The third installment of a little trilogy about the basics of quantum field theory. First we explained free fields, and why they led to particles; then we added interactions and used Feynman diagrams to calculate them; and today we’re going to deal with pesky infinities by introducing effective field theories. A wild ride!
The Biggest Ideas in the Universe | 11. Renormalization
And here is the associated Q&A video:
The Biggest Ideas in the Universe | Q&A 11 - Renormalization
I appreciate all the time you’ve put into these! Would you add it to the same YouTube play list as the others? I’ve been using the play list to make sure I watch in order and I don’t miss any…
Hi Sean,
Doesn’t the “Hierarchy Problem” of the Higgs mass show that arguments based on naturalness are simply flawed? This is what Sabine Hossenfelder is arguing for in her book, right?
Hi Sean! Thanks for the awesome video! Please keep this level of complexity!
This was the hardest video in the series to me so far. I am still a little lost about how does the fields interact (is it like when one field get a high energy, it bumps into other fields?), what superposition of states in the field means… The example you gave with the electron and the positrons in the end was really helpful! Maybe a little bit more examples would help too… Also, some concepts like lagrangians, operators, momentum, eingenstates, eigenvalues, symmetry… all those things are still hard to me to understand…
I would like to suggest a big recap video, with focus on the meaning of key concepts and practical examples!
Thanks again! Your videos is the best thing that happened in the quarantine! I am always anxious for the next video. Please, keep it up! =)
You mentioned that E_bar could be any number from negative infinity to infinity. At 9:20, can the sum of the individual Feynman diagrams over E_bar be infinitely small, i.e., negative infinity instead of infinity? You mentioned that E_bar —> infinity. Is it possible that E_bar —-> negative infinity?
I’m pushing toward programming a simple QED simulation self taught and your videos series is a perfect high level content! First time I see in depth explanation without swimming in the weight of technical formalism.
1) In the QM harmonic oscillator solutions, stationary solutions are a basis of all solutions, but by linearity we have much more solutions. So why are energy levels quantified if we can have for all (a,b) a*Phi_0 + b*Phi_1 also solution of the Schrödinger equation ?
2) In a musical instrument, we also get stationary solutions due to the length of the vibrating tube/string. How is the energy balanced between the different modes ? Why is there not all the energy in the fundamental frequency ? Can you describe the similarity and differences between the quantization of QM modes and musical instrument waves modes ?
3) Why is it so hard to find wave function simulations ? Why are science communicators never showing simulations of interactions in their talks ?
4) How computationally intensive is it to run a full standard model simulation of a H2O water molecule ? From the quarks and gluons of the nucleus of the oxygen to the electronic bond between atoms. QM would be so much to understand if we could see a H2O molecule, with the ability to switch between the fields of each type of elementary particle.
5) It’s shocking that we need to reach graduate level physics to get a simple electron-photon-electron interaction! Undergraduate QM is awful and not instructive at all, the way superposition and spins fit in the big picture is never explained clearly. Why did nobody manage to make QFT/QED easy to learn, assembling blocks by programming them. The oustanding course “NAND to Tetris” made computer architecture so intuitive, do we really need 5 years of college physics to understand how to implement a QED simulation ?
Thanks again for your great series.
Sean,
Thank you so very much for these videos.
For somebody like me, who is passionately curious about physics but lacks the time for proper formal education, your work (books, blog and now this series!) is both inspirational and alluring, and it constantly prods me to explore more of its quantitative foundations.
I don’t really feel qualified to ask any deep questions as I barely hang on to the gist of your presentations. I would however be particularly grateful if you could provide more insight into coupling operators.
Also, if the solution to the problem of the vanishing contribution from high energy states might be that of a multiverse, have experiments already been devised to provide support for this solution? And if they have, are we still very far from having the technical abilities to carry them out?
Again with many many thanks!
Hi there, despite the emoji (which I didn’t choose) I echo the appreciation for what you offer, and also relate to the non-quantum mechanics in the audience who really find these lectures insightful. (I was barely hanging on in this one!) Simple, big picture question that has me confused: when you explain that the vacuum energy is infinite, that seems to contradict conservation of energy from the previous lectures. Could you touch on this point? Is it related to the free lunch in inflation theory? It just seems like energy in our Universe keeps getting created as space is created? So confused…ok, maybe the emoji is appropriate!
In some sense, the effective field theory approach seems to be a more rigorous application of the cut-off calculation done almost on the “back of an envelope” by Hans Bethe on his way back to Cornell after Willis Lamb’s presentation at the first Shelter Island conference. The idea even goes further back to Kramers in the 1930s.
Is there any reason you see for it taking a quarter century for Ken Wilson to understand the full benefit of the approach or is it just one of those times when there’s a lag in putting a good insight to work. We’re folks just dazzled by the mathematical apparatus of Schwinger and ultimately relieved to see the more applicable technology of Feynman, giving up on what seemed a more pedestrian idea?
