Such a pleasure to watch your lectures….I’m a radiologist and you’ve given me a Eureka moment re PET and the fact that you get two photos rather than one in positron-electron interactions. Thank you!
Just because Sean hasn't answered, I'll take a stab (I have no formal experience, just watched a lot of videos and built up some intuition over some years): Q1: I think renormalization is the answer to this. I'll know more, i believe, after watching the next video in this series. I know renormalization takes absurd quantities (infinites) and makes them interpretable as physical quantities. The thing we renormalize is some experimental value to some theoretical predication (typically, as i understand it, an infinity). Q2: I believe this is just a simplified notation of the 3d gadient, aka, dx/da+dy/da+dz/da (where *a* could be time, a dimension of space, or any other quantity). I believe this was just a simplification of notation.
00:00:50 “We talk about fields interacting through Feynman diagrams, and we use them to calculate the interactions between certain quantum fields, fields that are thought of as collections of particles” 3:00 hammering home what modes are - really key So it seems like when we sin wave-ify a field, which we can imagine as plane waves, we need to define its wavelength, (not sure if we have to define frequency, as that can mean different things if we’re picturing a static frame or a wave through time. I’m also unsure of amplitude (h).) AND it’s direction. And that might be why we write phi sub k(vector, you know, since it’s directional!) (h). Going back to my confusion of frequency and amplitude, I’m not really sure what h is referring to - density? Density graphed against space? Density graphed against time? I think this is a case we’re Sean explicitly say what the axiis were, which is causing some of my confusion 5:00 “A QF is an organisation tool for talking about a superpositon(s?) of many collections of particles with different numbers of particles.” “There are cases were the Field-iness of the Fields really does matter, and talking about Fields is not just a cheap substitute for talking about particles.” “Unlike non-Field Theory QM, the number of particles doesn’t have to be conserved, the wavefunction of the QF is a superposition of different numbers of particles, AND the Schrödinger equation that tells you how that wavefunction evolves can change the number of particles through different kinds of interactions.” Damn it’s starting to pay off Omg it really is!!! 9:00 He says what I was assuming - that through the Fourier transform let’s us have a localized function by summing over sin waves that are non-localized!!!!! 18:30 particles direction vs ‘electron-ness’ direction in the notation of Feynman diagrams, left to right vs arrows 33:20 This is Perturbation Theory; “you start with something you understand perfectly (like Free Fields or a ball falling without air resistance) and add in tiny effects - add them in as perturbations” 45:00 criticisms of Wheeler’s 1 electron 50:00 Feynman diagrams are just a story, what is actually going on? Momentum conserved etc. The real parts and the virtual parts (where the fields are interacting locally and are doing complicated non-particle stuff). The mass of a virtual photon does not have to be zero, it is a way of talking about interacting Fields, not actual ‘particles’ We still don’t know what to do about the energy density of empty space.
I loved how you started from Feynman diagrams and then got into the concept of calculating it through the least action principle. Wonderful approach to teach QFT.
Great series! Are you going to do a "Lenny" and write a Theoretical Minimum based on this series? That would be great and something good would come out of lockdown.
You're getting better at this youtube business Sean! Totally lured me in with that tasty blue rather irrelevant CGI thumbnail! ...Glad you did. I love this series and I loved you latest book. And the one before that taught me a lot too. Like philosophy and the universe for dummies. I feel like I'm getting more and more inspired to learn calculus, differential equations and all that the more stuff you put up. Greetings from Sweden
Hawking demonstrated the most interesting interaction of QF, using a blend of GR and QM, when explaining radiation and calculating entropy of BH. A pair production of virtual particle and anti-particle from the QF, makes the anti-particle fall into the BH while a real particle is ejected into space. Implying the QF can simulate conscious intelligent 'observer', collapsing the field to produce particles (Adam Becker' question, can QF simulate/define cosmic consciousness).
Asking this because Lawrence Krauss has mentioned for number of times that electron emitting a photon is an example of “something from nothing”. Not sure how accurate that is.
@@papsaebus8606 Photons can be created and destroyed readily because they have no mass and no charge. There are still things that you must balance though: energy (in different forms), momentum, and spin. But, the conservation doesn't apply to lines that are entirely within the diagram -- only the lines entering/leaving must balance everything. The "virtual photons" are not bound by the familiar rules. If that vertex was a diagram in itself, then yes, the electron loses energy and momentum and flips its spin. This is exactly what happens when it crosses a magnetic field, for example. But he's showing these primitive vertexes as the alphabet, that can be stuck together to form complex diagrams. In context, it could represent a virtual photon, and it could be coming or going.
I feel that one of the deepest ideas in physics is the Wilsonian renormalization group theory. Not only does it give a way to think about the connection between high energy microscopic and low energy macroscopic theory, it gives a deep understanding of phase transitions, the space of quantum field theories, universality (the robustness and fundamentalness of low energy effective theories) etc etc. In particular, it gives a possible answer of the infinities quantum field theory implying that they should most likely be considered as effective theories rather than be seen as fundamental. I think there generally lacks a good exposition of these important ideas in theoretical physics for the general public. I can imagine that a version of Kadanoff block spin would give some intuition.
