Idea. We know a rock can be an observer and destroy the interference pattern.
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.
Sean, you might want to turn off notifications on your iPad. We can hear you get a text message at 7:21! :)
I was kept wondering whether effectiveness fo the field theory is somehow different than the domain of applicapbility of any theory. I would for example assume that with sound wave sonic theory at very high pressures for example air would ionize from gas to plasma or that the average kinetic energy of the individual molecyles would exceeed the speed of sound in the medium. A theory of sound probably doesn't predict at which points those happen.
With water waves if you make a big enough splash you get water droplets flying all over the place. Those would be badly modeled as "height of water at each location" as in effect where there is droplet there is the water surface and then "two extra surfaces" in the droplet in the air. The mechanism is that if a wave is very narrow ("spikey") the surface tension elements wilil favour forming new volumes over pulling the water level. Droplets will often fall nearby where the rejoin the large body of water making a new wave source.
Does the field approach come with assumtions whether there are "sideways" interactions that would be analogous to the droplet forming tension or is it all vertical plus derivates?
If one has a large body of water the effect of surface tension to the shape of the water level will be neglible. However if one has a small droplet resting on a leaf or other platform the tension will make it take over only a finite surface area and the waves there are probably analogous to a finite length string. Could bending of space affect what vibrations are possible?
In a loop diagram, doesn't the total energy around the loop need to be zero? Going around the loop arrives at the same spacetime coordinate as it started, it would be really surprising if it was two different values.
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