Thanks for all the work on these videos. Schwinger once apparently said that Feynman had brought computation to the masses. He may not have meant that to be a complete compliment but I’m sure all your viewer’s gratitude is fully sincere
When analyzing a case where the same particles go in and out (e.g. the electron and positron in, electron and positron out example) is there a term for no interaction, and does it dominate the calculation?
Maybe there’s no new physics up to Planck energy, which is beyond experimental capability but the Muon g-2 experiment may confirm a discrepancy between theory and experiment. It seems like a ridiculously tiny difference but is considered important by the experts. Would you care to comment on its potential significance.
As it’s unlikely that the LHC’s energy will be surpassed in the near future, what experimental options remain. Could those mysteriously high-energy particles from space offer any opportunities?
Question for the Q&A:
Can effective quantum theory of gravitational interaction account for the outcome of the Pound-Rebka experiment?
You mention: we can formulate an effective quantum theory of gravitational interaction to the extend that writing equations for scattering of two gravitons is within scope. How about the Pound-Repka experiment? My understanding is that quantum mechanics is confined to using Minkowski spacetime as the background structure. So it would be _very_ interesting to know whether the outcome of the Pound-Repka experiment is within scope of effective quantum theory of gravitational interaction.
(Incidentally: what is the proper place to submit a question for the Q&A session? This comment section? The comment section of the Youtube video? Direct email?)
in this talk you opened a much richer appreciation of virtual particles that i would like to understand. in popular books we hear of a froathy sea of particles. that black holes evaporate because of virtual particles at the horizon. but you seem to say that virtual particles are only a convenient story to explain something else. it seems like you were talking about readjustments of other quantum fields nearby. could you further elobrate
Hi Sean,
I just watched the Q&A.
The following point you made is, I think, very useful in communicating how to understand the concept of building an effective theory: by their nature effective theories are geared for a specific domain of applicability.
As I understand it:
The gravitational field is described as a field that:
– arises from energy density
– couples with energy density.
(Example: a spinning flywheel has kinetic energy that is confined to a finite volume of space, hence that kinetic energy will manifest itself as an energy density.)
There is an interesting historical parallel. In this case I guess it’s an anti-parallel.
I will use the expression ‘Lorentz Aether theory’ as a catch-all for all theories that in one form or another implement the concept of a Lorentz Aether.
Recapitulating:
In terms of Lorentz Aether theory there is an underlying absolute space and an absolute time, but all interactions are such that they are described by equations that transform in accordance with Lorentz transformation. These Lorentzian properties give rise to length effects and time rate effects that render the underlying absolute space and absolute time unobservable. Instead there is consistent appearance of Minkowski spacetime. In terms of Lorentz Aether theory Nature is laboriously conspiring to hide its nature.
I surmise: in terms of effective quantum theory of gravitational interaction there is an underlying Minkowski spacetime that is not subject to change. The equations for gravitational interaction are such that these interactions give rise to length effects and time rate effects that render the underlying Minkowski spacetime unobservable. The observed physics presents as if there is curvature of spacetime. I surmise: in terms of effective quantum theory of gravitational interaction Nature is conspiring to hide the underlying Minkowski spacetime.
Thanks for these videos Sean, it was very satisfying to learn about (the dimensions of) scalar fields.
I’m still confused about whether a scalar field (phi) can be thought of as an energy (or similarly, the mass of the Higgs boson), since energy is a component of a 4-momentum vector (not a scalar) and transforms accordingly.
Isn’t the cosmological constant a scalar field, with an energy density (temporal component of 4-vector) and a pressure (spatial components of 4-vector). So can scalar fields still have (non-imaginary) components, like a vector does, but somehow lack a specific direction (since the vacuum-energy pressure is omni-directional)?
Perhaps it’s just that when you speak of the energy of a scalar field, you mean the norm of the 4-momentum? That would clear things up for me.
Again, thanks for these videos. I also liked Dark Matter, Dark Energy 🙂
Kind regards,
Geert VS
Sorry, if this is not timely. I’ve been busy and am a couple weeks behind in watching these terrific videos. I have a question regarding marginal and ignorable terms in effective field theories. I understand the argument that if c4 ~O(1), c5 ~ O(1/E*), etc.. then c5 and above are ignorable. But wait! The full terms are c4 * f^4, c5 * f^5, etc. for field f which are all of the same order, as required to be able to sum them. This suggests that more needs to be said in order to justify ignoring higher order terms. For a discrete rather than a field theory, one could appeal to the fact the each f is a quantum amplitude with magnitude no greater than one, so higher powers of f will be no larger than lower powers. But in a field theory isn’t f(x) a quantum amplitude for a probability density, and as such can have arbitrarily large magnitude at any given x? How does one complete the argument for ignoring higher order terms in this situation? Presumably this must rely in some fashion on the fact that the integral of |f|^2 = 1.
Thanks!