I enjoyed the wrap-up to your chat #10 Interactions. (transcript quote) so we are left with both this wonderfully accurate calculational device of Feynman diagrams and this somewhat unnatural formalism of quantum field theory. we don't know what to do about that. we didn't ... I'm not gonna reveal what to do about that. We still don't know what to do about the energy density of empty space. But we're thinking, and it might be that we do in one way or the other have to replace quantum field theory. But in the mean time it is absolutely the best way we have of understanding nature currently available. (end quote) The "what to do about the energy density of empty space" is what intrigues me. As well as ways to do 3D visualizations of localized field interactions, like a electron vibration and "reverse" vibration (positron) annihilating.
I was more excited to go from particle diagram to understand how the wavelike nature of interactions works. Could one try to tell the story using the mode decompositions of the incmoing particles. Like electron momentum right encounters anti-electron momentum left plus other configurations like electron momentum north encounters anti-electron momentum going left. But maybe it's the case that the mathematics is not particularly elegant or that summed back up version is not very packety? It also feels that the feyman diagramms are in effects the "modes" of the interaction with added vertex being analogous to considering an increase of an energy quanta. If one tried to solve a hamilton with an interaction term in it would it have quantised solutions? With QED it should be enough to have most essential things handled with a electron-antielectron system. I was looking to understand the conditions where they keep circling each other vs annhilation vs flying far apart from each other. Because both partcile have uncertainty in position and momentum it seemed to be possibe to set up a situation where that wave-indeterminacy decides which of the three types of outcomes happens. And I had an incling that "time to decay" via a quantum uncertain path would be something I don't understand and could gain more insight on. I also feel that the construction of understanding fields via particles was a red herring in that it's applicability is already hit. When we start rolling our spherical cows we are going to get in trouble with cow-tipping. Part of the job of a particle physcicis was to come up with new hamiltoninan. However the interaction term seemd to be just combine all fields via multiplication and a scalar. There doesn't seem to be much room to make it any other way. Or is it rather a more general function f(e-,e+,y) that could in principle do more fancy stuff? Or is the complication hidden in the definition of what the fields are (complexity of combining the fields vs how rich the field ontology is)
These are great videos, but I'm failing this class.... Won't stop watching and rewatching. Just love listening to the Professor explain thing, go on tangents, the whole thing.
Question: How do we ensure that the sum of the probabilities for all variations of interactions converges to 1? If it exceeds 1 do we have to think of other version of alpha?
Hello Sean, I have a question: how can a particle or field be completely free or not entangled? I can’t envision that as everything interacts with everything else all the time. Thank you so much for these lectures; I have all your books and the lectures help to elucidate them.
If there would be such a field, my guess is that we would not know of it, as it doesn’t act on anything else in the universe. But you can still start your mathematical thought experiment with that kind of made up particle, as it’s the easiest to model.
49:20 "an electron, a positron and a photon..." walk into a bar. electron turns to the positron and says 'i'm feeling negative', positron asks responds 'are you positive?', photon interjects 'can you guys see where this is going?'
since photons are the force carriers of the EM field, do photos travel alongside the fieldlines when i charge my phone? referring to veritassiums video about energy flow perpendicular to the wire. thx
at 23:00, I think the Feynman diagram with one electron in, and an electron and photon out, is unphysical. Energy is not conserved, which is most easily seen from the centre-of-mass frame of the "in" electron. Instead, as Carroll says later, the two diagrams should be mirror images of one another. Edit: But I guess it's fine as a single vertex of a larger diagram
so if the reason for every electon having the same mass and charge is because they are vibrations in the same field,does it mean that every particle have its own specific field? Does the field defines the particles or the opposite ? Or is it both simultaneously and they are different ways of expressing the same thing ?
If some particle 'decays into...' does that imply that it was made up of those decay constituents? Or that it has changed the interacting fields in some way that those 'decay constituents' come into being in he relevant fields?
i think the reason you keep 'slipping' and calling these lectures is because you secretly want historians to refer to these videos as the Carroll Lectures
Enjoying your lectures....we are so lucky that corona seems to have you with us -a very real silver lining! So.... my question....Is gravity emergent and if so can it be manipulated by affecting entropy in a particular volume of space or even specifically here on Earth?
Another question...I believe you mentioned in an earlier video that vacuum entanglement is different from particle entanglement (since you have the idea that spacetime emerges from vacuum entanglement). How can these two things be separate if particles are just excitations in fields?
i think one future problem may be that there is no small metric for the density or energy level , if i had to guess id say those measurements are based on the individual doing the measurement,. once again thank you. great informational video*
Sorry if this was asked already. So, is a hydrogen atom the superposition of an electron wave and proton wave function (which is the superposition of quark and gluon wave functions) that travel through space-time together? Somehow, I think the answer is no.
"The positron can be thought of as an electron moving backwards in time..." The way this was stated makes me think that people don't think positrons are _actually_ electrons moving backward in time. Is that correct?
No. The formulas of motion don't have a notion of a direction of time. The combination of Time, Parity, and Charge has perfect symmetry. That is, if you reverse all three values, you'll get exactly the same formula and result. Thus, reversing P and C (only) is exactly the same as reversing T (only). The formulas already don't care about the direction of time, so doing that lets you just reuse what you already know.
@@JohnDlugosz This is kind of off subject, but weren't there some expiriments done that showed a violation of one or more parities? Although I can't remember which one/s.
@@spracketskooch All of them have been violated, but CPT has not been violated (if you reverse charge, parity, AND time then the laws of physics will be the same).
I'm pretty sure it's like "glass half-empty vs. glass half-full". There is no one thing it "really" is, it's a matter of perspective. Both are valid and equivalent.
If I grow up to be a particle physicist, what fields will I be inventing? Standard model is bunch of interacting fields and they are all described, right? So is my job to imagine some new interactions and new particles and see what happens even though I have no indications from experiments there are any other fields? Clearly, I am confused about why should anyone invent new fields when it seems we've got them all.
I thought QM was about unifying fields and particles? So does QFT give a multi-variable function depending on x and phi? (Probability that x will have a certain field value phi). Is that what he is saying? I'm just confused because its probabilities of probabilities.
If electrons move forward in time and positrons move backwards in time, does that mean that at the no bang two universes were created. On with our matter moving forwards in time and one with antimatter moving backwards in time?
The field is up and down. 18 squared. 324 group 18 periodic system is All gassens together is 324. From 1 to 18.. So the field is up +up- and down+down-..
Now fields interact with each other?? I feel that if I don’t understand how, I’m going to grow a giant moustache and pretend I live in the XIXth century, just to keep what’s left of my sanity. PS: the level of math you introduce is very satisfying. If it depends on me, the more the better.
Is there a Field Theory (classical or quantum) that uses Special Relativity? Field configurations defined in spacetime coordinates rather than R3 real coordinates? How about higher dimensional space (rolled-up dimensions?)
55:00 The reasons given for why Wheeler's 'one electron universe' is wrong don't actually logically falsify the theory.. Just because the [same underlying] 'field description' _works_ as an explanation for why all the electrons are the same mass and charge, doesn't mean it's the right one and Wheeler's is wrong. That's like saying the 'round globe theory' is wrong because the flat earth 'theory' has a working alternative explanation for the motion of the 'heavenly bodies' (or the geocentric/ptolemaic model explanation for planetary motion, etc.) And the fact that electrons can turn into other particles doesn't falsify it either because whatever the electron turns into can still be the 'one electron/particle' just undergoing 'transformation'. I'm not saying the 'one electron universe' theory is correct, but are there other more compelling reasons why it's wrong?
@@michaelsommers2356 Theoretically, the electron 'produced' by the muon decay with the neutrinos could just be a time-displaced version displaced [by relativity] of the 'other' spacetime manifestations of the 'one electron'. The muon _is_ the electron in a different 'state'. Particles _essentially_ are just different forms or fluctuations of the same universal wavefunction(s) [and not fundamentally disparate/unique entities in terms of their 'essence'].
I'm sure it's hidden in all the Lagrangian stuff, but where in the fields do these interactions take place...like, do the interactions always happen where both the electron field and positron field have relatively large values?
The electron splits into another electron and photon. The new electron must be at a lower energy level, since it lost a photon worth of energy. Is this correct?
It would be very cool to see the field depiction of an electron and a positron, as to understand what you mean by “electronness “. In a more detailed way, in prior depictions particles were lobes in a wave, no matter if they were pointing up or down. So... I guess it all boils down to what defines charge in the electron field. Note: by depiction I mean literally a drawing.
The electric field refers to the charge: what force would a probe particle feel in every position on the map. The electron field refers to the presence of electrons and virtual electrons (and positrons). They are descriptions on different "levels" of reality. If you level it, you find that the electric field is a cross section or shadow (so to speak) of the *photon* field, where the photon field is in the same level as the electron field (QFT).
Sean, I know this is kinda the wrong place to ask, but it's been bothering me since I saw the Big Idea video on Space. In your two dimensional example of space, you drew a cylinder, which I cannot help but notice is a three dimensional object. It seems to me, the (small) circular dimension is in fact two dimensions. That makes no sense to me. Is this something that can be explained to the lay person?
That cilinder is only its surface, like a rolled piece of paper. And the “available space” would be only the outer side of that sheet. So, in order to describe the position of a point on that surface you would need two numbers, so two dimensions, one of which would be cyclical. I get that your confusion comes from the need of a third dimension in order to roll the paper, but if the space everything you investigated happened in was the paper, space for you would be bidimensional. Spaces can be weird. Imagine the “space” your mathematical theory is concerned with are the numbers on a clock. 6 -5= 1. 8-7 = 1 , but 1 - 12 = 1, if minus sign means “ calculate the distance”. That clock is one dimensional, as you only need one number to say at which point in that line you are. Even if that line is a circle.
Continuing on from Alvaro, in these types of explanations people often talk about an ant crawling on the surface. The ant only sees and traverses the two dimensional surface. You can define any place it can crawl with just two dimensions. Even though our visualization of it requires three dimensions it exists only in two. Hope that helps.
I'm a little lost on how many degrees of freedom we're talking about. You explain that we can decompose any field as a collection of waves, waves have modes, modes have energy levels, and the Nth energy level corresponds to N particles. That's for a classical field and on top we have the wave function. That sounds like "for each" is expanded too many times. Is there a way to count the infinities? For example there's an R^3 infinity of k plane waves, then a Z infinity of coefficients of each mode? then you take the set of all of the above to make Ψ? I don't know. Roughly how large is everything? EDIT: And I'm guessing part of the answer is that this "how big" doesn't change with many worlds because the the wave function is already there. It's implied by what you say here that you, an object, is not defined locally anyway. We're all defined holographically as components of the vibration modes of the whole universe. All versions of us. In a way that should make Many Worlds more plausible, or at least no less plausible than expressing everyday things that way.
I always wonder how you can top it...what's next...Sean Caroll is the best sherpa you can get (free!!) on the way to the summit of Everest of Physics...but you still have to climb high on your own feet...
Hi if you don't know tomorrow there will be a debate review on "capturing Christianity" RUclips channel of your debate with William L.C maybe you would be interested in it
W L C made the mistake of trying to argue physics with Sean Carroll about ? 5 years ago. He was hopelessly out of his depth. I suspect that Capturing Christianity's review will be highly edited and highly misleading. But I could be wrong.
I wonder what sort of person clicks on a theoretical physicist's lecture during a pandemic and gives it a thumbs down. Must have been an anti-Everettian.
koho Well, I'm an anti-Everettian, but I'm more than willing to listen to Sean perform and teach. This series is great even if he keeps talking about the rather ridiculous "manyworlds" not-really an interpretation.
@@dwinsemius Why are you an anti-Everettian? I'm legitimately curious, since it seems like the most plausible and simple interpretation to me, but I'm no expert.
@@dwinsemius I can see how Many Worlds could be wrong, improbable, or untestable - but how could it not be an interpretation of of quantum mechanics? Anyway, yeah, I don't have to agree on every philosophical standpoint of Sean to learn from his physics lectures.
@@nibblrrr7124 The reason I don't see it as an interpretation is that it doesn't really make a physical statement. There's not actually a transition, just two unresolved possibilities. Nothing is really happening if both paths are "real". It seems to be an admission of failure. "Since we cannot figure out how transitions or collapses occur, we'll just brush it under the rug and say either there was no transition. but perhaps that all transitions occurred.." It seems very non-probabilistic. In the cat box you would require that at every point in time that there would need to be a branch. Would also seem to play havoc with any need for reversibility.
This series will be the best thing on RUclips for decades.
Thanks for hitting the technical complexity sweet spot. These are great videos!
Such a pleasure to watch your lectures….I’m a radiologist and you’ve given me a Eureka moment re PET and the fact that you get two photos rather than one in positron-electron interactions. Thank you!
Such an amazing physicist and communicator. Such a terrible arrow head drawer. 23:15 :D
"The Biggest Ideas in the Universe" series is fantastic! They are timeless content. This format of explaining one concept is great.
Stopping everything to watch the new video! =)
Even time?
Neat spherical-cyberpunk cow in the background!
Great series you made here. I love how you take care of the details but still stay sufficiently on the surface
QUESTION 1:
- 27:26 "These diagrams have a typical size of alpha, but can have different signs"
Just because Sean hasn't answered, I'll take a stab (I have no formal experience, just watched a lot of videos and built up some intuition over some years):
Q1: I think renormalization is the answer to this. I'll know more, i believe, after watching the next video in this series. I know renormalization takes absurd quantities (infinites) and makes them interpretable as physical quantities. The thing we renormalize is some experimental value to some theoretical predication (typically, as i understand it, an infinity).
Q2: I believe this is just a simplified notation of the 3d gadient, aka, dx/da+dy/da+dz/da (where *a* could be time, a dimension of space, or any other quantity). I believe this was just a simplification of notation.
00:00:50 “We talk about fields interacting through Feynman diagrams, and we use them to calculate the interactions between certain quantum fields, fields that are thought of as collections of particles”
3:00 hammering home what modes are - really key
So it seems like when we sin wave-ify a field, which we can imagine as plane waves, we need to define its wavelength, (not sure if we have to define frequency, as that can mean different things if we’re picturing a static frame or a wave through time. I’m also unsure of amplitude (h).) AND it’s direction. And that might be why we write phi sub k(vector, you know, since it’s directional!) (h). Going back to my confusion of frequency and amplitude, I’m not really sure what h is referring to - density? Density graphed against space? Density graphed against time?
I think this is a case we’re Sean explicitly say what the axiis were, which is causing some of my confusion
5:00 “A QF is an organisation tool for talking about a superpositon(s?) of many collections of particles with different numbers of particles.”
“There are cases were the Field-iness of the Fields really does matter, and talking about Fields is not just a cheap substitute for talking about particles.”
“Unlike non-Field Theory QM, the number of particles doesn’t have to be conserved, the wavefunction of the QF is a superposition of different numbers of particles, AND the Schrödinger equation that tells you how that wavefunction evolves can change the number of particles through different kinds of interactions.”
Damn it’s starting to pay off
Omg it really is!!! 9:00 He says what I was assuming - that through the Fourier transform let’s us have a localized function by summing over sin waves that are non-localized!!!!!
18:30 particles direction vs ‘electron-ness’ direction in the notation of Feynman diagrams, left to right vs arrows
33:20 This is Perturbation Theory; “you start with something you understand perfectly (like Free Fields or a ball falling without air resistance) and add in tiny effects - add them in as perturbations”
45:00 criticisms of Wheeler’s 1 electron
50:00 Feynman diagrams are just a story, what is actually going on? Momentum conserved etc. The real parts and the virtual parts (where the fields are interacting locally and are doing complicated non-particle stuff). The mass of a virtual photon does not have to be zero, it is a way of talking about interacting Fields, not actual ‘particles’
We still don’t know what to do about the energy density of empty space.
I have bought Seans book and its good. Sean is pushing the limits.
I loved how you started from Feynman diagrams and then got into the concept of calculating it through the least action principle. Wonderful approach to teach QFT.
I think it was John Wheeler who gave Feynman the idea that the positron is an electron moving backwards in time.
A piece of gold!
@Sean Carroll. Thanks Prof, if you happen to see my gratitude. Wonderful series.
Great series! Are you going to do a "Lenny" and write a Theoretical Minimum based on this series? That would be great and something good would come out of lockdown.
You're getting better at this youtube business Sean! Totally lured me in with that tasty blue rather irrelevant CGI thumbnail!
...Glad you did. I love this series and I loved you latest book. And the one before that taught me a lot too. Like philosophy and the universe for dummies. I feel like I'm getting more and more inspired to learn calculus, differential equations and all that the more stuff you put up.
Greetings from Sweden
I am old so these videos are as relaxing as music... playful and honest. Carl Sagan in 1980 was also reassuring and fun.
Very clear and concise talks. Continue
Hawking demonstrated the most interesting interaction of QF, using a blend of GR and QM, when explaining radiation and calculating entropy of BH. A pair production of virtual particle and anti-particle from the QF, makes the anti-particle fall into the BH while a real particle is ejected into space. Implying the QF can simulate conscious intelligent 'observer', collapsing the field to produce particles (Adam Becker' question, can QF simulate/define cosmic consciousness).
Sean: There is only one diagram we can draw for this
Sean 5 minutes later: There is an infinite amount of diagrams we can draw for this
thank you so much, this was extremely helpful and insightful.
I've always wanted to know more quantum field theory without taking a course on it. much appreciated Sean
Thank you Sean for the video.
Reminder : at 41:00 This video, (no. 10 - Interactions) is where the "Lagrangian" & "Lagrange Density" is discussed & explained. Fully.
Does an electron lose energy in the interaction 22:46? Or does the energy conservation simply not apply in this scenario?🤔
Asking this because Lawrence Krauss has mentioned for number of times that electron emitting a photon is an example of “something from nothing”. Not sure how accurate that is.
@@papsaebus8606 Photons can be created and destroyed readily because they have no mass and no charge. There are still things that you must balance though: energy (in different forms), momentum, and spin.
But, the conservation doesn't apply to lines that are entirely within the diagram -- only the lines entering/leaving must balance everything. The "virtual photons" are not bound by the familiar rules.
If that vertex was a diagram in itself, then yes, the electron loses energy and momentum and flips its spin. This is exactly what happens when it crosses a magnetic field, for example.
But he's showing these primitive vertexes as the alphabet, that can be stuck together to form complex diagrams. In context, it could represent a virtual photon, and it could be coming or going.
Would an Eternalist look at a Feynmann diagram as not going from right to left or left to right, but just *being there*?
I feel that one of the deepest ideas in physics is the Wilsonian renormalization group theory. Not only does it give a way to think about the connection between high energy microscopic and low energy macroscopic theory, it gives a deep understanding of phase transitions, the space of quantum field theories, universality (the robustness and fundamentalness of low energy effective theories) etc etc. In particular, it gives a possible answer of the infinities quantum field theory implying that they should most likely be considered as effective theories rather than be seen as fundamental.
I think there generally lacks a good exposition of these important ideas in theoretical physics for the general public. I can imagine that a version of Kadanoff block spin would give some intuition.
re 10:00 outgoing dispersive wavefront combined (additive/subtractive) harmonic spectra
Thanks, Sean!
Rad, every video gets better!
I enjoyed the wrap-up to your chat #10 Interactions.
(transcript quote)
so we are left with both this wonderfully accurate calculational device of Feynman diagrams and this somewhat unnatural formalism of quantum field theory. we don't know what to do about that. we didn't ... I'm not gonna reveal what to do about that.
We still don't know what to do about the energy density of empty space. But we're thinking, and it might be that we do in one way or the other have to replace quantum field theory. But in the mean time it is absolutely the best way we have of understanding nature currently available.
(end quote)
The "what to do about the energy density of empty space" is what intrigues me. As well as ways to do 3D visualizations of localized field interactions, like a electron vibration and "reverse" vibration (positron) annihilating.
These ideas are too big for me, but it’s nice listening to Sean tell me stuff so I listen anyway.
I was more excited to go from particle diagram to understand how the wavelike nature of interactions works. Could one try to tell the story using the mode decompositions of the incmoing particles. Like electron momentum right encounters anti-electron momentum left plus other configurations like electron momentum north encounters anti-electron momentum going left. But maybe it's the case that the mathematics is not particularly elegant or that summed back up version is not very packety?
It also feels that the feyman diagramms are in effects the "modes" of the interaction with added vertex being analogous to considering an increase of an energy quanta. If one tried to solve a hamilton with an interaction term in it would it have quantised solutions? With QED it should be enough to have most essential things handled with a electron-antielectron system. I was looking to understand the conditions where they keep circling each other vs annhilation vs flying far apart from each other. Because both partcile have uncertainty in position and momentum it seemed to be possibe to set up a situation where that wave-indeterminacy decides which of the three types of outcomes happens. And I had an incling that "time to decay" via a quantum uncertain path would be something I don't understand and could gain more insight on.
I also feel that the construction of understanding fields via particles was a red herring in that it's applicability is already hit. When we start rolling our spherical cows we are going to get in trouble with cow-tipping.
Part of the job of a particle physcicis was to come up with new hamiltoninan. However the interaction term seemd to be just combine all fields via multiplication and a scalar. There doesn't seem to be much room to make it any other way. Or is it rather a more general function f(e-,e+,y) that could in principle do more fancy stuff? Or is the complication hidden in the definition of what the fields are (complexity of combining the fields vs how rich the field ontology is)
These are great videos, but I'm failing this class....
Won't stop watching and rewatching. Just love listening to the Professor explain thing, go on tangents, the whole thing.
Question:
How do we ensure that the sum of the probabilities for all variations of interactions converges to 1? If it exceeds 1 do we have to think of other version of alpha?
Hello Sean, I have a question: how can a particle or field be completely free or not entangled? I can’t envision that as everything interacts with everything else all the time. Thank you so much for these lectures; I have all your books and the lectures help to elucidate them.
If there would be such a field, my guess is that we would not know of it, as it doesn’t act on anything else in the universe. But you can still start your mathematical thought experiment with that kind of made up particle, as it’s the easiest to model.
I'm wondering the exact same thing. How would it be possible for anything to ever be not entangled?
Thank you.
I hope to understand more.
25:20 was a bit of hand-waving?
49:20 "an electron, a positron and a photon..." walk into a bar. electron turns to the positron and says 'i'm feeling negative', positron asks responds 'are you positive?', photon interjects 'can you guys see where this is going?'
What's the matter with that massless joke?
since photons are the force carriers of the EM field, do photos travel alongside the fieldlines when i charge my phone? referring to veritassiums video about energy flow perpendicular to the wire. thx
at 23:00, I think the Feynman diagram with one electron in, and an electron and photon out, is unphysical. Energy is not conserved, which is most easily seen from the centre-of-mass frame of the "in" electron. Instead, as Carroll says later, the two diagrams should be mirror images of one another. Edit: But I guess it's fine as a single vertex of a larger diagram
this is a completely new concept for me
What about Gauge Invariance?
so if the reason for every electon having the same mass and charge is because they are vibrations in the same field,does it mean that every particle have its own specific field? Does the field defines the particles or the opposite ? Or is it both simultaneously and they are different ways of expressing the same thing ?
Thank you sir, nice lecture.
If some particle 'decays into...' does that imply that it was made up of those decay constituents? Or that it has changed the interacting fields in some way that those 'decay constituents' come into being in he relevant fields?
The two lowest order electron>γ
i think the reason you keep 'slipping' and calling these lectures is because you secretly want historians to refer to these videos as the Carroll Lectures
Enjoying your lectures....we are so lucky that corona seems to have you with us -a very real silver lining! So.... my question....Is gravity emergent and if so can it be manipulated by affecting entropy in a particular volume of space or even specifically here on Earth?
Another question...I believe you mentioned in an earlier video that vacuum entanglement is different from particle entanglement (since you have the idea that spacetime emerges from vacuum entanglement). How can these two things be separate if particles are just excitations in fields?
i think one future problem may be that there is no small metric for the density or energy level , if i had to guess id say those measurements are based on the individual doing the measurement,. once again thank you. great informational video*
Is there anything analogous to Feynman diagrams that can be used to diagram philosophical arguments or texts?
Sorry if this was asked already. So, is a hydrogen atom the superposition of an electron wave and proton wave function (which is the superposition of quark and gluon wave functions) that travel through space-time together? Somehow, I think the answer is no.
I'm the spherical cow everyone is talking about.
"The positron can be thought of as an electron moving backwards in time..." The way this was stated makes me think that people don't think positrons are _actually_ electrons moving backward in time. Is that correct?
No. The formulas of motion don't have a notion of a direction of time. The combination of Time, Parity, and Charge has perfect symmetry. That is, if you reverse all three values, you'll get exactly the same formula and result.
Thus, reversing P and C (only) is exactly the same as reversing T (only).
The formulas already don't care about the direction of time, so doing that lets you just reuse what you already know.
@@JohnDlugosz This is kind of off subject, but weren't there some expiriments done that showed a violation of one or more parities? Although I can't remember which one/s.
@@spracketskooch All of them have been violated, but CPT has not been violated (if you reverse charge, parity, AND time then the laws of physics will be the same).
I'm pretty sure it's like "glass half-empty vs. glass half-full". There is no one thing it "really" is, it's a matter of perspective. Both are valid and equivalent.
If I grow up to be a particle physicist, what fields will I be inventing? Standard model is bunch of interacting fields and they are all described, right? So is my job to imagine some new interactions and new particles and see what happens even though I have no indications from experiments there are any other fields? Clearly, I am confused about why should anyone invent new fields when it seems we've got them all.
I thought QM was about unifying fields and particles? So does QFT give a multi-variable function depending on x and phi? (Probability that x will have a certain field value phi). Is that what he is saying? I'm just confused because its probabilities of probabilities.
If electrons move forward in time and positrons move backwards in time, does that mean that at the no bang two universes were created. On with our matter moving forwards in time and one with antimatter moving backwards in time?
The field is up and down. 18 squared. 324 group 18 periodic system is All gassens together is 324. From 1 to 18.. So the field is up +up- and down+down-..
Now fields interact with each other?? I feel that if I don’t understand how, I’m going to grow a giant moustache and pretend I live in the XIXth century, just to keep what’s left of my sanity.
PS: the level of math you introduce is very satisfying. If it depends on me, the more the better.
interact and generate new fieilds in other dimensions
Is there a Field Theory (classical or quantum) that uses Special Relativity? Field configurations defined in spacetime coordinates rather than R3 real coordinates? How about higher dimensional space (rolled-up dimensions?)
Yep! The field theory of spacetime coordinates is General Relativity.
55:00 The reasons given for why Wheeler's 'one electron universe' is wrong don't actually logically falsify the theory..
Just because the [same underlying] 'field description' _works_ as an explanation for why all the electrons are the same mass and charge, doesn't mean it's the right one and Wheeler's is wrong. That's like saying the 'round globe theory' is wrong because the flat earth 'theory' has a working alternative explanation for the motion of the 'heavenly bodies' (or the geocentric/ptolemaic model explanation for planetary motion, etc.) And the fact that electrons can turn into other particles doesn't falsify it either because whatever the electron turns into can still be the 'one electron/particle' just undergoing 'transformation'.
I'm not saying the 'one electron universe' theory is correct, but are there other more compelling reasons why it's wrong?
@@michaelsommers2356
Theoretically, the electron 'produced' by the muon decay with the neutrinos could just be a time-displaced version displaced [by relativity] of the 'other' spacetime manifestations of the 'one electron'.
The muon _is_ the electron in a different 'state'. Particles _essentially_ are just different forms or fluctuations of the same universal wavefunction(s) [and not fundamentally disparate/unique entities in terms of their 'essence'].
Beautiful
I'm sure it's hidden in all the Lagrangian stuff, but where in the fields do these interactions take place...like, do the interactions always happen where both the electron field and positron field have relatively large values?
Do you mean *lepton number* rather than *fermion number* for conserving electron-ness?
The electron splits into another electron and photon. The new electron must be at a lower energy level, since it lost a photon worth of energy. Is this correct?
Much More on Alpha Please! I'm sure α is a Big Idea.
YES! Just in time for my particle physics exam tomorrow!!!
Why I keep watching all his videos even when I skip most of the part?
It would be very cool to see the field depiction of an electron and a positron, as to understand what you mean by “electronness “.
In a more detailed way, in prior depictions particles were lobes in a wave, no matter if they were pointing up or down. So... I guess it all boils down to what defines charge in the electron field.
Note: by depiction I mean literally a drawing.
The famous MIT Physics FAQ has a section on that.
Don’t know it. Have a link?
How is the electron field different from electric field? Or How are they related?
The electric field refers to the charge: what force would a probe particle feel in every position on the map.
The electron field refers to the presence of electrons and virtual electrons (and positrons).
They are descriptions on different "levels" of reality. If you level it, you find that the electric field is a cross section or shadow (so to speak) of the *photon* field, where the photon field is in the same level as the electron field (QFT).
Definitely a _Tempest_ theme going on here ; _)_
What is actually real? Is it just the connections between things?
Sean, I know this is kinda the wrong place to ask, but it's been bothering me since I saw the Big Idea video on Space. In your two dimensional example of space, you drew a cylinder, which I cannot help but notice is a three dimensional object. It seems to me, the (small) circular dimension is in fact two dimensions. That makes no sense to me. Is this something that can be explained to the lay person?
That cilinder is only its surface, like a rolled piece of paper. And the “available space” would be only the outer side of that sheet.
So, in order to describe the position of a point on that surface you would need two numbers, so two dimensions, one of which would be cyclical.
I get that your confusion comes from the need of a third dimension in order to roll the paper, but if the space everything you investigated happened in was the paper, space for you would be bidimensional.
Spaces can be weird. Imagine the “space” your mathematical theory is concerned with are the numbers on a clock. 6 -5= 1. 8-7 = 1 , but 1 - 12 = 1, if minus sign means “ calculate the distance”. That clock is one dimensional, as you only need one number to say at which point in that line you are. Even if that line is a circle.
@@alvarorodriguez1592 well said
@@alvarorodriguez1592 Good reply. That does make sense. It escaped me that the space was limited to the surface of the object.
Continuing on from Alvaro, in these types of explanations people often talk about an ant crawling on the surface. The ant only sees and traverses the two dimensional surface. You can define any place it can crawl with just two dimensions. Even though our visualization of it requires three dimensions it exists only in two. Hope that helps.
Interactions?? Nice!!!!!
So droplets of energy called particle are suspended in a cloud called electron and agitated by a wind called photon?
33:22
Can you explain how a Quantum computer works?
No I can't
Love you from India sir
Center of mass of a two photon system ? :-)
Shoutout to Greg Gutfeld who I believe has been watching your videos.
What if all the missing antimatter is in the future?
*aggresively nodding along*
I'm a little lost on how many degrees of freedom we're talking about. You explain that we can decompose any field as a collection of waves, waves have modes, modes have energy levels, and the Nth energy level corresponds to N particles. That's for a classical field and on top we have the wave function. That sounds like "for each" is expanded too many times. Is there a way to count the infinities? For example there's an R^3 infinity of k plane waves, then a Z infinity of coefficients of each mode? then you take the set of all of the above to make Ψ? I don't know. Roughly how large is everything?
EDIT: And I'm guessing part of the answer is that this "how big" doesn't change with many worlds because the the wave function is already there. It's implied by what you say here that you, an object, is not defined locally anyway. We're all defined holographically as components of the vibration modes of the whole universe. All versions of us. In a way that should make Many Worlds more plausible, or at least no less plausible than expressing everyday things that way.
I feel like Ogre watching this... "What if C A T really spells dog?"
I always wonder how you can top it...what's next...Sean Caroll is the best sherpa you can get (free!!) on the way to the summit of Everest of Physics...but you still have to climb high on your own feet...
18:00 Hola, wait a minute! Particles traveling backwards in time? Say what?
Lol right. Came out of nowhere
Sir it’s turtles all the way down!!
If Feynman diagrams are just visualizations of series expansions, not real things happening in physical reality, why teach them to a general audience?
Hi if you don't know tomorrow there will be a debate review on "capturing Christianity" RUclips channel of your debate with William L.C maybe you would be interested in it
W L C made the mistake of trying to argue physics with Sean Carroll about ? 5 years ago. He was hopelessly out of his depth. I suspect that Capturing Christianity's review will be highly edited and highly misleading. But I could be wrong.
Mess me up space daddy. I’m here to learn
I truly wish I remembered enough mathematics to do justice to this wonderful knowledge. Thank you
My mind is in a superposition of understanding and not understanding
I wonder what sort of person clicks on a theoretical physicist's lecture during a pandemic and gives it a thumbs down. Must have been an anti-Everettian.
I got that.
koho Well, I'm an anti-Everettian, but I'm more than willing to listen to Sean perform and teach. This series is great even if he keeps talking about the rather ridiculous "manyworlds" not-really an interpretation.
@@dwinsemius Why are you an anti-Everettian? I'm legitimately curious, since it seems like the most plausible and simple interpretation to me, but I'm no expert.
@@dwinsemius I can see how Many Worlds could be wrong, improbable, or untestable - but how could it not be an interpretation of of quantum mechanics?
Anyway, yeah, I don't have to agree on every philosophical standpoint of Sean to learn from his physics lectures.
@@nibblrrr7124 The reason I don't see it as an interpretation is that it doesn't really make a physical statement. There's not actually a transition, just two unresolved possibilities. Nothing is really happening if both paths are "real". It seems to be an admission of failure. "Since we cannot figure out how transitions or collapses occur, we'll just brush it under the rug and say either there was no transition. but perhaps that all transitions occurred.." It seems very non-probabilistic. In the cat box you would require that at every point in time that there would need to be a branch. Would also seem to play havoc with any need for reversibility.
hmmm, the energy of "empty" space.............I have an idea, should I email?comon you must get a laugh out of some of them :)
hej
TIL: Physicists desperately need to adopt new alphabets to steal letters from. I suggest Chinese ideograms (not strictly letters, but never mind).
Who the hell hits the dislike button and what does he do here?
I wonder what his neighbours think when he calls "Taliban !"
: )
@@michaelsommers2356 Yes, thanks I noticed his post introducing
his cats.Others have also commented in error, so maybe
he felt the need to clarify.